tokenpocket钱包官网下载安装|kubo
久保建英_百度百科
_百度百科 网页新闻贴吧知道网盘图片视频地图文库资讯采购百科百度首页登录注册进入词条全站搜索帮助首页秒懂百科特色百科知识专题加入百科百科团队权威合作下载百科APP个人中心久保建英播报讨论上传视频2001年6月出生的日本足球运动员收藏查看我的收藏0有用+10久保建英(Takefusa Kubo),2001年6月4日出生于日本神奈川县川崎市,日本足球运动员,场上司职前锋,现效力于西班牙足球甲级联赛的皇家社会足球俱乐部。 [8] [28] [30]2011年8月7日,久保建英成为巴塞罗那足球俱乐部青年梯队球员。2015年3月,久保建英返回日本,成为东京足球俱乐部梯队,并于2017年11月正式与俱乐部一线队签订职业合同。2019年6月14日,久保建英加盟皇家马德里足球俱乐部。 [1]同年8月,久保建英租借加盟皇家马略卡。 [3]同年11月10日,久保健英完成个人在西甲联赛赛事的处子球。2020-21赛季,久保健英分别租借至西甲联赛的比利亚雷亚尔足球俱乐部和赫塔菲足球俱乐部。2021年8月,久保建英再度被租借至皇家马略卡。 [18]2022年7月,久保建英正式加盟皇家社会足球俱乐部。 [30]2019年5月,久保建英首次入选日本国家男子足球队,代表球队征战2019年巴西美洲杯。6月9日,久保建英首次代表日本国家队登场。2022年,久保健英随日本国家队征战2022年卡塔尔世界杯。 [35]中文名久保建英外文名Takefusa Kubo别 名日本梅西 [2]国 籍日本民 族大和族出生地神奈川县川崎市出生日期2001年6月4日身 高173 cm体 重67 kg运动项目足球所属运动队皇家社会足球俱乐部 [31]目录1早年经历2运动生涯▪俱乐部生涯▪国家队生涯3生涯数据▪俱乐部数据▪国家队数据4获奖记录5社会评价早年经历播报编辑2004年,久保建英加入坂浜足球俱乐部,两年后转至百合之丘足球俱乐部,刚满七岁的久保建英就加盟了川崎市内专门为少年开设的足球俱乐部。2009年8月,在久保建英就读小学二年级时,恰逢巴塞罗那足球俱乐部在日本横滨举办训练营。久保建英在训练营举办的系列比赛中表现优异,被评为赛事MVP,并且获得了代表巴萨参加在比利时举办的欧洲俱乐部U9足球锦标赛的资格。11月,在日本J联赛球队川崎前锋足球俱乐部举办青少年选拔中,久保建英在选拔测试中一次性通过,成为同一年龄段仅有的三名合格学生中的一员,并在2010年4月正式成为川崎前锋U10梯队球员。 2011年8月7日,年仅10岁的久保建英在母亲和弟弟的陪同下远赴西班牙,正式成为了巴萨青年梯队中的一员。 [25]运动生涯播报编辑俱乐部生涯东京队2015年5月,久保建英加盟FC东京。12日,久保建英完成在FC东京U15梯队的注册。 [2]2016年11月5日,在2016赛季J3联赛第28轮东京U23队1-2不敌AC长野帕塞罗足球俱乐部的比赛中,久保健英在第46分钟替补小山拓哉登场,完成个人在J3联赛的处子秀。2017年11月26日,在2017赛季J1联赛第33轮东京队1-2不敌广岛三箭足球俱乐部的比赛中,久保健英在第67分钟替补永井谦佑登场,完成个人在J1联赛的处子秀。横滨水手2018年,久保健英被租借至J1联赛的横滨水手足球俱乐部。8月22日,在2018赛季日本天皇杯第4轮横滨水手2-3不敌胜仙台维加泰足球俱乐部的比赛中,久保健英首发登场,完成个人在日本天皇杯赛事的处子秀。2018赛季,久保健英代表横滨水手出场6次,取得1粒进球,场均登场41.7分钟。重回东京队2019年,久保健英在横滨水手的租借期结束之后,返回东京FC队。6月1日,2019赛季J1联赛第14轮东京FC3-1战胜大分三神足球俱乐部的比赛中,久保健英分别在第39分钟和90分钟攻入2粒进球完成“梅开二度”,这是久保健英在J1联赛的首次“梅开二度”。2019赛季,久保健英代表东京FC出场16次,取得5粒进球及4次助攻,场均登场69.4分钟。皇家马略卡马略卡时期(8张)2019年6月14日,皇家马德里足球俱乐部宣布久保建英加盟球队,合同期6年。 [1]8月,皇家马德里官方宣布久保建英租借加盟皇家马略卡,租期一年。 [3]9月1日,在2019-20赛季西甲联赛第3轮皇家马略卡0-2不敌瓦伦西亚足球俱乐部的比赛中,久保健英在第79分钟替补安特·布迪米尔登场,完成个人在西甲联赛的处子秀。11月10日,在2019-20赛季西甲联赛第13轮皇家马略卡3-1战胜比利亚雷亚尔的比赛中,久保健英在第53分钟攻入一球,完成个人在西甲联赛赛事的处子球。2020年1月21日,在2019-20赛季西班牙国王杯第3轮皇家马略卡1-3不敌皇家萨拉戈萨足球俱乐部的比赛中,久保健英首发登场,完成个人在西班牙国王杯赛事的处子秀。2019-20赛季,久保建英代表皇家马略卡出场36次,取得4粒进球及5次助攻,场均登场66.6分钟。比利亚雷亚尔比利亚雷亚尔时期(2张)2020年8月10日,久保建英被租借加盟同在西甲联赛的比利亚雷亚尔足球俱乐部,租期至2021年8月,久保建英的租借费为200-300万欧元,没有买断条款。 [4-5]10月22日,在2020-21赛季欧洲联赛小组赛比利亚雷亚尔5-3战胜锡瓦斯体育足球俱乐部的比赛中,久保健英首发登场,完成个人在欧洲联赛的处子秀。同时久保健英在该场1射2传直接缔造3球,创造了日本球员的欧战最年轻进球纪录。 [7]2020-21赛季,久保健英代表比利亚雷亚尔出场19次,取得1粒进球及3次助攻,场均登场36.2分钟。赫塔菲赫塔菲时期(2张)2021年1月8日 ,久保建英租借加盟赫塔菲足球俱乐部,租借期至2020-21赛季结束。 [6]1月11日,2020-21赛季西甲联赛第18轮赫塔费3-1战胜埃尔切足球俱乐部的比赛中,久保健英在第64分钟替补内马尼亚·马克西莫维奇登场,这是久保健英加盟赫塔费的首次登场。2021年5月16日,2020-21赛季西甲联赛第37轮赫塔费2-1战胜莱万特足球俱乐部的比赛中,久保健英在第84分钟攻入致胜一球,这是久保健英加盟赫塔费的首粒进球。2020-21赛季,久保健英代表赫塔菲出场18次,取得1粒进球及1次助攻,场均登场44.5分钟。重回马略卡2021年8月,久保建英再度被租借至皇家马略卡,时隔一年再度披上马略卡战袍,与韩国球员李刚仁组成东亚搭档。 [18]12月5日,在2021-22赛季西甲联赛第16轮皇家马略卡2-1战胜马德里竞技足球俱乐部的比赛中,久保建英下半场替补出场16分钟并在比赛第90分钟命中单刀,帮助球队在客场2-1战胜马竞,成为第三位攻破马竞球门的亚洲球员。 [19-20]2022年1月15日,在2021-22赛季西班牙国王杯1/8决赛中,久保建英于上半时任意球直接破门,帮助皇家马略卡在主场2-1战胜西班牙人。 [21]2021-22赛季,久保建英出场31次,进2球。 [31]皇家社会皇家社会时期(10张)2022年7月,久保建英正式加盟皇家社会。 [29-30]8月14日,西甲第1轮,久保建英首发出战,在处子秀中收获了处子球,帮助皇家社会在客场1-0小胜加的斯,并以21岁71天的年龄成为21世纪代表皇家社会西甲首秀破门第二年轻的球员。 [32-33]10月3日,西甲第7轮,久保建英传射建功,帮助皇家社会在客场5-3战胜升班马赫罗纳。 [34]2023年2月14日,西甲第21轮,久保建英抽射破门,帮助皇家社会3-2战胜西班牙人。 [37]3月19日,西甲第26轮,久保建英低射远角破门,帮助皇家社会在主场2-0战胜埃尔切,并以5球追平乾贵士,并列成为西甲单赛季进球最多的日本球员。 [38-39]4月9日,西甲第28轮,久保建英破门,帮助皇家社会在主场2-0战胜赫塔费,并以6个西甲联赛进球超过乾贵士,成为首个单赛季西甲打进6球的日本球员。 [40-41]5月3日,西甲第33轮,久保建英破门,帮助皇家社会在主场2-0战胜皇马,成为首位在西甲赛场攻破皇马球门的日本球员。 [42-43]5月24日,西甲第36轮。久保建英兜射破门,帮助皇家社会在主场1-0战胜阿尔梅里亚。 [44]5月29日,西甲第37轮,久保建英帮助皇家社会提前一轮锁定联赛前四,获得下赛季欧冠资格。 [45]2022-23赛季,久保建英为皇家社会出战44场比赛,贡献9粒进球和9次助攻,当选皇家社会队内最佳球员。 [46]2023年8月12日,2023-24赛季西甲第1轮,久保建英破门,帮助皇家社会在主场1-1战平赫罗纳。 [48] [55]8月20日,2023-24赛季西甲第2轮,久保建英助攻巴雷内切亚进球,收获本赛季首个助攻,帮助皇家社会1-1战平塞尔塔。 [49-50] [55]9月2日,2023-24赛季西甲第4轮,久保建英梅开二度,帮助皇家社会5-3战胜格拉纳达;这也使得他在西甲联赛中的进球数达到了18个,超过乾贵士,成为西甲联赛进球最多的日本球员。 [51] [54]10月7日消息,久保建英当选西甲9月最佳球员。 [56]12月10日,2023-24赛季西甲第16轮,久保建英传射,帮助皇家社会在客场3-0完胜比利亚雷亚尔。 [59]12月31日,久保建英入选JPFA(日本职业足球运动员协会)2023年度最佳11人阵。 [60]2024年2月,久保建英与皇家社会续约至2029年。 [65]国家队生涯久保健英在日本国家队(10张)2019年5月24日,日本足协公布了2019年巴西美洲杯大名单,久保建英入选其中。 [24]6月9日,在日本队2-0战胜萨尔瓦多国家男子足球队的友谊赛中,久保建英在第67分钟替补南野拓实登场,完成个人代表日本国家男子足球队首次登场。6月18日,在2019年巴西美洲杯小组赛日本队0-4不敌智利国家男子足球队的比赛中,久保建英获得首发登场并打满全场,这是久保健英在国家队首次首发。在整个美洲杯赛事,久保健英共出场3次,未取得粒进球及助攻,场均登场62.3分钟。2022年5月,久保建英入选日本足协公布的出征6月麒麟杯赛事男足28人大名单。 [27]6月10日,在对阵加纳的麒麟杯足球邀请赛中,久保建英攻入自己在日本国家队的第一个进球。 [26]11月,久保建英入选日本国家队官方公布的2022年卡塔尔世界杯26人大名单。 [35]2023年6月15日,在对阵萨尔瓦多的麒麟杯比赛中,久保建英2传1射,帮助日本6-0取胜。 [47]9月10日,在对阵德国的友谊赛中,久保建英两次送出助攻,帮助日本4-1取胜,并以22岁97天的年龄成为至少是2006年9月以来对德国单场送出两助攻的最年轻球员。 [52-53]10月17日,在对阵突尼斯的友谊赛中,久保建英边路突入禁区助攻伊东纯也破门,帮助日本在主场2-0取胜。 [57]11月21日,世预赛亚洲区第二阶段第2轮,久保建英远射破门,帮助日本5-0战胜叙利亚。 [58]2024年1月,入选日本国家男子足球队参加2023年卡塔尔亚洲杯的大名单。 [61]1月14日,亚洲杯D组第1轮,日本对阵越南,下半场久保建英助攻上田绮世抽射锁定胜局,帮助日本4-2战胜越南。 [62]1月31日,亚洲杯1/8决赛,久保建英低射扩大优势,帮助日本3-1战胜巴林。 [63]2月,入选卡塔尔亚洲杯16强最佳阵容。 [64]生涯数据播报编辑俱乐部数据联赛数据赛季赛事俱乐部出场进球助攻黄牌红牌登场时间2016 J3联赛东京FC3----1032017 J1联赛东京FC 2----332017 J3联赛东京FC 21211-16292018 J1联赛东京FC 4----582018 J3联赛东京FC 10312-8482018 J1联赛横滨水手 51-1-1602019 J1联赛东京FC 1344--10262019-20 西甲联赛皇家马略卡 35454-23082020-21 西甲联赛比利亚雷亚尔 13---12912020-21 西甲联赛赫塔费 18112-8012021-22 西甲联赛皇家马略卡 21113-12872022-23西甲联赛皇家社会35973-24542023-24西甲联赛皇家社会19631-1509参考资料: [66](数据截止于2024年2月18日)杯赛数据赛季赛事俱乐部出场进球助攻黄牌登场时间2017日本联赛杯东京FC2---332018日本联赛杯东京FC61-24252018日本天皇杯横滨水手1-1-902019日本联赛杯东京FC31--852019-20西班牙国王杯皇家马略卡1---902020-21西班牙国王杯比利亚雷亚尔1---212021-22西班牙国王杯皇家马略卡312-161洲际数据赛季赛事俱乐部 出场进球 助攻 黄牌 登场时间2020-21欧洲联赛比利亚雷亚尔513-37国家队数据日本国家队年份球队出场进球2015-2017日本U-15、U-16、U-17国家男子足球队24142016-日本U-19、U-20国家男子足球队602018-日本U-21、U-22国家男子足球队--2019日本国家男子足球队70202040202120202220(国家队数据参考资料: [8])大型赛事年份赛事名称出场进球2015马恩河谷省U-16国际足球邀请赛 [9]3120162016年亚足联U-16亚洲杯 [10]4420172017年韩国U-20世界杯 [11]3020172017年印度U-17世界杯 [12]4120182018年亚足联U-19亚洲杯 [13]512018迪拜杯U-23邀请赛 [14]2020192020年亚足联U-23亚洲杯预选赛 [15]3120192019年麒麟挑战杯 [16]1020192019年巴西美洲杯 [16]--获奖记录播报编辑2020年6月,久保建英入选2020年欧洲金童奖100人候选名单。 [17]2023年1月18日,久保建英入选JPFA2022最佳十一人。 [36]社会评价播报编辑无论是身高形象、场上位置,还是惯用左脚,久保建英都像极了利昂内尔·梅西,西班牙媒体也把他叫做“日本梅西”。 [25](《东方体育日报》评)久保建英的天赋是显而易见的,作为亚洲球员,能够成为像中田英寿、朴智星这样的亚洲明星球员,能成为亚洲领军人物之一。 [22](日本球员本田圭佑评)久保建英能挑起进攻大梁,勇敢地在场上撕裂着对手的后防线,创造出致胜机会。尤其是在断下对手皮球后,能第一时间为队友提供足够的帮助,从战术上盘活球队。 [23](马洛卡新帅阿吉雷评)新手上路成长任务编辑入门编辑规则本人编辑我有疑问内容质疑在线客服官方贴吧意见反馈投诉建议举报不良信息未通过词条申诉投诉侵权信息封禁查询与解封©2024 Baidu 使用百度前必读 | 百科协议 | 隐私政策 | 百度百科合作平台 | 京ICP证030173号 京公网安备110000020000久保同学不放过我|Kubo Formula的非线性响应理论 - 知乎
久保同学不放过我|Kubo Formula的非线性响应理论 - 知乎首发于O空O扬O的物理碎碎念切换模式写文章登录/注册久保同学不放过我|Kubo Formula的非线性响应理论O空O扬O 以色列魏兹曼研究所 物理学硕士在读本文旨在推导Kubo Formula的非线性响应理论。IntroductionKubo Formula的线性和非线性响应理论本质上都是量子力学的微扰论。其中线性响应更为常见,例如实验测量的电导率、磁化率、电极化率等susceptibility均为线性响应函数(Retarded Green Function)。但非线性响应也有其应用价值,例如半导体中的二阶电流响应,包括2nd Harmonic Generation,Injection and Shift Current等等。二阶响应甚至可以用来解释上一节Fermi Golden Rule中的常跃迁速率和二倍频跃迁速率两种响应。可见只要胆够大,处处皆是非线性响应(bushi。Density Matrix in Dirac PictureKubo Formula的推导从相互作用(Dirac)绘景下,系统密度矩阵的演化开始。在Fermi Golden Rule那节中,我们已经推导了相互作用(Dirac)绘景下波函数的运动方程。简单将密度矩阵看成\hat{\rho}_D(t) \sim | \psi (t) \rangle_D \langle \psi(t) |_D,有利于我们快速回忆起相互作用(Dirac)绘景下密度矩阵的运动方程:\frac{d}{dt} \hat{\rho}_D(t) = - \frac{i}{\hbar} [ \hat{\rho}_D(t) , \hat{V}_D(t) ]积分后重复迭代,我们可以得到密度矩阵的展开式:\begin{aligned}\hat{\rho}_D(t) = \hat{\rho}_0 + \sum_{n = 1}^{\infty} (-\frac{\mathrm{i}}{\hbar})^n \int_{-\infty}^{t} dt_1 \int_{-\infty}^{t_1} dt_2 \dots \int_{-\infty}^{t_{n-1}} dt_n [\hat{V}_D(t_1),[\dots[\hat{V}_D(t_n),\hat{\rho}_0]\dots] ]\end{aligned}注意每个积分的上界并非均为t。Linear Response只考虑线性响应:\hat{\rho}_D(t) \approx \hat{\rho}_0 + (-\frac{\mathrm{i}}{\hbar}) \int_{-\infty}^t \mathrm{~d} t^{\prime} \left[\hat{V}_{D}\left(t^{\prime}\right), \hat{\rho}_0 \right]其中\hat{\rho}_0为平衡态密度矩阵:\hat{\rho}_0 = \frac{\exp \left(-\beta \mathcal{H}_0\right)}{\operatorname{Tr}[\exp \left(-\beta \mathcal{H}_0\right)]}我们希望考察可观测量\hat{A}随时间的变化:\langle\hat{A}\rangle_t = \operatorname{Tr}\{ \hat{\rho}_D(t) \hat{A}_D(t) \}\langle\hat{A}\rangle_t = \langle\hat{A}\rangle_0 +(-\frac{\mathrm{i}}{\hbar}) \int_{-\infty}^t \mathrm{~d} t^{\prime} \operatorname{Tr}\left\{\left[\hat{V}_{D}\left(t^{\prime}\right), \hat{\rho}_0 \right] \hat{A}_D(t) \right\}其中,\langle\dots\rangle_0 = \operatorname{Tr}\{ \hat{\rho}_0 (\dots) \}\hat{A}_D(t) = \exp \left(\frac{\mathrm{i}}{\hbar} \mathcal{H}_0 t\right) \hat{A}_S(t) \exp \left(-\frac{\mathrm{i}}{\hbar} \mathcal{H}_0 t\right)对于下面的微扰形式:\hat{V}_S(t) = \hat{B}_S(t) F(t)\langle\hat{A}\rangle_t = \langle\hat{A}\rangle_0 +(-\frac{\mathrm{i}}{\hbar}) \int_{-\infty}^t \mathrm{~d} t^{\prime} F(t^{\prime}) \operatorname{Tr}\left\{\left[\hat{B}_{D}\left(t^{\prime}\right), \hat{\rho}_0 \right] \hat{A}_D(t) \right\}利用Trace的轮换不变性,可以证明:\operatorname{Tr}\left\{\left[\hat{B}_{D}\left(t^{\prime}\right), \hat{\rho}_0 \right] \hat{A}_D(t) \right\} = \operatorname{Tr}\left\{\rho_0\left[\hat{A}_D(t), \hat{B}_{D}\left(t^{\prime}\right)\right]\right\}从而:\langle\hat{A}\rangle_t = \langle\widehat{A}\rangle_0 +(-\frac{\mathrm{i}}{\hbar}) \int_{-\infty}^t \mathrm{~d} t^{\prime} F(t^{\prime}) \operatorname{Tr}\left\{\rho_0\left[\hat{A}_D(t), \hat{B}_{D}\left(t^{\prime}\right)\right]\right\}这样可以将表达式中的物理量都写成\operatorname{Tr}\left\{\rho_0(\dots)\right\}的形式。这说明,用平衡态的可观测量就可以确定近平衡态的响应。一般而言,我们考虑可观测量\hat{A}在微扰下与平衡态的区别,从而我们还可以把线性响应写成以下形式:\Delta A_t =\langle\hat{A}\rangle_t-\langle\widehat{A}\rangle_0=-\frac{\mathrm{i}}{\hbar} \int_{-\infty}^t \mathrm{~d} t^{\prime} F(t^{\prime})\left\langle\left[\widehat{A}^{\mathrm{D}}(t), \widehat{B}^{\mathrm{D}}\left(t^{\prime}\right)\right]_{-}\right\rangle_0或者写成:\Delta A_t = \int_{-\infty}^{+ \infty} \mathrm{~d} t^{\prime} G_{A B}^{\mathrm{ret}}\left(t; t^{\prime}\right) F(t^{\prime})这便是线性响应的Kubo Formula在Time Domain的形式。其中包含了retarded Green Function,G_{A B}^{\mathrm{ret}}\left(t; t^{\prime}\right) = -\frac{\mathrm{i}}{\hbar} \Theta\left(t-t^{\prime}\right)\left\langle\left[\hat{A}_D(t), \hat{B}_D\left(t^{\prime}\right)\right]\right\rangle_0 = -\frac{\mathrm{i}}{\hbar} \Theta\left(t-t^{\prime}\right)\left\langle\left[\hat{A}_H(t), \hat{B}_H\left(t^{\prime}\right)\right]\right\rangle_0这里由于是求平衡态的性质,所以下标D,\,H代表的Dirac,Heisenberg Picture没有区别,从另一个方面体现了系统的近平衡态响应由系统的平衡态性质完全确定。目前给出的线性响应公式是general的,没有考虑时间平移对称性等性质(当\hat{A}_S,\,\hat{B}_S不显含时间t)。若retarded Green FunctionG_{A B}^{\mathrm{ret}}\left(t; t^{\prime}\right)具有时间平移对称性:G_{A B}^{\mathrm{ret}}\left(t; t^{\prime}\right) = G_{A B}^{\mathrm{ret}}\left(t - t^{\prime}\right)可以在频率空间(Frequency Domain)中得到更加简洁的线性响应理论。我们将在推导完general的二阶响应后,进一步讨论这一点。Nonlinear Response现在我们想求非线性(高阶响应),我们直接把微扰后的密度矩阵展开到高阶,重复上面的推导即可。把微扰后的密度矩阵展开到高阶(以二阶响应为例),\begin{aligned}\hat{\rho}_D(t) & \approx \hat{\rho}_0 + (-\frac{\mathrm{i}}{\hbar}) \int_{-\infty}^t \mathrm{~d} t^{\prime} \left[\hat{V}_{D}\left(t^{\prime}\right), \hat{\rho}_0 \right] \\& + (-\frac{\mathrm{i}}{\hbar})^2 \int_{-\infty}^t \mathrm{~d} t^{\prime} \int_{-\infty}^{t'} \mathrm{~d} t'' \left[\hat{V}_{D}\left(t^{\prime}\right), \left[\hat{V}_{D}\left(t''\right), \hat{\rho}_0 \right] \right] \\& + \dots\end{aligned}从而可观测量\hat{A}的响应为:\langle\hat{A}\rangle_t = \langle\hat{A}\rangle_0 + \langle\hat{A}\rangle_1 + \langle\hat{A}\rangle_2 + \dots\begin{aligned}\langle\hat{A}\rangle_2 & = (-\frac{\mathrm{i}}{\hbar})^2 \int_{-\infty}^t \mathrm{~d} t^{\prime} \int_{-\infty}^{t'} \mathrm{~d} t'' \operatorname{Tr} \{ \left[\hat{V}_{D}\left(t^{\prime}\right), \left[\hat{V}_{D}\left(t''\right), \hat{\rho}_0 \right] \right] \hat{A}_D(t) \}\end{aligned}利用Trace的轮换不变性,有:\operatorname{Tr} \left\{ \left[\hat{V}_{D}\left(t^{\prime}\right), \left[\hat{V}_{D}\left(t''\right), \hat{\rho}_0 \right] \right] \hat{A}_D(t) \right\} = \operatorname{Tr} \left\{\rho_0\left[ \left[\hat{A}_D(t), \hat{V}_{D}\left(t^{\prime}\right)\right] , \hat{V}_{D}\left(t''\right)\right] \right\}从而:\begin{aligned}\langle\hat{A}\rangle_2 & = (-\frac{\mathrm{i}}{\hbar})^2 \int_{-\infty}^t \mathrm{~d} t^{\prime} \int_{-\infty}^{t'} \mathrm{~d} t'' \operatorname{Tr} \left\{\rho_0\left[ \left[\hat{A}_D(t), \hat{V}_{D}\left(t^{\prime}\right)\right] , \hat{V}_{D}\left(t''\right)\right] \right\}\end{aligned}事实上有更general的结论:\operatorname{Tr} \left\{ \left[\hat{V}_{D}\left(t_1\right), \dots ,\left[\hat{V}_{D}\left(t_n\right), \hat{\rho}_0 \right] \dots \right] \hat{A}_D(t) \right\} = \operatorname{Tr} \left\{\rho_0\left[ \dots\left[\hat{A}_D(t), \hat{V}_{D}\left(t_1\right)\right], \dots , \hat{V}_{D}\left(t_n\right)\right]\right\}可以计算任意阶响应\begin{aligned}\langle\hat{A}\rangle_n & = (-\frac{\mathrm{i}}{\hbar})^2 \int_{-\infty}^t \mathrm{~d} t_1 \int_{-\infty}^{t_1} \mathrm{~d} t_2 \dots \int_{-\infty}^{t_{n-1}} \mathrm{~d} t_n \operatorname{Tr} \left\{\rho_0\left[ \dots\left[\hat{A}_D(t), \hat{V}_{D}\left(t_1\right)\right], \dots , \hat{V}_{D}\left(t_n\right)\right]\right\}\end{aligned}重复之前的操作,若可以把微扰分成外场(不一定要是标量场)和算符部分:\hat{V}_S(t) = \hat{B}^\mu_S(t) F_\mu(t)则二阶响应可以写成,\begin{aligned}\langle\hat{A}\rangle_2 & = (-\frac{\mathrm{i}}{\hbar})^2 \int_{-\infty}^t \mathrm{~d} t^{\prime} \int_{-\infty}^{t'} \mathrm{~d} t'' \operatorname{Tr} \left\{\rho_0\left[ \left[\hat{A}_D(t), \hat{B}^\mu_{D}\left(t^{\prime}\right)\right] , \hat{B}^\nu_{D}\left(t''\right)\right] \right\} F_\mu(t')F_\nu(t'') \\& = \int_{-\infty}^{+ \infty} \mathrm{~d} t^{\prime} \int_{-\infty}^{+\infty} \mathrm{~d} t'' \chi_2^{\mu\nu}(t;t',t'') F_\mu(t')F_\nu(t'')\end{aligned}其中\chi_2^{\mu\nu}(t;t',t'')为二阶响应率,定义为:\chi_2^{\mu\nu}(t;t',t'') \equiv (-\frac{\mathrm{i}}{\hbar})^2 \Theta(t - t') \Theta(t' - t'') \operatorname{Tr} \left\{\rho_0\left[ \left[\hat{A}_D(t), \hat{B}^\mu_{D}\left(t^{\prime}\right)\right] , \hat{B}^\nu_{D}\left(t''\right)\right] \right\}可以推广到任意阶响应:\begin{aligned}\langle\hat{A}\rangle_n & = (-\frac{\mathrm{i}}{\hbar})^2 \int_{-\infty}^t \mathrm{~d} t_1 \int_{-\infty}^{t_1} \mathrm{~d} t_2 \dots \int_{-\infty}^{t_{n-1}} \mathrm{~d} t_n \\ & \times \operatorname{Tr} \left\{\rho_0\left[ \dots\left[\hat{A}_D(t), \hat{B}^{\mu_1}_{D}\left(t_1\right)\right], \dots , \hat{B}^{\mu_n}_{D}\left(t_n\right)\right]\right\}\\ & \times F_{\mu_1}(t_1) \dots F_{\mu_n}(t_n) \\& = \int_{-\infty}^{+ \infty} \mathrm{~d} t_1 \dots \int_{-\infty}^{+\infty} \mathrm{~d} t_n \\ & \times \chi_n^{\mu_1 \dots \mu_n}(t;t_1,\dots,t_n) F_{\mu_1}(t_1) \dots F_{\mu_n}(t_n)\end{aligned}Frequency Domain先不考虑系统是否有时间平移对称性等性质,从Time Domain换到Frequency Domain,只是将所有时间参量作Fourier Transformation。\chi_n(t;t_1,\dots,t_n) \xrightarrow{F.T.} \chi_n(\omega ;\omega_1,\dots,\omega_n)这样做的好处是,一般的外场都是单一频率的,例如单色电磁波。而Frequency Domain的Kubo Formula可以直接告诉我们响应的频率和振幅。不过本质还是Fourier Transformation。具体而言:\chi_n(\omega ;\omega_1,\dots,\omega_n) \equiv \int_{- \infty}^{+ \infty} \mathrm{~d} t e^{-i\omega t} \int_{- \infty}^{+ \infty} \mathrm{~d} t_1 e^{-i\omega_1 t_1} \dots \int_{- \infty}^{+ \infty} \mathrm{~d} t_n e^{-i\omega_n t_n} \chi_n(t;t_1,\dots,t_n)\chi_n(t;t_1,\dots,t_n) = \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \omega}{2 \pi} e^{i\omega t} \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \omega_1}{2 \pi} e^{i\omega_1 t_1} \dots \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \omega_n}{2\pi} e^{i\omega_n t_n} \chi_n(\omega ;\omega_1,\dots,\omega_n)类似的将可观测量和外场也Fourier Transform到频率空间,\langle\hat{A}\rangle_n(\omega) = \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \omega}{2 \pi} e^{i\omega t} \langle\hat{A}\rangle_n(t)F(\omega_i) = \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \omega_i}{2 \pi} e^{i\omega_i t_i} F(t_i)从而Frequency Domain中的Kubo Formula为:\begin{aligned}\langle\hat{A}\rangle_n(\bar{\omega}) & = \int_{- \infty}^{+ \infty} \mathrm{~d} t e^{-i \bar{\omega} t} \langle\hat{A}\rangle_n(t) \\& = \int_{- \infty}^{+ \infty} \mathrm{~d} t e^{-i \bar{\omega} t} \int_{-\infty}^{+ \infty} \mathrm{~d} t_1 \dots \int_{-\infty}^{+\infty} \mathrm{~d} t_n \\& \times \chi_n^{\mu_1 \dots \mu_n}(t;t_1,\dots,t_n) F_{\mu_1}(t_1) \dots F_{\mu_n}(t_n)\end{aligned}\begin{aligned}& = \int_{- \infty}^{+ \infty} \mathrm{~d} t e^{-i \bar{\omega} t} \int_{-\infty}^{+ \infty} \mathrm{~d} t_1 \dots \int_{-\infty}^{+\infty} \mathrm{~d} t_n \\& \times \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \omega}{2 \pi} e^{i\omega t} \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \omega_1}{2 \pi} e^{i\omega_1 t_1} \dots \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \omega_n}{2\pi} e^{i\omega_n t_n} \\& \times \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \bar{\omega}_1}{2 \pi} e^{i\bar{\omega}_1 t_1} \dots \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \bar{\omega}_n}{2\pi} e^{i\bar{\omega}_n t_n}\\& \times \chi_n^{\mu_1 \dots \mu_n}(\omega ;\omega_1,\dots,\omega_n) F_{\mu_1}(\bar{\omega}_1) \dots F_{\mu_n}(\bar{\omega}_n)\end{aligned}\begin{aligned}& = \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \omega}{2 \pi} \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \omega_1}{2 \pi} \dots \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \omega_n}{2\pi} \\& \times \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \bar{\omega}}{2 \pi} \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \bar{\omega}_1}{2 \pi} \dots \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \bar{\omega}_n}{2\pi} \\& \times \int_{- \infty}^{+ \infty} \mathrm{~d} t e^{i (\omega - \bar{\omega}) t} \int_{-\infty}^{+ \infty} \mathrm{~d} t_1 e^{i (\omega_1 + \bar{\omega}_1) t_1}\dots \int_{-\infty}^{+\infty} \mathrm{~d} t_n e^{i (\omega_n + \bar{\omega}_n) t_n} \\& \times \chi_n^{\mu_1 \dots \mu_n}(\omega ;\omega_1,\dots,\omega_n) F_{\mu_1}(\bar{\omega}_1) \dots F_{\mu_n}(\bar{\omega}_n)\end{aligned}\begin{aligned}& = \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \omega}{2 \pi} \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \omega_1}{2 \pi} \dots \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \omega_n}{2\pi} \\& \times \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \bar{\omega}}{2 \pi} \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \bar{\omega}_1}{2 \pi} \dots \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \bar{\omega}_n}{2\pi} \\& \times 2 \pi \delta(\bar{\omega} - \omega) \times 2 \pi \delta (\omega_1 + \bar{\omega}_1) \times \dots \times 2 \pi \delta (\omega_n + \bar{\omega}_n) \\& \times \chi_n^{\mu_1 \dots \mu_n}(\omega ;\omega_1,\dots,\omega_n) F_{\mu_1}(\bar{\omega}_1) \dots F_{\mu_n}(\bar{\omega}_n)\end{aligned}最终Frequency Domain中的Kubo Formula为:\begin{aligned}\langle\hat{A}\rangle_n(\bar{\omega}) & = \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \omega_1}{2 \pi} \dots \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \omega_n}{2\pi} \\ & \times \chi_n^{\mu_1 \dots \mu_n}(\bar{\omega} ;\omega_1,\dots,\omega_n) F_{\mu_1}(-\omega_1) \dots F_{\mu_n}(-\omega_n)\end{aligned}此处的负号也可以通过重新定义\{t;t_1,\dots,t_n\}这些参量的Fourier Transformation来去掉。例如对“;”左右侧进行不同的Fourier Transformation:\chi_n(\omega ;\omega_1,\dots,\omega_n) \equiv \int_{- \infty}^{+ \infty} \mathrm{~d} t e^{-i\omega t} \int_{- \infty}^{+ \infty} \mathrm{~d} t_1 e^{i\omega_1 t_1} \dots \int_{- \infty}^{+ \infty} \mathrm{~d} t_n e^{i\omega_n t_n} \chi_n(t;t_1,\dots,t_n)\chi_n(t;t_1,\dots,t_n) = \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \omega}{2 \pi} e^{i\omega t} \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \omega_1}{2 \pi} e^{-i\omega_1 t_1} \dots \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \omega_n}{2\pi} e^{-i\omega_n t_n} \chi_n(\omega ;\omega_1,\dots,\omega_n)则有:\begin{aligned}\langle\hat{A}\rangle_n(\bar{\omega}) & = \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \omega_1}{2 \pi} \dots \int_{- \infty}^{+ \infty} \frac{\mathrm{~d} \omega_n}{2\pi} \chi_n^{\mu_1 \dots \mu_n}(\bar{\omega} ;\omega_1,\dots,\omega_n) F_{\mu_1}(\omega_1) \dots F_{\mu_n}(\omega_n)\end{aligned}但事实上,正负频率的微扰总是同时存在的,上述讨论只是一个定义问题。为了Kubo Formula尽量不出现“-”号,之后的讨论我们都采用后一种定义此处推导的general的情形,对于\{\bar{\omega} ;\omega_1,\dots,\omega_n\}之间的关系并没有限制,任意频率的微扰都有可能激发另一个频率的响应。但对于时间平移不变的响应函数,会对响应函数在Frequency Domain的形式有一定限制。以最常见的线性响应为例,响应的频率一定和外场的频率相同,即\chi_1(\omega; \omega_1) \sim \delta(\omega \pm \omega_1)而对于更一般的非线性响应,可以证明响应的频率是外场频率的和,即\chi_n(\omega; \omega_1,\dots,\omega_n) \sim \delta(\omega \pm \sum_{i=1}^n \omega_i)其中"\pm"号取决于Frequency Domain中响应函数的定义。Time Translation Symmetry当响应函数具有时间平移对称性时,可以证明响应函数有以下性质:\chi_1(t;t') \equiv G_{A B}^{\mathrm{ret}}\left(t; t^{\prime}\right) = G_{A B}^{\mathrm{ret}}\left(t - t^{\prime}\right)\chi_2(t;t',t'') = \chi_2^{\mathcal{T}} (t-t',t'-t'')\chi_n(t;t_1,\dots,t_n) = \chi_n^{\mathcal{T}}(t-t_1,t_1-t_2,\dots,t_{n-1} - t_n)这是因为时间平移对称性使得响应函数中的时间全部改变相同量时不变,即:\chi_n(t;t_1,\dots,t_n) = \chi_n(t + \tau;t_1+ \tau,\dots,t_n+ \tau)从而在\{t;t_1,\dots,t_n\}这些参量中,独立的只是他们的相对值,可以定义:\begin{aligned}& \chi_n^{\mathcal{T}}(t-t_1,t_1-t_2,\dots,t_{n-1} - t_n) \\& = \chi_n(t_n + \sum_{i=1}^{n-1}(t_{i} - t_{i+1}) + (t - t_1) ;t_n + \sum_{i=1}^{n-1}(t_{i} - t_{i+1}),\dots,t_n + (t_{n-1} - t_n),t_n) \\& = \chi_n(\sum_{i=1}^{n-1}(t_{i} - t_{i+1}) + (t - t_1) ; \sum_{i=1}^{n-1}(t_{i} - t_{i+1}),\dots, (t_{n-1} - t_n),0)\end{aligned}下面考虑响应函数具有时间平移对称性的物理含义,这事实上表示系统以及涉及响应的可观测量\hat{A},\,\hat{B}均是时间平移不变的,但这在不同的绘景下有不同的含义。以我们最熟悉的Schrodinger Picture为例,算符不显含时间即可:\hat{A}_S(t) = \hat{A},\,\hat{B}_S(t) = \hat{B}但在Dirac/Heisenberg Picture下表现为:\hat{A}_H(t) = \exp \left(\frac{\mathrm{i}}{\hbar} \mathcal{H}_0 t\right) \hat{A} \exp \left(-\frac{\mathrm{i}}{\hbar} \mathcal{H}_0 t\right),\,\hat{B}_H(t) = \exp \left(\frac{\mathrm{i}}{\hbar} \mathcal{H}_0 t\right) \hat{B} \exp \left(-\frac{\mathrm{i}}{\hbar} \mathcal{H}_0 t\right)可以证明,“响应函数具有时间平移对称性”和“系统以及涉及响应的可观测量\hat{A},\,\hat{B}均是时间平移不变的”说的是一回事,以一阶响应函数为例:\begin{aligned}G_{A B}^{\mathrm{ret}}\left(t; t^{\prime}\right) & = -\frac{\mathrm{i}}{\hbar} \Theta\left(t-t^{\prime}\right) \operatorname{Tr} \left\{ \hat{\rho}_0\left[\hat{A}_H(t), \hat{B}_H\left(t^{\prime}\right)\right]\right\}\end{aligned}利用Trace的轮换不变性:\begin{aligned}& \operatorname{Tr} \left\{ \hat{\rho}_0\left[\hat{A}_H(t), \hat{B}_H\left(t^{\prime}\right)\right]\right\} \\& = \operatorname{Tr} \left\{ \hat{\rho}_0\left[ \exp \left(\frac{\mathrm{i}}{\hbar} \mathcal{H}_0 t\right) \hat{A} \exp \left(-\frac{\mathrm{i}}{\hbar} \mathcal{H}_0 t\right) , \exp \left(\frac{\mathrm{i}}{\hbar} \mathcal{H}_0 t'\right) \hat{B} \exp \left(-\frac{\mathrm{i}}{\hbar} \mathcal{H}_0 t'\right) \right]\right\} \\& = \operatorname{Tr} \left\{ \hat{\rho}_0\left( \exp \left(\frac{\mathrm{i}}{\hbar} \mathcal{H}_0 t\right) \hat{A} \exp \left(-\frac{\mathrm{i}}{\hbar} \mathcal{H}_0 (t - t')\right) \hat{B} \exp \left(-\frac{\mathrm{i}}{\hbar} \mathcal{H}_0 t'\right) - \exp \left(\frac{\mathrm{i}}{\hbar} \mathcal{H}_0 t'\right) \hat{B} \exp \left(\frac{\mathrm{i}}{\hbar} \mathcal{H}_0 (t - t')\right) \hat{A} \exp \left(-\frac{\mathrm{i}}{\hbar} \mathcal{H}_0 t\right) \right) \right\} \\& = \operatorname{Tr} \left\{ \hat{\rho}_0\left( \exp \left(\frac{\mathrm{i}}{\hbar} \mathcal{H}_0 (t - t') \right) \hat{A} \exp \left(-\frac{\mathrm{i}}{\hbar} \mathcal{H}_0 (t - t')\right) \hat{B} - \hat{B} \exp \left(\frac{\mathrm{i}}{\hbar} \mathcal{H}_0 (t - t')\right) \hat{A} \exp \left(-\frac{\mathrm{i}}{\hbar} \mathcal{H}_0 (t-t')\right) \right) \right\} \\& = \operatorname{Tr} \left\{ \hat{\rho}_0\left( \hat{A}_H(t-t') \hat{B} - \hat{B} \hat{A}_H(t-t') \right) \right\} \\& = \operatorname{Tr} \left\{ \hat{\rho}_0\left[ \hat{A}_H(t-t') , \hat{B} \right] \right\}\end{aligned}从而\chi_1(t;t') \equiv G_{A B}^{\mathrm{ret}}\left(t; t^{\prime}\right)仅显含(t-t')。推导中利用了\hat{\rho}_0 = \frac{\exp \left(-\beta \mathcal{H}_0\right)}{\operatorname{Tr}[\exp \left(-\beta \mathcal{H}_0\right)]}与时间演化算符\exp \left(\pm\frac{\mathrm{i}}{\hbar} \mathcal{H}_0 t \right)可对易的性质,因为两者均为\mathcal{H}_0的函数。类似的,可以证明:系统以及涉及响应的可观测量\hat{A},\,\hat{B}均有时间平移不变对称性时,任意阶的响应函数均具有时间平移对称性,这等价于响应函数可以写成\chi_n(t;t_1,\dots,t_n) = \chi_n^{\mathcal{T}}(t-t_1,t_1-t_2,\dots,t_{n-1} - t_n)的形式。Linear Order Susceptibility下面来证明,时间平移不变性将导致响应的频率一定和外场的频率相同,即\chi_1(\omega; \omega_1) \sim \delta(\omega - \omega_1)时间平移对称性要求:\chi_1(t;t_1) = \chi_1^{\mathcal{T}}(t - t_1)从而Frequency Domain的线性响应函数为:\begin{aligned}\chi_1(\omega ;\omega_1) & \equiv \int_{- \infty}^{+ \infty} \mathrm{~d} t e^{-i\omega t} \int_{- \infty}^{+ \infty} \mathrm{~d} t_1 e^{i\omega_1 t_1} \chi_1(t; t_1) \\& = \int_{- \infty}^{+ \infty} \mathrm{~d} t_1 e^{i(\omega_1 - \omega) t_1} \int_{- \infty}^{+ \infty} \mathrm{~d} (t - t_1) e^{-i\omega (t - t_1)} \chi_1^{\mathcal{T}}(t - t_1) \\& = 2 \pi \delta(\omega - \omega_1) \tilde{\chi}_1^{\mathcal{T}}(\omega) \\& \sim \delta(\omega - \omega_1)\end{aligned}其中\tilde{\chi}_1^{\mathcal{T}}(\omega)为{\chi}_1^{\mathcal{T}}(t - t_1)的Fourier Transformation:\tilde{\chi}_1^{\mathcal{T}}(\omega) \equiv \int_{- \infty}^{+ \infty} \mathrm{~d} \tau e^{-i\omega \tau} \chi_1^{\mathcal{T}}(\tau)Nonlinear Order Susceptibility对于更一般的非线性响应,可以证明响应的频率是外场频率的和,即\chi_n(\omega; \omega_1,\dots,\omega_n) \sim \delta(\omega - \sum_{i=1}^n \omega_i)时间平移对称性要求(注意此处全部写成和t_n的差):\chi_n(t;t_1,\dots,t_n) = \chi_n^{\mathcal{T}}(t-t_n,t_1-t_n,\dots,t_{n-1} - t_n)从而Frequency Domain的响应函数为:\begin{aligned}\chi_n(\omega ;\omega_1,\dots,\omega_n) & \equiv \int_{- \infty}^{+ \infty} \mathrm{~d} t e^{-i\omega t} \int_{- \infty}^{+ \infty} \mathrm{~d} t_1 e^{i\omega_1 t_1} ... \int_{- \infty}^{+ \infty} \mathrm{~d} t_n e^{i\omega_n t_n} \chi_n(t; t_1,\dots,t_n) \\& = \int_{- \infty}^{+ \infty} \mathrm{~d} t_n e^{-i(\omega - \sum_{i=1}^n \omega_i) t_n} \int_{- \infty}^{+ \infty} \mathrm{~d} (t - t_n) e^{-i\omega (t - t_n)} \int_{- \infty}^{+ \infty} \mathrm{~d} (t_1 - t_n) e^{i\omega_1 (t_1 - t_n)} \dots \int_{- \infty}^{+ \infty} \mathrm{~d} (t_{n-1} - t_n) e^{i\omega_{n-1} (t_{n-1} - t_n)} \chi_n^{\mathcal{T}}(t - t_n,\dots,t_{n-1} - t_n) \\& = 2 \pi \delta(\omega - \sum_{i=1}^n \omega_i) \tilde{\chi}_n^{\mathcal{T}}(\omega,\omega_1,\dots,\omega_{n-1}) \\& \sim \delta(\omega - \sum_{i=1}^n \omega_i)\end{aligned}其中\tilde{\chi}_n^{\mathcal{T}}(\omega,\omega_1,\dots,\omega_{n-1})为\chi_n^{\mathcal{T}}(t - t_n,\dots,t_{n-1} - t_n)的Fourier Transformation:\tilde{\chi}_n^{\mathcal{T}}(\omega,\omega_1,\dots,\omega_{n-1}) \equiv \int_{- \infty}^{+ \infty} \mathrm{~d} \tau e^{-i\omega \tau} \int_{- \infty}^{+ \infty} \mathrm{~d} \tau_1 e^{i\omega_1 \tau_1} \dots \int_{- \infty}^{+ \infty} \mathrm{~d} \tau_{n-1} e^{i\omega_{n-1} \tau_{n-1}} \chi_n^{\mathcal{T}}(\tau,\dots,\tau_{n-1})总之,有了二阶响应的一般Kubo Formula,我们就能轻松(并不)地将之前考虑的各式各样的线性响应推广到非线性响应了,例如计算非线性电导率,非线性磁化率,非线性电极化率,etc.Kubo Formula in Momentum Space对于连续介质(连续空间平移对称性)或者晶体(离散空间平移对称性),教科书中往往也会给出动量空间中的Kubo Formula。但这本质上只是对另一种参数——坐标——进行了Fourier Transform罢了,本质上Time Domain与Frequency Domain之间的Fourier Transform没有本质区别。甚至没有空间平移对称性时,也可以对每一个坐标参量作变换,得到最最general的形式。可以想像,与具有时间平移对称性体系的响应函数类似,具有空间平移对称性的系统的响应函数也会满足类似(准)动量守恒的形式,即:\chi_n(k; k_1,\dots,k_n) \sim \delta(k - \sum_{i=1}^n k_i)Second Harmonic Generation & Zero Frequency Term下面考虑一种常见的含时微扰,频率为\omega_0>0的时谐微扰:\hat{V}_S (t) = \hat{H'} e^{-i\omega_0 t} + \hat{H'}^\dagger e^{i\omega_0 t}可以看出外场的频率有\pm \omega_0的贡献,对于时间平移不变的体系,其一阶响应也应该是只有\pm \omega_0频率的项。而对于二阶响应:\langle \mathcal{O} \rangle_2(\omega) \sim \int d \omega_1 \int d \omega_2 \chi_2(\omega; \omega_1, \omega_2) F(\omega_1) F(\omega_2)若体系有时间平移对称性:\langle \mathcal{O} \rangle_2(\omega) \sim \int d \omega_1 \int d \omega_2 \delta(\omega- \omega_1-\omega_2) F(\omega_1) F(\omega_2)而外场的频谱为:F(\omega) \sim \delta(\omega \pm \omega_0)从而二阶响应可以有二倍频响应,即所谓的“2nd Harmonic Generation”:\langle \mathcal{O} \rangle_2(\omega) \sim \int d \omega_1 \int d \omega_2 \delta(\omega- \omega_1-\omega_2) \delta(\omega_1 \pm \omega_0) \delta(\omega_2 \pm \omega_0) \sim \delta(\omega \pm 2\omega_0)也可以有Zero Frequency Response,即:\langle \mathcal{O} \rangle_2(\omega) \sim \int d \omega_1 \int d \omega_2 \delta(\omega- \omega_1-\omega_2) \delta(\omega_1 \pm \omega_0) \delta(\omega_2 \mp \omega_0) \sim \delta(\omega)不论是2nd Harmonic Generation还是Zero Frequency Response,在半导体的nonlinear electro-optical response中都是凝聚态物理中有趣的topic。Kubo Formula for Fermi Golden Rule事实上,量子系统在光激发下的跃迁速率(概率)也可以看成是一种系统对外界微扰的响应。此时,系统的观测量为末态投影算符,未受微扰的密度矩阵则为初态投影算符,外场则为光波的时谐电磁场:\hat{\mathcal{O}} = | f \rangle \langle f |\hat{\rho}_0 = |i \rangle \langle i |跃迁速率则为:\mathcal{I}_{i \rightarrow f} = \frac{d}{dt} \langle \hat{\mathcal{O}} \rangle我们暂且跳过推导细节,直接看系统的二阶响应(可以证明一阶响应为0),也将会有2nd Harmonic Generation对应的二倍频响应和Zero Frequency Response。后者对应一般的Fermi Golden Rule计算的常跃迁速率,而前者则是我们上一节提到的,Fermi Golden Rule中略去的二倍频响应。在长时间平均近似下,便完全对应Fermi Golden Rule的结果。所以Fermi Golden Rule本质上是一种二阶响应,可以用Nonlinear Order Kubo Formula来计算。编辑于 2023-03-07 17:37・IP 属地北京量子多体理论非线性光学量子力学赞同 11639 条评论分享喜欢收藏申请转载文章被以下专栏收录O空O扬O的物理碎碎念面向知乎排版的学
Takefusa Kubo - Player profile 23/24 | Transfermarkt
Takefusa Kubo - Player profile 23/24 | Transfermarkt
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#14
Takefusa Kubo
1
Real Sociedad
LaLiga
League level:
First Tier
Joined: Jul 19, 2022
Contract expires: Jun 30, 2029
IMAGO
+
Date of birth/Age:
Jun 4, 2001 (22)
Place of birth:
Kawasaki, Kanagawa
Citizenship:
Japan
Height:
1,73 m
Position:
Right Winger
Current international:
Japan
Caps/Goals:
34 /
4
€60.00m Last update: Dec 22, 2023
Player data
Main position
Main position:
Right Winger
Other position:
Attacking Midfield
Left Winger
Facts and data
Name in home country:
久保 建英
Date of birth/Age:
Jun 4, 2001 (22)
Place of birth:
Kawasaki, Kanagawa
Height:
1,73 m
Citizenship:
Japan
Position:
Attack - Right Winger
Foot:
left
Player agent:
Roberto Tukada
Current club:
Real Sociedad
Joined:
Jul 19, 2022
Contract expires:
Jun 30, 2029
Last contract extension:
Feb 12, 2024
Social-Media:
Further information
Real Madrid: 50% capital gains from a future sale, no repurchase option.
Real Sociedad: 100% player rights. Termination clause is 60 million.
Youngest player in J.League history that has played in a match: 15y 5m 1d
Youngest goalscorer in J.League history: 15y, 10m, 11d
Youth clubs
FC Persimmon (2008–2009), Kawasaki Frontale (2009-2011), FC Barcelona (2011-2015), FC Tokyo (2015-2017)
Stats of Takefusa Kubo
View full stats
National team career
#
National team
Debut
20
Japan
Jun 9, 2019
34
4
7
Japan U23
Mar 26, 2021
4
-
21
Japan U21
Nov 17, 2018
2
-
20
Japan U20
Mar 24, 2017
5
-
9
Japan U19
Oct 19, 2018
5
1
7
Japan U17
Aug 22, 2017
7
3
9
Japan U16
Sep 16, 2016
12
4
7
Japan Olympic
Jul 22, 2021
6
3
9
Japan U15
Sep 16, 2015
5
8
17
Japan U22
Nov 17, 2019
1
-
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KUBO亮相中国说唱巅峰对决 泡泡玛特持续运营潮流圈层_科技_中国网
KUBO亮相中国说唱巅峰对决 泡泡玛特持续运营潮流圈层_科技_中国网
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KUBO亮相中国说唱巅峰对决 泡泡玛特持续运营潮流圈层
2023年05月11日20:11 中国网科技
新闻爆料: alltech@china.org.cn 电话:(010)82081166-6059
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日前,泡泡玛特携手爱奇艺、猫宇星河,邀请热门IP KUBO出任综艺《中国说唱巅峰对决2023》“巅峰见证官”。KUBO在节目中一经亮相,便引来潮流圈层密切关注,更有多位参赛选手在社交平台晒出了与KUBO的合影。
《中国说唱巅峰对决》是爱奇艺自制华语乐坛说唱歌手顶级联赛,其前身为《中国新说唱》系列。在2022年《中国说唱巅峰对决》正式上线,7年以来,新说唱IP热度持续高涨,颇受年轻人的青睐,每年夏天都会引领一波说唱浪潮。
KUBO是一个热血、喜欢运动、向往自由的男生。作为当下最受年轻人喜爱的潮玩IP之一,具有极高的热度与影响力。艺术家为《中国说唱巅峰对决2023》特别设计了两款专属KUBO形象。全新形象的KUBO,被爱奇艺授予“巅峰见证官”职位,通过爱奇艺官方在节目内外进行了大量曝光。
艺术家表示,走向舞台的说唱歌手KUBO对自己有很强的认同感,彰显实力的同时也希望自己能在潮流圈层中大显身手,给观众们带去有独特审美观点、作品及自我表达。他不需要华丽昂贵的装饰,简单的街头风格代表着自由随性的态度,oversize的穿搭既是街头、说唱文化的识别元素,也彰显着说唱文化纯粹及real的精神内核。“I listen therefore I am”,KUBO所喜爱的说唱文化就是他自我的投射。
KUBO×中国说唱巅峰对决2023
2022年,《中国说唱巅峰对决》强势霸榜,全网热搜8877次,其中微博热搜1146个;斩获云合Q3网综有效播放、市占率 TOP1、Vlinkage2022年上半年综艺及网络综艺播放指数双榜TOP1;爱奇艺热度值最高达到9297;节目内产出136首歌曲热搜上榜率89%,歌曲在网易云单平台总播放量达5.7亿。今年的《中国说唱巅峰对决2023》将在去年的基础上全面升级,聚集更多说唱厂牌和各地区有代表性的rapper,赛制上新增厂牌大战,为比赛更添赛事竞技感。
伴随着节目的热播,KUBO的知名度与人气持续走高。舞台上,巨大的KUBO玻璃钢雕塑伴随选手出场,给观众极大的视觉冲击力。社交平台上,参赛选手多次晒出以KUBO为背景的照片,吸引了众多喜爱说唱文化的粉丝。观众小桃儿表示,自己之前就超喜欢这个IP,这次的形象不管是设计、服饰、外形等各种细节都“很说唱”。观众Lily则表示,“坚毅的眼神和酷酷的外形,钟爱各类运动和街头文化的KUBO就是我心中说唱文化的代表形象,完全符合节目定位。”
泡泡玛特市场部负责人表示,“潮流”是泡泡玛特产品的内核,不管是与全球艺术家合作,还是开发MEGA、萌粒等新产品线,以及与Moncler、UT等潮流品牌联名,泡泡玛特始终在探索潮玩的边界。未来,泡泡玛特也将继续围绕“潮流”内核,持续推出引领风潮的产品与业务。
(责任编辑:朱赫)
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场论笔记3: Interaction picture and Kubo formula - 知乎
场论笔记3: Interaction picture and Kubo formula - 知乎首发于笔记切换模式写文章登录/注册场论笔记3: Interaction picture and Kubo formula皇甫伤逝记得开心Schrödinger picture薛定谔表象下态随时间演化满足薛定谔方程: i\hbar\frac{\partial |\psi\rangle_S}{\partial t}=H_S|\psi\rangle_S 其中 H_{S}为薛定谔表象下的厄米的哈密顿量。时间演化算符定义为: |\psi(t)\rangle_S=U_S(t,t_0)|\psi(t_0)\rangle_S ,代入薛定谔方程得到 U_S(t) 满足:\\ i\hbar \frac{\partial U_S(t,t_0)}{\partial t}=H_SU_S(t,t_0) 如果哈密顿量不含时,则可得到时间演化算符: U_S(t,t_0)=e^{-iH_S(t-t_0)/\hbar} 。特别地,对于本征态:H_S|\psi_n\rangle_S=E_n|\psi_n\rangle_S=i\hbar\frac{\partial |\psi\rangle_S}{\partial t}\rightarrow |\psi_n(t)\rangle_S=e^{-iE_n(t-t_0)/\hbar}|\psi_n(t_0)\rangle_S 另一方面: |\psi_n(t)\rangle_S=U_S(t,t_0)|\psi_n(t_0)\rangle_S=e^{-iH_S(t-t_0)/\hbar}|\psi_n(t_0)\rangle_S=e^{-iE_n(t-t_0)/\hbar}|\psi_n(t_0)\rangle_S 对于不显含时的哈密顿量,薛定谔表象下态随时间演化,但算符(时间演化算符除外)不随时间演化。Heisenberg picture考虑算符 \hat O_S 的期望: _S\langle\psi(t)|\hat O_S|\psi(t)\rangle_S= {}_S\langle\psi(t_0)|U_S^\dagger(t,t_0)\hat O_SU_S(t,t_0)|\psi(t_0)\rangle_S={}_H\langle\psi|\hat O_H(t)|\psi\rangle_H 其中海森堡表象下的态和算符定义为: |\psi\rangle_H=|\psi(t_0)\rangle_S , \hat O_H(t,t_0)=U^\dagger_S(t,t_0)\hat O_S U_S(t,t_0) 这里 t_0 定义为时间“起点”,通常是相互作用开始作用的时刻。尽管S和H表象下并没有引入相互作用这个概念,有哈密顿量和时间演化算符即可建立这两个表象下的所有关系。当然这也是为什么这两个表象不好处理相互作用的问题的原因之一。为方便起见,以下推导(包括interaction picture)都省略不写 t_0 ,或者默认 t_0 为零。但必须牢记, t 其实代表的是从相互作用开始作用后的“时间差”,在最后推导kubo formula的时候会回到再次用到时间差表示。可以看出,海森堡表象下态不随时间演化,而算符随时间演化为:\frac{d}{dt}\hat O_H(t)=(\frac{\partial}{\partial t}U^\dagger_S(t))\hat O_S U_S(t)+U^\dagger_S(t)(\frac{\partial}{\partial t}\hat O_S )U_S(t)+U^\dagger_S(t)\hat O_S (\frac{\partial}{\partial t}U_S(t))=\frac{i}{\hbar}[H_H,\hat O_H(t)]+(\frac{\partial \hat O}{\partial t})_H 其中最后一步用到了薛定谔表象下时间演化算符满足的薛定谔方程和 H_H\equiv U_S^\dagger(t) H_S U_S(t) 特别地,如果哈密顿量不含时: H_H=H_S 对于时间演化算符 U_H(t)=U_S(t) ,从而对于海森堡表象下推出的式子 \\ \frac{d}{dt}\hat O_H(t)=\frac{i}{\hbar}[H_H,\hat O_H(t)]+(\frac{\partial \hat O}{\partial t})_H 如果我们带入 U_H(t) 则还原回薛定谔表象下时间演化算符满足的方程(练习)。Interaction picture把哈密顿量拆分成能解出本征值的部分和相互作用的部分: H_S=H_{0,S}+V_S 则利用 H_{0,S} 可以定义相互作用表象下的态: |\psi(t)\rangle_I\equiv U_{0,S}^\dagger|\psi(t)\rangle_S=e^{iH_{0,S}t/\hbar}|\psi(t)\rangle_S 其中 U_{0,S}=e^{-iH_0t/\hbar} 。对于相互作用表象下的算符,定义为 \hat O_{I}(t)\equiv U_{0,S}^\dagger\hat O_S(t)U_{0,S}=e^{iH_{0,S}t/\hbar}\hat O_S(t)e^{-iH_{0,S}t/\hbar} 通常来说, \hat O_S(t) 不随时间变化,除非薛定谔表象下该算符显含时间。特别地,对于 H_{0} 本身有: H_{0,I}=H_{0,S} 考虑相互作用表象下态的演化: i\hbar\frac{d|\psi(t)\rangle_I}{dt}=i\hbar(\frac{\partial}{\partial t}U_{0,S}^\dagger|\psi(t)\rangle_S+U_{0,S}^\dagger\frac{\partial}{\partial t}|\psi(t)\rangle_S)=(-U_{0,S}^\dagger H_{0,S}|\psi(t)\rangle_S+U_{0,S}^\dagger(H_{0,S}+V_S)|\psi(t)\rangle_S) \\i\hbar\frac{d|\psi(t)\rangle_I}{dt}=U^\dagger_{0,S}V_S|\psi(t)\rangle_S=U^\dagger_{0,S}V_SU_{0,S}|\psi(t)\rangle_I=V_{I}|\psi(t)\rangle_I 上式即为相互作用表象下态满足的薛定谔方程,其中相互作用扮演着“哈密顿量”的角色。考虑相互作用表象下算符的演化: \frac{d}{dt}\hat O_{I}(t)=(iH_{0,S}/\hbar)e^{iH_{0,S}t/\hbar} \hat O_S(t)e^{-iH_{0,S}t/\hbar}+e^{iH_{0,S}t/\hbar}\partial_t\hat O_S(t)e^{-iH_{0,S}t/\hbar}+e^{iH_{0,S}t/\hbar}\hat O_S(t)e^{-iH_{0,S}t/\hbar}(-iH_{0,S}/\hbar) 从而得到: \\ \frac{d}{dt}\hat O_{I}(t)=\frac{i}{\hbar}[H_{0,S},\hat O_I(t)]+(\frac{\partial \hat O(t)_S}{\partial t})_I 算符的演化方程和海森堡的表象下的方程很类似,只不过对易子中的哈密顿量是不包含相互作用的 H_{0,S} ,从而在知道 H_{0,S} 及其本征态后,为解决相互作用 V_I 的问题带来“便利”。此外可以看出, V_I 决定了态的演化, H_{0,S} 决定了算符的演化。 Dyson series类似地,如果在相互作用表象下想要有 |\psi(t)\rangle_I=U_I(t)|\psi(0)\rangle_I ,代入态满足的方程后发现相互作用表象下的时间演化算子必须满足方程: i\hbar\frac{dU_I(t)}{dt}=V_I(t)U_I 。需要注意的是,这并不意味着 U_I(t)=e^{-\frac{i}{\hbar}V_I t} 除非相互作用 V_I 不含时。当然,另一种看似更直接的猜想是把时间演化算子写成积分的形式 U_I(t)=e^{-\frac{i}{\hbar}\int_0^tV_I(t') dt'} 。但是注意不同时间下的算符不一定对易,而时间演化算符显然要满足 U_I(t,0)=U_I(t,t^*)U_I(t^*,0) 。这也就是说猜测的积分形式需要满足关系: e^{-\frac{i}{\hbar}\int_0^{t}V_I(t') dt'}=e^{-\frac{i}{\hbar}\int_{t^*}^{t}V_I(t') dt'-\frac{i}{\hbar}\int_0^{t^*}V_I(t') dt'}=e^{-\frac{i}{\hbar}\int_{t^*}^{t}V_I(t') dt'}e^{-\frac{i}{\hbar}\int_0^{t^*}V_I(t') dt'} 而由BCH formula知: e^X e^Y=e^{X+Y+\frac{1}{2}[X,Y]+\frac{1}{12}[X,[X,Y]]-\frac{1}{12}[Y,[X,Y]]+\cdots} ,即在算符不对易的情况下上式最后一个等号不成立,之前简单的积分猜想结果也就不成立。对相互作用表象下的时间演化算子必须满足的方程两边积分可得到一个迭代关系:\\ U_I(t)=1-\frac{i}{\hbar}\int_{0}^{t}dt'V_I(t')U_I(t') 其中第一项单位算符常数项是因为初始条件 U_I(0)=I 所带来的。把等式右边的时间演化算符再用这个式子本身反复迭代即可求出:U_I(t)=1-\frac{i}{\hbar}\int_{t_0}^{t}dt_1 V_I(t_1)+(\frac{-i}{\hbar})^2\int_{0}^t dt_1 \int_0^{t_1}dt_2 V_I(t_1)V_I(t_2)+\cdots+(\frac{-i}{\hbar})^n\int_{0}^t dt_1 \cdots\int_0^{t_{n-1}}dt^n V_I(t_1)\cdots V_I(t_n)+\cdots 上式被称为Dyson series。需要注意的是由于不对易乘积 V_I(t_1)\cdots V_I(t_n) 中不同时刻的 V_I 位置很重要。由于积分迭代关系,可以看出 t_1>t_2>\cdots >t_n 。定义 U_n(t)=(\frac{-i}{\hbar})^n\int_{0}^t dt_1\int_0^{t_1 }dt_2 \cdots\int_0^{t_{n-1}}dt^n T[V_I(t_1)\cdots V_I(t_n)] 其中算符 T 是time-ordering operator,它把 V_I 的乘积中按照 t_1>t_2>\cdots >t_n 顺序从左到右乘好。这也就意味着我们作用了这个 T 算符后乘积中我们怎么写 t_i 的顺序不重要了,换句话说, U_n(t) 对于 t_i 具有交换对称性。对于具有交换对称性的函数 K(t_1,\cdots,t_n) ,可以得到如下关系(注意积分上限):\int_0^tdt_1\int_0^{t_1}dt_2\cdots\int_0^{t_{n-1}}dt_n K(t_1,\cdots,t_n)=\frac{1}{n!}\int_0^tdt_1\int_0^{t}dt_2\cdots\int_0^{t}dt_n K(t_1,\cdots,t_n) 这是因为对于后者的积分区域,总可以把他划分为一些小区域的相加:t_1>t_2>\cdots t_n , t_2>t_1>\cdots t_n ......以此类推,共有 n! 可能排列组合。由于K(t_1,\cdots,t_n) 对于 t_i 是对称的,所以每一个小区域的积分值相同。从而上式成立。下图为一个简单的n=2的积分区域划分的例子:所以 U_n(t)=\frac{(-i/\hbar)^n}{n!}\int_{0}^t dt_1 \int_0^{t}dt_2 \cdots\int_0^{t}dt^n T[V_I(t_1)\cdots V_I(t_n)] 并且时间演化算符:U_I(t)=\sum_{n=0}U_n(t)=\sum_{n=0}\frac{(-i/\hbar)^n}{n!}\int_{0}^t dt_1 \int_0^{t}dt_2 \cdots\int_0^{t}dt^n T[V_I(t_1)\cdots V_I(t_n)]=Te^{-\frac{i}{\hbar}\int_0^td\tau V_I(\tau)} 上式最后只是形式上写成e指数的形式,需和外边的 T 算子一起作用后,应理解为展开时必须按照时间顺序 t_1>t_2>\cdots t_n 排列好 V_I ,即等号左边的求和项。可以看出,相互作用表象下的时间演化算子和我们一开始最初猜想的结果 U_I(t)=e^{-\frac{i}{\hbar}\int_0^tV_I(t') dt'} ,形式上多出了一个时间排序算子 T 。题外话:time-ordering operator T 的引入是因为不同时间下的算符不对易以及要求时间演化算子满足 U_I(t,0)=U_I(t,t^*)U_I(t^*,0) 的结果。对于含时哈密顿量,且参数随时间缓慢变化,在绝热近似下演化后的本征态除了包含能量的积分项(dynamical phase factor),还应包含Berry phase项: |\psi_n(t)\rangle=e^{i\gamma_n (t)}e^{-\frac{i}{\hbar}\int_0^tdt' E_n(R(t'))}|n(R(t))\rangle 。其中dynamical phase factor 是由于微分方程 i\hbar\frac{\partial_n |\psi\rangle_S}{\partial t}=H_S|\psi_n\rangle_S=E_n(R(t))|\psi_n\rangle_S 所引入的。这里之所以不需要time-ordering operator T 是因为我们并没有引入“时间演化算符”这一算符表述来求末态,也就不存在对不对易的说法,自然也就不需要 T 了。一个简单的小结:Kubo Formula 接下来利用相互作用表象简单地讨论一下线性响应。对于算符 \hat A(t) ,我们想知道其在 t=-\infty 开始的外势 V(t) 的影响下,t 时刻的期望 \langle\hat A(t)\rangle 是多少。\langle\hat A(t)\rangle=\sum_n{}_S\langle\psi_n(t)|\hat A_S(t)|\psi_n(t)\rangle_S=\sum_n{}_I\langle\psi_n(t)|\hat A_I(t)|\psi_n(t)\rangle_I=\sum_n {}_I\langle\psi_n(-\infty)|U^\dagger_I(t)\hat A_I(t)U_I(t)|\psi_n(-\infty)\rangle_I 把时间演化算子展开到一阶项: U_I(t)=1-\frac{i}{\hbar}\int_{-\infty}^tdt'V_I(t') 并只保留到一阶项:\langle\hat A(t)\rangle=\sum_n {}_I\langle\psi_n(-\infty)|\{\hat A_I(t)+\frac{i}{\hbar}\int_{-\infty}^{t}dt' [\hat V_I(t'),\hat A_I(t)]\}|\psi_n(-\infty)\rangle_I=\langle\hat A(t)\rangle_0+\frac{i}{\hbar}\int_{-\infty}^{t}dt'\langle[\hat V_I(t'),A_I(t)]\rangle_0 上式即为零温下线性响应公式(Kubo formula),其中 \langle\cdots\rangle_0 代表着 \sum_n{}_I\langle\psi_n(-\infty)|\cdots|\psi_n(-\infty)\rangle_I 。这个公式的好处在于利用了已经知道的 t=-\infty 时刻的非微扰态去求之后的线性响应结果。在知道了微扰的具体含时形式 \hat V_I(t) 和我们所关心的算符 \hat A_I(t) 后,总可以通过数值积分求出 t 时刻的响应结果(如果收敛的话)。对于有限温度的情况,可以利用配分函数在求平均时变为: \frac{1}{Z_0}\sum_n e^{-\beta E_n}{}_I\langle\psi_n(-\infty)|\cdots|\psi_n(-\infty)\rangle_I 。作为一个简单的例子,尝试利用Kubo formula计算霍尔电导:假设所加电场为交流的 E=Ee^{-iwt} (含时),最后再让 \omega\rightarrow0 即可得到DC的情况(通常来说,先取 \omega\rightarrow0 极限再取零温极限,这里我们直接在零温结果下取 \omega\rightarrow0对于霍尔电导计算没问题,但在一些无能隙体系则可能会出问题)。选取规范使得 E=-\partial_t A ,则 A=\frac{E}{iw}e^{-iwt} 微扰 V_I(t)=-J(t)\cdot A(t)=\frac{J_n(t)E_n}{iw}e^{-iwt} ,这里 J 和 A 都是相互作用表象下的算子。其中由于 A 的特殊e指数形式,易知其变换后在相互作用表象下的式子和薛定谔表象下的一样。(但是 J 不和 H_{0,S} 对易,所以 J 在不同表象下会不一样。)考虑单条能带 n=0 即态 |\psi_0 (-\infty)\rangle 的贡献:\\ \langle J_i(t)\rangle=\frac{1}{\hbar w}\int_{-\infty}^{t}dt'\langle\psi_0(-\infty)|[J_n(t'),J_i(t)]E_n e^{-iwt'}|\psi_0(-\infty)\rangle 这里我们省略了 \langle\hat A(t)\rangle_0 因为在没有微扰时不会有流。由于实际系统响应是取静态极限下的结果,系统具有时间平移不变性(直流),则上述电流的关联函数只和时间差有关,则可定义 t''=t-t' 来变换积分变量:\\ \langle J_i(t)\rangle=\frac{1}{\hbar w}\int_0^{+\infty}dt''\langle\psi_0(-\infty)|[J_n(t'),J_i(t''+t')]E_n e^{-iwt}e^{iwt''}|\psi_0(-\infty)\rangle 这么代换后也可以看出积分和 t' 无关。令 t' 为负无穷,即电流微扰刚开始的时刻:\\ \langle J_i(t)\rangle=\frac{1}{\hbar w}\int_0^{+\infty}dt''\langle\psi_0(-\infty)|[J_n(-\infty),J_i(-\infty+t'')]E_n e^{-iwt}e^{iwt''}|\psi_0(-\infty)\rangle 考虑 i=y,n=x ,则由上式可以读出: \sigma_{yx}=\frac{1}{\hbar w}\int_0^{+\infty}dt\langle\psi_0(-\infty)|[J_x(-\infty),J_y(-\infty+t)] e^{iwt}|\psi_0(-\infty)\rangle 在还原回 t_0 利用“时间差”表示的规定下我们有表象变换关系:J_{I,y}(t,t_0)=e^{iH_{0,S}(t-t_0)/\hbar}J_{S,y}(t,t_0)e^{-iH_{0,S}(t-t_0)/\hbar} 假定取静态极限下薛定谔表象下算符不随时间改变 J_{S,y}(t,t_0)=J_{S,y}(t_0,t_0) ,我们有: J_{I,y}(t_0,t_0)=J_{S,y}(t_0,t_0) ,以及 J_{I,y}(t,t_0)=e^{iH_{0,S}(t-t_0)/\hbar}J_{I,y}(t_0,t_0)e^{-iH_{0,S}(t-t_0)/\hbar} 现在令 t_0=-\infty 并回到我们省略 t_0 的规定下,上式即是说:J_{y}(-\infty+t)=e^{iH_{0,S}t/\hbar}J_{y}(-\infty)e^{-iH_{0,S}t/\hbar} 从而得到:\sigma_{yx}=\frac{1}{\hbar w}\int_0^{+\infty}dt\langle\psi_0(-\infty)|[J_x(-\infty),e^{iH_{0,S}t/\hbar}J_y(-\infty)e^{-iH_{0,S}t/\hbar}] e^{iwt}|\psi_0(-\infty)\rangle 注意上式中所有的态和算符都是相互作用表象下的,但是由于是在负无穷时刻,所以它们即等于薛定谔表象下的态和算符。更一般地,利用表象之间的变换关系,可以得出只要是在算算符的期待值时,算符和态都是同一时刻的(不一定得是负无穷微扰没开始的时候),则计算时无论把算符和态都认为是哪一个表象下的都不会影响结果。插入完备关系 \sum_n |n\rangle\langle n| (为方便,在这和之后省略“负无穷”这一符号)。\sigma_{yx}=\frac{1}{\hbar w}\int_0^{+\infty}dte^{iwt}\sum_n\langle0|J_x|n\rangle\langle n|J_y |0\rangle e^{i(E_n-E_0)t/\hbar}-\langle0|J_y|n\rangle\langle n|J_x|0\rangle e^{i(E_0-E_n)t/\hbar} 为了保证积分收敛,一个不严谨的技巧是给 w 添上无限小的正虚部 w\rightarrow w+i\epsilon 。并且注意到 n=0 时对上述求和没有贡献,我们有:\\ \sigma_{yx}=\frac{i}{ w}\sum_{n\neq 0}\frac{\langle0|J_x|n\rangle\langle n|J_y |0\rangle }{\hbar w+E_n-E_0}-\frac{\langle0|J_y|n\rangle\langle n|J_x|0\rangle }{\hbar w+E_0-E_n} 利用展开式: \frac{1}{\hbar w+E-E_0}\approx\frac{1}{E_n-E_0}-\frac{\hbar w}{(E_n-E_0)^2}+O(w^3) 在取 w\rightarrow0 的极限后得到: \sigma_{yx}=-i\hbar \sum_{n\neq 0}\frac{\langle0|J_x|n\rangle\langle n|J_y |0\rangle }{(E_n-E_0)^2}-\frac{\langle0|J_y|n\rangle\langle n|J_x|0\rangle }{(E_0-E_n)^2} 以上即为经过修改后的David Tong的QHE里的笔记推导。另外一种不做时间变量代换而做Fourier变换到频域的方法在这个回答中给出:单粒子电流算符(e为正) J=-e\dot r=-e\frac{i}{\hbar}[\hat H,\hat r]=-e\frac{i}{\hbar}[\hat H i\partial_k-i\partial_k \hat H]=\frac{-e}{\hbar}\frac{\partial \hat H}{\partial k} 另一种思路是对哈密顿量展开到一阶项: H(k-\frac{e}{\hbar}A)\approx H(k)-\frac{e}{\hbar}A\cdot \frac{\partial H}{\partial k} 再考虑所有 k 的电子贡献(在第一布里渊区积分):\\ \sigma_{yx}=-i\frac{e^2}{\hbar}\sum_{n\neq 0}\int_{BZ}\frac{dk_xdk_y}{(2\pi)^2}\frac{\langle 0|\frac{\partial H}{\partial k_x}|n\rangle\langle n|\frac{\partial H}{\partial k_y} |0\rangle }{(E_0-E_n)^2}-\frac{\langle 0|\frac{\partial H}{\partial k_y}|n\rangle\langle n|\frac{\partial H}{\partial k_x}|0\rangle }{(E_0-E_n)^2} 上式即为利用Berry curvature推出的单带霍尔电导: \sigma_{yx}=n_c\frac{e^2}{h} 其中 n_c=i\sum_{n\neq 0}\int_{BZ}\frac{dk_xdk_y}{2\pi}\frac{\langle 0|\frac{\partial H}{\partial k_y}|n\rangle\langle n|\frac{\partial H}{\partial k_x} |0\rangle }{(E_0-E_n)^2}-\frac{\langle 0|\frac{\partial H}{\partial k_x}|n\rangle\langle n|\frac{\partial H}{\partial k_y}|0\rangle }{(E_0-E_n)^2} 。在闭合流行上的积分出的n_c (比如二维布里渊区)即为Chern number,为整数。ReferenceDavid Tong: The Quantum Hall EffectQuantum Theory of Radiation InteractionsREVIEWS OF MODERN PHYSICS, VOLUME 82, JULY–SEPTEMBER 2010编辑于 2022-03-19 05:13场论量子力学量子物理赞同 633 条评论分享喜欢收藏申请转载文章被以下专栏收录笔记“Ad astra abyssosqu
久保建英 - 搜狗百科
- 搜狗百科久保建英(Takefusa Kubo,2001年6月4日-),出生于神奈川县川崎市,日本男子足球运动员,司职边锋,现效力于皇家社会足球俱乐部。[1] 久保建英出自巴塞罗那青训,后曾效力过东京FC、横滨水手等队。2019年6月14日,皇家马德里足球俱乐部宣布久保建英加盟球队,合同期6年。加盟后,久保建英将先在皇家马德里卡斯蒂利亚效力1年;[2][3]同年8月1日(北京时间),帮助皇家马德里获2019年奥迪杯季军。[4]2021年5月,随比利亚雷亚尔俱乐部获2020-2021赛季欧罗巴联赛冠军;[5][6]同年6月,入选东京奥运会名单。同年12月,当选为IFFHS2021年度亚洲最佳年轻球员(U20)、IFFHS2021年度亚洲最佳组织核心;以及入选IFFHS亚足联2021年度最佳阵容。[7][8]2022年6月,随日本队获2022年麒麟杯亚军。[9]6月12日,久保建英当选皇家社会赛季最佳球员。[10] 2024年2月12日,皇家社会宣布与久保建英续约至2029年。[11] 久保建英也就此以21岁71天的年纪,成为了本世纪代表皇家社会西甲首秀破门第二年轻的球员,仅次于2021年8月代表皇家社会攻破巴萨球门的洛韦特(20岁331天)。[12]网页微信知乎图片视频医疗汉语问问百科更多»登录帮助首页任务任务中心公益百科积分商城个人中心久保建英编辑词条添加义项同义词收藏分享分享到QQ空间新浪微博久保建英(Takefusa Kubo,2001年6月4日-),出生于神奈川县川崎市,日本男子足球运动员,司职边锋,现效力于皇家社会足球俱乐部。[1]久保建英出自巴塞罗那青训,后曾效力过东京FC、横滨水手等队。2019年6月14日,皇家马德里足球俱乐部宣布久保建英加盟球队,合同期6年。加盟后,久保建英将先在皇家马德里卡斯蒂利亚效力1年;[2][3]同年8月1日(北京时间),帮助皇家马德里获2019年奥迪杯季军。[4]2021年5月,随比利亚雷亚尔俱乐部获2020-2021赛季欧罗巴联赛冠军;[5][6]同年6月,入选东京奥运会名单。同年12月,当选为IFFHS2021年度亚洲最佳年轻球员(U20)、IFFHS2021年度亚洲最佳组织核心;以及入选IFFHS亚足联2021年度最佳阵容。[7][8]2022年6月,随日本队获2022年麒麟杯亚军。[9]6月12日,久保建英当选皇家社会赛季最佳球员。[10]2024年2月12日,皇家社会宣布与久保建英续约至2029年。[11]久保建英也就此以21岁71天的年纪,成为了本世纪代表皇家社会西甲首秀破门第二年轻的球员,仅次于2021年8月代表皇家社会攻破巴萨球门的洛韦特(20岁331天)。[12]中文名久保建英展开外文名Takefusa Kubo展开别名日本梅西[13]展开国籍日本展开民族大和族展开出生日期2001年6月4日展开出生地日本神奈川县川崎市展开惯用脚左脚[5]展开主要荣誉IFFHS亚洲U20最佳年轻球员(2021年)[7]IFFHS亚洲最佳组织核心(2021年)[7]IFFHS亚足联最佳阵容(2021年)[8]麒麟杯亚军(2022年)[9]Sofascore2023年西甲最佳阵容[15]展开性别男展开身高173cm[5]展开体重67kg[5]展开运动项目足球展开所属运动队皇家社会足球俱乐部[1]展开场上位置边锋展开球衣号码11号(国家队)[14]、14号(俱乐部)展开星座双子座展开展开参考资料:1. 官方:久保建英正式加盟皇家社会直播吧[引用日期2022-07-19]2. Takefusa Kubo is a new Real Madrid player. He joins Castilla from next season | Real Madrid CF(英文)皇家马德里足球俱乐部官网2019-06-143. 久保建英选手 レアル・マドリードへ完全移籍のお知らせ|ニュース|FC东京オフィシャルホームページ(日文)东京足球俱乐部官网2019-06-144. 皇马5-3费内巴切夺奥迪杯季军,本泽马戴帽,马里亚诺建功懂球帝2019-08-01[引用日期2019-08-01]5. 久保建英直播吧[引用日期2021-07-01]6. 比利亚雷亚尔夺得欧联杯冠军,下赛季西甲将有五队参加欧冠直播吧[引用日期2022-11-18]7. IFFHS官方:孙兴慜当选2021年度亚洲最佳球员直播吧[引用日期2021-12-19]8. IFFHS亚足联年度最佳阵容:武磊、孙兴慜在列|亚足联|IFFHS|日本_新浪新闻新浪[引用日期2021-12-26]9. 突尼斯3-0日本捧得麒麟杯,镰田大地失空门吉田麻也送点+送礼懂球帝[引用日期2022-06-14]10. 44场9球9助!久保建英当选皇家社会赛季最佳球员直播吧[引用日期2023-06-12]11. 身价6000万欧亚洲第1!官方:22岁久保建英与皇家社会续约至2029直播吧[引用日期2024-02-12]12. 21岁71天,久保建英是本世纪皇社西甲首秀破门第二年轻的球员PP体育[引用日期2022-11-18]13. 日本梅西正式加盟东京FC腾讯体育2015-05-14[引用日期2016-07-31]14. 日本26人世界杯名单:南野拓实、富安健洋、久保在列,古桥落选-直播吧直播吧[引用日期2022-11-07]15. Sofascore西甲年度最佳阵容:格列兹曼、德容、久保建英在列直播吧[引用日期2023-12-31]16. 皇马官方宣布日本天才小将租借加盟升班马 租期1年腾讯2019-08-23[引用日期2019-08-23]17. 皇马官方:久保建英租借加盟比利亚雷亚尔懂球帝[引用日期2020-08-11]18. 仅次于苏亚雷斯,久保建英上赛季联赛射正率名列西甲第二懂球帝[引用日期2020-08-11]19. 欧战首秀13分钟进球!久保建英刷新日本球员1纪录新浪[引用日期2020-10-23]20. 皇马日本妖人租借加盟赫塔菲 租期至本赛季结束新浪[引用日期2021-01-09]21. 欧足联50大未来之星:穆科科、曼联新援阿马德入选懂球帝[引用日期2021-01-09]22. 久保建英上半时直接参与5次射门,赫塔费赛季至今队内第一懂球帝2021-01-21[引用日期2021-01-23]23. 马略卡官宣李刚仁加盟 将与久保建英组成东亚搭档新浪网[引用日期2022-11-18]24. 久保建英单刀绝杀!第三位攻破马竞球门的亚洲球员_国际足球_新浪竞技风暴_新浪网新浪网[引用日期2022-11-18]25. 国王杯-武磊替补久保健英破门 西人1-2马洛卡遭淘汰网易体育[引用日期2022-11-18]26. 本田圭佑:久保建英能成为亚洲足坛领军人物直播吧[引用日期2022-11-18]27. 西甲-皇马0-2不敌皇家社会 米利唐失误送大礼久保建英破门PP视频体育频道[引用日期2023-05-12]28. 日本美洲杯大名单:日本梅西在列 一名大学生球员入选腾讯网[引用日期2022-11-18]29. 日本世预赛23人名单:J联赛仅4人 久保建英在列_国际足球_新浪竞技...新浪体育2019-08-30[引用日期2019-08-30]30. 日本世预赛名单:久保建英入选,J联赛仅3人腾讯网2019-10-03[引用日期2019-10-03]31. 日本U22大名单:久保建英和堂安律领衔懂球帝[引用日期2019-11-05]32. 日本新一期国奥队名单:久保建英、吉田麻也领衔12人留洋阵容-直播吧zhibo8.cc直播吧[引用日期2021-05-20]33. 2021金童奖百人候选:佩德里、贝林厄姆领衔,久保建英在列-直播吧zhibo8.cc直播吧[引用日期2021-06-16]34. 日本公布奥运会大名单:久保建英入选,远藤航、堂安律在列直播吧[引用日期2021-06-22]35. 日本公布世预赛大名单:久保建英、古桥亨梧入选,9月7日将战国足直播吧[引用日期2021-08-31]36. 日本队麒麟杯大名单:富安健洋、远藤航等悉数入选新浪网[引用日期2022-11-18]37. 麒麟杯-久保2传1射三笘薫2助上田绮世造红点 日本6-0十人萨尔瓦多-直播吧-直播吧[引用日期2023-08-14]38. MF/FW 久保 建英(日文)日本足球协会官网[引用日期2023-05-16]39. 日程・結果 | バル・ド・マルヌU-16国際親善トーナメント2015 | 日本サッカー協会日程・結果[引用日期2023-08-14]40. 日程・结果│AFC U-16选手権インド2016|U-16|日本代表|JFA|日本サッカー协会 (日文)日本足球协会官网日本足球协会官网[引用日期2023-08-14]41. 日程・结果 | FIFA U-20 ワールドカップ韩国2017|日本代表|JFA|日本サッカー协会 (日文)日本足球协会官网日本足球协会官网[引用日期2023-08-14]42. 日程・結果 | FIFA U-17 ワールドカップインド2017|日本代表|JFA|日本サッカー協会日程・結果[引用日期2023-08-14]43. 日程・结果│AFC U-19选手権インドネシア2018|U-21|日本代表|JFA|日本サッカー协会 (日文)日本足球协会官网日本足球协会官网[引用日期2023-08-14]44. 日程・结果│ドバイカップU-23|U-21|日本代表|JFA|日本サッカー协会 (日文)日本足球协会官网日本足球协会官网[引用日期2023-08-14]45. 日程・结果│AFC U-23选手権タイ2020予选|U-22|日本代表|JFA|日本サッカー协会 (日文)日本足球协会官网日本足球协会官网[引用日期2023-08-14]46. 选手(2019年招集)・スタッフ|SAMURAI BLUE|JFA|公益财団法人日本サッカー协会 (日文)日本足球协会官网日本足球协会官网[引用日期2023-08-14]47. 日本职业足球运动员协会2022年度各奖项出炉,三笘薰当选最佳球员直播吧[引用日期2023-05-18]48. 马洛卡新帅:期待久保建英挑起进攻大梁,还有时间做好保级准备直播吧[引用日期2022-11-18]词条标签:运动员人物免责声明搜狗百科词条内容由用户共同创建和维护,不代表搜狗百科立场。如果您需要医学、法律、投资理财等专业领域的建议,我们强烈建议您独自对内容的可信性进行评估,并咨询相关专业人士。词条信息词条浏览:47255次最近更新:24.02.12编辑次数:51次创建者:那(-)抹温柔突出贡献者:新手指引了解百科编辑规范用户体系商城兑换问题解答关于审核关于编辑关于创建常见问题意见反馈及投诉举报与质疑举报非法用户未通过申诉反馈侵权信息对外合作邮件合作任务领取官方微博微信公众号搜索词条编辑词条 收藏 查看我的收藏分享分享到QQ空间新浪微博投诉登录企业推广免责声明用户协议隐私政策编辑帮助意见反馈及投诉© SOGOU.COM 京ICP备11001839号-1 京公网安备110000020000taobao | 淘寶
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Takefusa Kubo Stats, Goals, Records, Assists, Cups and more | FBref.com
Takefusa Kubo Stats, Goals, Records, Assists, Cups and more | FBref.com
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You are here: FB Home Page > Players > Takefusa Kubo
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Takefusa Kubo
久保建英
Position: FW-MF (AM-WM) ▪ Footed: Left
170cm, 63kg (5-7, 139lb)
Born:
June 4, 2001
in Kawasaki-shi, Japan
jp
National Team: Japan jp
Club: Real Sociedad
Wages:
€ 48,077 Weekly
Expires June 2029. Via Capology.
Instagram: @takefusa.kubo
More Player Info
2023-2024
La Liga
Champions Lg
MP
21
8
Min
1683
559
Gls
7
0
Ast
3
1
xG
3.4
0.4
npxG
3.4
0.4
xAG
4.6
2.2
SCA
85
39
GCA
5
1
* see our coverage note
Takefusa Kubo Overview
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Real Sociedad
Real Sociedad(10-10-7, 7th place in La Liga)
Roster
Mohamed Ali Cho
Jon Aramburu
Gaizka Ayesa
Ander Barrenetxea
Sheraldo Becker
Alberto Dadie
Aritz Elustondo
Carlos Fernández
Bryan Fiabema
Aitor Fraga
Javi Galán
Urko González
Jon Karrikaburu
Takefusa Kubo
Robin Le Normand
Jon Magunacelaya
Pablo Marín
Unai Marrero
Jon Martin
Brais Méndez
Mikel Merino
Aihen Muñoz
Roberto Navarro
Álvaro Odriozola
Olasagasti
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Takefusa Kubo Scouting Report
Last 365 DaysView Complete Scouting Report
Takefusa Kubo Scouting Report
Last 365 DaysView Complete Scouting Report
Takefusa Kubo Scouting Report
Last 365 DaysView Complete Scouting Report
vs. Att Mid / Wingers
vs. Midfielders
vs. Forwards
Takefusa Kubo Scouting Report Table Statistic Per 90 Percentile Non-Penalty Goals0.3482 npxG: Non-Penalty xG0.1943 Shots Total2.4261 Assists0.1436 xAG: Exp. Assisted Goals0.2675 npxG + xAG0.4557 Shot-Creating Actions4.7982 Passes Attempted34.4836 Pass Completion %70.5%25 Progressive Passes3.3637 Progressive Carries5.5090 Successful Take-Ons2.5980 Touches (Att Pen)5.5076 Progressive Passes Rec9.6178 Tackles0.9930 Interceptions0.5166 Blocks1.1670 Clearances0.3433 Aerials Won0.3432
Player compared to positional peers in Men's Big 5 Leagues, UCL, UEL over the last 365 days. Based on 3192 minutes played.How scouting reports are calculatedPowered by Opta
Takefusa Kubo Scouting Report Table Statistic Per 90 Percentile Non-Penalty Goals0.3499 npxG: Non-Penalty xG0.1994 Shots Total2.4299 Assists0.1473 xAG: Exp. Assisted Goals0.2698 npxG + xAG0.4598 Shot-Creating Actions4.7998 Passes Attempted34.489 Pass Completion %70.5%4 Progressive Passes3.3613 Progressive Carries5.5099 Successful Take-Ons2.5999 Touches (Att Pen)5.5099 Progressive Passes Rec9.6199 Tackles0.992 Interceptions0.5110 Blocks1.1642 Clearances0.341 Aerials Won0.3410
Player compared to positional peers in Men's Big 5 Leagues, UCL, UEL over the last 365 days. Based on 3192 minutes played.How scouting reports are calculatedPowered by Opta
Takefusa Kubo Scouting Report Table Statistic Per 90 Percentile Non-Penalty Goals0.3442 npxG: Non-Penalty xG0.193 Shots Total2.4237 Assists0.1454 xAG: Exp. Assisted Goals0.2696 npxG + xAG0.4542 Shot-Creating Actions4.7999 Passes Attempted34.4894 Pass Completion %70.5%49 Progressive Passes3.3692 Progressive Carries5.5098 Successful Take-Ons2.5997 Touches (Att Pen)5.5074 Progressive Passes Rec9.6196 Tackles0.9983 Interceptions0.5193 Blocks1.1694 Clearances0.3418 Aerials Won0.345
Player compared to positional peers in Men's Big 5 Leagues, UCL, UEL over the last 365 days. Based on 3192 minutes played.How scouting reports are calculatedPowered by Opta
Similar Players to Takefusa Kubo
Last 365 Days
Similar Players to Takefusa Kubo
Last 365 Days
Similar Players to Takefusa Kubo
Last 365 Days
Att Mid / Wingers
Midfielders
Forwards
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Compare Takefusa Kubo to Top 5 Similar PlayersSimilar players are based on their statistical profiles.How similar players are calculated.
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Match Report
2024-02-23FriMatchweek 26HomeL 1–3Real SociedadVillarrealYRM9000003200720000.10.10.270426267.73491162Match Report
2024-02-18SunMatchweek 25AwayW 2–1Real SociedadMallorcaYRW9010002100590010.10.10.250344575.6839553Match Report
2024-02-10SatMatchweek 24HomeL 0–1Real SociedadOsasunaYRW9000006200580110.60.60.570364776.6739541Match Report
2024-01-02TueMatchweek 19HomeD 1–1Real SociedadAlavésYRW8900002000402110.10.10.370122352.2224354Match Report
2023-12-21ThuMatchweek 18AwayD 0–0Real SociedadCádizYRM9000000000422020.00.00.150202969.0128784Match Report
Next Match:
Saturday March 09, 2024 vs
Granada
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Standard Stats: Domestic Leagues
Goal Logs
Standard Stats: Domestic Leagues Table Playing Time Performance Expected Progression Per 90 Minutes Season Age Squad Country Comp LgRank MP Starts Min 90s Gls Ast G+A G-PK PK PKatt CrdY CrdR xG npxG xAG npxG+xAG PrgC PrgP PrgR Gls Ast G+A G-PK G+A-PK xG xAG xG+xAG npxG npxG+xAG Matches 201715FC Tokyojp JPN1. J1 League13th20350.4000000000.000.000.000.000.00Matches 201816Marinosjp JPN1. J1 League12th521611.8101100100.560.000.560.560.56Matches 201816FC Tokyojp JPN1. J1 League6th40620.7000000000.000.000.000.000.00Matches 201917FC Tokyojp JPN1. J1 League2nd13121,02111.3437400000.350.260.620.350.62Matches 2019-202018Mallorcaes ESP1. La Liga19th35232,31225.7448400403.03.02.75.7102941530.160.160.310.160.310.120.110.220.120.22Matches 2020-202119Villarreales ESP1. La Liga7th1322993.3000000211.51.51.12.51815310.000.000.000.000.000.450.320.760.450.76Matches 2020-202119Getafees ESP1. La Liga15th1888058.9112100200.70.71.21.92125570.110.110.220.110.220.080.130.210.080.21Matches 2021-202220Mallorcaes ESP1. La Liga16th28171,60517.8101100402.82.83.05.765681070.060.000.060.060.060.150.170.320.150.32Matches 2022-202321Real Sociedades ESP1. La Liga4th35292,43927.19413900305.95.96.011.9117812390.330.150.480.330.480.220.220.440.220.44Matches 2023-202422Real Sociedades ESP1. La Liga7th21191,68318.77310700103.43.44.68.0109651820.370.160.530.370.530.180.250.430.180.43Matches 7 Seasons6 Clubs2 Leagues17411210,422115.8271542270017117.217.218.535.74323487690.230.130.360.230.360.170.180.350.170.35 Country Comp LgRank MP Starts Min 90s Gls Ast G+A G-PK PK PKatt CrdY CrdR xG npxG xAG npxG+xAG PrgC PrgP PrgR Gls Ast G+A G-PK G+A-PK xG xAG xG+xAG npxG npxG+xAG Matches FC Tokyo (3 Seasons)1 League19121,11812.4437400000.320.240.560.320.56 Mallorca (2 Seasons)1 League63403,91743.5549500805.75.75.711.41671622600.110.090.210.110.210.130.130.260.130.26 Real Sociedad (2 Seasons)1 League56484,12245.8167231600409.39.310.619.92261464210.350.150.500.350.500.200.230.430.200.43 Getafe (1 Season)1 League1888058.9112100200.70.71.21.92125570.110.110.220.110.220.080.130.210.080.21 Villarreal (1 Season)1 League1322993.3000000211.51.51.12.51815310.000.000.000.000.000.450.320.760.450.76 Marinos (1 Season)1 League521611.8101100100.560.000.560.560.56 La Liga (5 Seasons)150989,143101.6221234220016117.217.218.535.74323487690.220.120.330.220.330.170.180.350.170.35 J1 League (3 Seasons)24141,27914.2538500100.350.210.560.350.56
Totals may not be complete for all senior-level play, see coverage note.Expected Goals (xG explained) and other Advanced Data provided by Opta, and is available for these competitions.
Shooting: Domestic Leagues
Goal Logs
Shooting: Domestic Leagues Table Standard Expected Season Age Squad Country Comp LgRank 90s Gls Sh SoT SoT% Sh/90 SoT/90 G/Sh G/SoT Dist FK PK PKatt xG npxG npxG/Sh G-xG np:G-xG Matches 201715FC Tokyojp JPN1. J1 League13th0.4022100.05.145.140.000.0000Matches 201816Marinosjp JPN1. J1 League12th1.813266.71.681.120.330.5000Matches 201816FC Tokyojp JPN1. J1 League6th0.702150.02.901.450.000.0000Matches 201917FC Tokyojp JPN1. J1 League2nd11.3423834.82.030.710.170.5000Matches 2019-202018Mallorcaes ESP1. La Liga19th25.74552545.52.140.970.070.1619.96003.03.00.05+1.0+1.0Matches 2020-202119Villarreales ESP1. La Liga7th3.308562.52.411.510.000.0013.50001.51.50.19-1.5-1.5Matches 2020-202119Getafees ESP1. La Liga15th8.9115746.71.680.780.070.1419.04000.70.70.05+0.3+0.3Matches 2021-202220Mallorcaes ESP1. La Liga16th17.8148816.72.690.450.020.1320.72002.82.80.06-1.8-1.8Matches 2022-202321Real Sociedades ESP1. La Liga4th27.19723041.72.661.110.130.3017.83005.95.90.08+3.1+3.1Matches 2023-202422Real Sociedades ESP1. La Liga7th18.77431841.92.300.960.160.3917.52003.43.40.08+3.6+3.6Matches 7 Seasons6 Clubs2 Leagues115.82727110639.12.340.920.100.2518.7170017.217.20.07+4.8+4.8 Country Comp LgRank 90s Gls Sh SoT SoT% Sh/90 SoT/90 G/Sh G/SoT Dist FK PK PKatt xG npxG npxG/Sh G-xG np:G-xG Matches FC Tokyo (3 Seasons)1 League12.44271140.72.170.890.150.3600 Mallorca (2 Seasons)1 League43.551033332.02.370.760.050.1520.38005.75.70.06-0.7-0.7 Real Sociedad (2 Seasons)1 League45.8161154841.72.511.050.140.3317.75009.39.30.08+6.7+6.7 Getafe (1 Season)1 League8.9115746.71.680.780.070.1419.04000.70.70.05+0.3+0.3 Villarreal (1 Season)1 League3.308562.52.411.510.000.0013.50001.51.50.19-1.5-1.5 Marinos (1 Season)1 League1.813266.71.681.120.330.5000 La Liga (5 Seasons)101.6222419338.62.370.920.090.2418.7170017.217.20.07+4.8+4.8 J1 League (3 Seasons)14.25301343.32.110.910.170.3800
Totals may not be complete for all senior-level play, see coverage note.Expected Goals (xG explained) and other Advanced Data provided by Opta, and is available for these competitions.
Passing: Domestic Leagues
Passing: Domestic Leagues Table Total Short Medium Long Expected Season Age Squad Country Comp LgRank 90s Cmp Att Cmp% TotDist PrgDist Cmp Att Cmp% Cmp Att Cmp% Cmp Att Cmp% Ast xAG xA A-xAG KP 1/3 PPA CrsPA PrgP Matches 201715FC Tokyojp JPN1. J1 League13th0.40Matches 201816Marinosjp JPN1. J1 League12th1.80Matches 201816FC Tokyojp JPN1. J1 League6th0.70Matches 201917FC Tokyojp JPN1. J1 League2nd11.33Matches 2019-202018Mallorcaes ESP1. La Liga19th25.752676668.76991207932940481.414620371.9155825.942.73.5+1.3343636694Matches 2020-202119Villarreales ESP1. La Liga7th3.39913672.81422404506280.6304075.091850.001.10.7-1.11087015Matches 2020-202119Getafees ESP1. La Liga15th8.914821568.819446999211083.6435874.151926.311.20.9-0.2986025Matches 2021-202220Mallorcaes ESP1. La Liga16th17.834950469.25067187619723882.810615269.7254951.003.02.8-3.0323323568Matches 2022-202321Real Sociedades ESP1. La Liga4th27.162187571.08389234038245484.117424969.9296544.646.05.4-2.0393334481Matches 2023-202422Real Sociedades ESP1. La Liga7th18.745564370.87159207825830086.013819471.1429146.234.65.1-1.6452526565Matches 7 Seasons6 Clubs2 Leagues115.82198313970.03097294761308156883.463789671.112530041.71518.518.4-3.516914313220348 Country Comp LgRank 90s Cmp Att Cmp% TotDist PrgDist Cmp Att Cmp% Cmp Att Cmp% Cmp Att Cmp% Ast xAG xA A-xAG KP 1/3 PPA CrsPA PrgP Matches FC Tokyo (3 Seasons)1 League12.43 Mallorca (2 Seasons)1 League43.5875127068.912058395552664281.925235571.04010737.445.76.4-1.766695911162 Real Sociedad (2 Seasons)1 League45.81076151870.915548441864075484.931244370.47115645.5710.610.5-3.68458609146 Getafe (1 Season)1 League8.914821568.819446999211083.6435874.151926.311.20.9-0.2986025 Villarreal (1 Season)1 League3.39913672.81422404506280.6304075.091850.001.10.7-1.11087015 Marinos (1 Season)1 League1.80 La Liga (5 Seasons)101.62198313970.03097294761308156883.463789671.112530041.71218.518.4-6.516914313220348 J1 League (3 Seasons)14.23
Totals may not be complete for all senior-level play, see coverage note.Expected Goals (xG explained) and other Advanced Data provided by Opta, and is available for these competitions.
Pass Types: Domestic Leagues
Pass Types: Domestic Leagues Table Pass Types Corner Kicks Outcomes Season Age Squad Country Comp LgRank 90s Att Live Dead FK TB Sw Crs TI CK In Out Str Cmp Off Blocks Matches 201715FC Tokyojp JPN1. J1 League13th0.41Matches 201816Marinosjp JPN1. J1 League12th1.84Matches 201816FC Tokyojp JPN1. J1 League6th0.71Matches 201917FC Tokyojp JPN1. J1 League2nd11.351Matches 2019-202018Mallorcaes ESP1. La Liga19th25.776672042821803251170526441Matches 2020-202119Villarreales ESP1. La Liga7th3.3136129730110043009904Matches 2020-202119Getafees ESP1. La Liga15th8.9215200145012818510148113Matches 2021-202220Mallorcaes ESP1. La Liga16th17.85044663486251617541349422Matches 2022-202321Real Sociedades ESP1. La Liga4th27.18758234253572529101216211035Matches 2023-202422Real Sociedades ESP1. La Liga7th18.76435687085211306133150455523Matches 7 Seasons6 Clubs2 Leagues115.8313929062093716124111514467392219824138 Country Comp LgRank 90s Att Live Dead FK TB Sw Crs TI CK In Out Str Cmp Off Blocks Matches FC Tokyo (3 Seasons)1 League12.453 Mallorca (2 Seasons)1 League43.51270118676168313194216111875863 Real Sociedad (2 Seasons)1 League45.81518139111213871855904327110761558 Getafe (1 Season)1 League8.9215200145012818510148113 Villarreal (1 Season)1 League3.3136129730110043009904 Marinos (1 Season)1 League1.84 La Liga (5 Seasons)101.6313929062093716123541514467392219824138 J1 League (3 Seasons)14.257
Totals may not be complete for all senior-level play, see coverage note.Expected Goals (xG explained) and other Advanced Data provided by Opta, and is available for these competitions.
Goal and Shot Creation: Domestic Leagues
Goal and Shot Creation: Domestic Leagues Table SCA SCA Types GCA GCA Types Season Age Squad Country Comp LgRank 90s SCA SCA90 PassLive PassDead TO Sh Fld Def GCA GCA90 PassLive PassDead TO Sh Fld Def Matches 201715FC Tokyojp JPN1. J1 League13th0.4Matches 201816Marinosjp JPN1. J1 League12th1.8Matches 201816FC Tokyojp JPN1. J1 League6th0.7Matches 201917FC Tokyojp JPN1. J1 League2nd11.3Matches 2019-202018Mallorcaes ESP1. La Liga19th25.7973.78653153101160.621102120Matches 2020-202119Villarreales ESP1. La Liga7th3.3133.91100210000.00000000Matches 2020-202119Getafees ESP1. La Liga15th8.9222.46133330030.34200100Matches 2021-202220Mallorcaes ESP1. La Liga16th17.8754.204768310140.22300010Matches 2022-202321Real Sociedades ESP1. La Liga4th27.1963.55631075101110.41602021Matches 2023-202422Real Sociedades ESP1. La Liga7th18.7854.554918945050.27311000Matches 7 Seasons6 Clubs2 Leagues115.83883.82247404419353390.382515251 Country Comp LgRank 90s SCA SCA90 PassLive PassDead TO Sh Fld Def GCA GCA90 PassLive PassDead TO Sh Fld Def Matches FC Tokyo (3 Seasons)1 League12.4 Mallorca (2 Seasons)1 League43.51723.951129236202200.461402130 Real Sociedad (2 Seasons)1 League45.81813.9611228169151160.35913021 Getafe (1 Season)1 League8.9222.46133330030.34200100 Villarreal (1 Season)1 League3.3133.91100210000.00000000 Marinos (1 Season)1 League1.8 La Liga (5 Seasons)101.63883.82247404419353390.382515251 J1 League (3 Seasons)14.2
Totals may not be complete for all senior-level play, see coverage note.Expected Goals (xG explained) and other Advanced Data provided by Opta, and is available for these competitions.
Defensive Actions: Domestic Leagues
Defensive Actions: Domestic Leagues Table Tackles Challenges Blocks Season Age Squad Country Comp LgRank 90s Tkl TklW Def 3rd Mid 3rd Att 3rd Tkl Att Tkl% Lost Blocks Sh Pass Int Tkl+Int Clr Err Matches 201715FC Tokyojp JPN1. J1 League13th0.410Matches 201816Marinosjp JPN1. J1 League12th1.832Matches 201816FC Tokyojp JPN1. J1 League6th0.700Matches 201917FC Tokyojp JPN1. J1 League2nd11.3146Matches 2019-202018Mallorcaes ESP1. La Liga19th25.7342216126154434.129191182357100Matches 2020-202119Villarreales ESP1. La Liga7th3.3110011520.042021220Matches 2020-202119Getafees ESP1. La Liga15th8.9742321147.11314014142140Matches 2021-202220Mallorcaes ESP1. La Liga16th17.8311912145102441.7142432183940Matches 2022-202321Real Sociedades ESP1. La Liga4th27.14426181610163842.1222912895340Matches 2023-202422Real Sociedades ESP1. La Liga7th18.71814105361637.5101921792761Matches 7 Seasons6 Clubs2 Leagues115.81351045850274914134.892107710072199301 Country Comp LgRank 90s Tkl TklW Def 3rd Mid 3rd Att 3rd Tkl Att Tkl% Lost Blocks Sh Pass Int Tkl+Int Clr Err Matches FC Tokyo (3 Seasons)1 League12.41560 Mallorca (2 Seasons)1 League43.56541282611256836.843434393196140 Real Sociedad (2 Seasons)1 League45.86240282113225440.732483451880101 Getafe (1 Season)1 League8.9742321147.11314014142140 Villarreal (1 Season)1 League3.3110011520.042021220 Marinos (1 Season)1 League1.8320 La Liga (5 Seasons)101.6135865850274914134.892107710064199301 J1 League (3 Seasons)14.21880
Totals may not be complete for all senior-level play, see coverage note.Expected Goals (xG explained) and other Advanced Data provided by Opta, and is available for these competitions.
Possession: Domestic Leagues
Possession: Domestic Leagues Table Touches Take-Ons Carries Receiving Season Age Squad Country Comp LgRank 90s Touches Def Pen Def 3rd Mid 3rd Att 3rd Att Pen Live Att Succ Succ% Tkld Tkld% Carries TotDist PrgDist PrgC 1/3 CPA Mis Dis Rec PrgR Matches 201715FC Tokyojp JPN1. J1 League13th0.4Matches 201816Marinosjp JPN1. J1 League12th1.8Matches 201816FC Tokyojp JPN1. J1 League6th0.7Matches 201917FC Tokyojp JPN1. J1 League2nd11.3Matches 2019-202018Mallorcaes ESP1. La Liga19th25.71117151433946099411171256451.26148.88365949323510277467745804153Matches 2020-202119Villarreales ESP1. La Liga7th3.31863226810417186161275.0425.013410525501812614614031Matches 2020-202119Getafees ESP1. La Liga15th8.93366329621326336341544.11955.92091267637211411332022457Matches 2021-202220Mallorcaes ESP1. La Liga16th17.8758811129836463758644062.52437.5486330117356531255930513107Matches 2022-202321Real Sociedades ESP1. La Liga4th27.1124069443173614112401174941.95042.78415895328111760669042929239Matches 2023-202422Real Sociedades ESP1. La Liga7th18.78801176291527106880894247.23236.05815084272610947525022627182Matches 7 Seasons6 Clubs2 Leagues115.845174947815782553447451744522249.919042.7308722548121644322412063231653237769 Country Comp LgRank 90s Touches Def Pen Def 3rd Mid 3rd Att 3rd Att Pen Live Att Succ Succ% Tkld Tkld% Carries TotDist PrgDist PrgC 1/3 CPA Mis Dis Rec PrgR Matches FC Tokyo (3 Seasons)1 League12.4 Mallorca (2 Seasons)1 League43.5187523254692973157187518910455.08545.013229250497016710871136751317260 Real Sociedad (2 Seasons)1 League45.8212017170722126324721202069144.28239.81422109796007226107118140641556421 Getafe (1 Season)1 League8.93366329621326336341544.11955.92091267637211411332022457 Villarreal (1 Season)1 League3.31863226810417186161275.0425.013410525501812614614031 Marinos (1 Season)1 League1.8 La Liga (5 Seasons)101.645174947815782553447451744522249.919042.7308722548121644322412063231653237769 J1 League (3 Seasons)14.2
Totals may not be complete for all senior-level play, see coverage note.Expected Goals (xG explained) and other Advanced Data provided by Opta, and is available for these competitions.
Playing Time: Domestic Leagues
Playing Time: Domestic Leagues Table Playing Time Starts Subs Team Success Team Success (xG) Season Age Squad Country Comp LgRank MP Min Mn/MP Min% 90s Starts Mn/Start Compl Subs Mn/Sub unSub PPM onG onGA +/- +/-90 On-Off onxG onxGA xG+/- xG+/-90 On-Off Matches 201715FC Tokyojp JPN1. J1 League13th235181.10.40021700.500000.00+0.15Matches 201816Marinosjp JPN1. J1 League12th5161325.31.8261031361.203300.000.00Matches 201816FC Tokyojp JPN1. J1 League6th462162.00.70041570.2501-1-1.45-1.63Matches 201917FC Tokyojp JPN1. J1 League2nd131,0217933.411.31283612802.31207+13+1.15+0.97Matches 2019-202018Mallorcaes ESP1. La Liga19th352,3126667.625.7238414123110.832849-21-0.82-0.4926.647.0-20.4-0.79-0.63Matches 2020-202119Villarreales ESP1. La Liga7th13299238.73.32590111631.6921+1+0.30-0.134.92.5+2.4+0.73+0.39Matches 2020-202119Getafees ESP1. La Liga15th188054523.58.98732102240.89912-3-0.34+0.0810.38.5+1.8+0.20+0.47Matches 2021-202220Mallorcaes ESP1. La Liga16th281,6055746.917.817783112611.042033-13-0.73-0.0319.922.8-2.9-0.16+0.21Matches 2022-202321Real Sociedades ESP1. La Liga4th352,4397071.327.12977763421.913821+17+0.63+0.7237.420.6+16.9+0.62+0.35Matches 2023-202422Real Sociedades ESP1. La Liga7th211,6838069.318.719851123821.523019+11+0.59+0.9524.419.7+4.8+0.26+0.29Matches 7 Seasons6 Clubs2 Leagues17410,4226032.8115.811280436224261.34150146+4+0.03+0.09123.6121.0+2.6+0.03+0.05 Country Comp LgRank MP Min Mn/MP Min% 90s Starts Mn/Start Compl Subs Mn/Sub unSub PPM onG onGA +/- +/-90 On-Off onxG onxGA xG+/- xG+/-90 On-Off Matches FC Tokyo (3 Seasons)1 League191,1185912.212.41283671771.69208+12+0.97+0.91 Mallorca (2 Seasons)1 League633,9176257.343.5408217232920.924882-34-0.78-0.2346.569.8-23.3-0.53-0.24 Real Sociedad (2 Seasons)1 League564,1227470.545.848801883541.766840+28+0.61+0.8261.940.2+21.6+0.47+0.33 Getafe (1 Season)1 League188054523.58.98732102240.89912-3-0.34+0.0810.38.5+1.8+0.20+0.47 Villarreal (1 Season)1 League13299238.73.32590111631.6921+1+0.30-0.134.92.5+2.4+0.73+0.39 Marinos (1 Season)1 League5161325.31.8261031361.203300.000.00 La Liga (5 Seasons)1509,1436146.8101.69880375226131.30127135-8-0.08+0.09123.6121.0+2.6+0.03+0.05 J1 League (3 Seasons)241,2795310.414.2148061016131.582311+12+0.84+0.80
Totals may not be complete for all senior-level play, see coverage note.Expected Goals (xG explained) and other Advanced Data provided by Opta, and is available for these competitions.
Miscellaneous Stats: Domestic Leagues
Miscellaneous Stats: Domestic Leagues Table Performance Aerial Duels Season Age Squad Country Comp LgRank 90s CrdY CrdR 2CrdY Fls Fld Off Crs Int TklW PKwon PKcon OG Recov Won Lost Won% Matches 201715FC Tokyojp JPN1. J1 League13th0.4000000101000Matches 201816Marinosjp JPN1. J1 League12th1.8100620423000Matches 201816FC Tokyojp JPN1. J1 League6th0.7000010100000Matches 201917FC Tokyojp JPN1. J1 League2nd11.300017292516140Matches 2019-202018Mallorcaes ESP1. La Liga19th25.740035644802322200114112629.7Matches 2020-202119Villarreales ESP1. La Liga7th3.32113110101100019030.0Matches 2020-202119Getafees ESP1. La Liga15th8.920018224281440003451722.7Matches 2021-202220Mallorcaes ESP1. La Liga16th17.84001747551819000101111444.0Matches 2022-202321Real Sociedades ESP1. La Liga4th27.130035482172926200107162539.0Matches 2023-202422Real Sociedades ESP1. La Liga7th18.7100154281139140007671335.0Matches 7 Seasons6 Clubs2 Leagues115.817111462664441172104400451509833.8 Country Comp LgRank 90s CrdY CrdR 2CrdY Fls Fld Off Crs Int TklW PKwon PKcon OG Recov Won Lost Won% Matches FC Tokyo (3 Seasons)1 League12.40001730253615000 Mallorca (2 Seasons)1 League43.58005211191313141200215224035.5 Real Sociedad (2 Seasons)1 League45.84005090291851840200183233837.7 Getafe (1 Season)1 League8.920018224281440003451722.7 Villarreal (1 Season)1 League3.32113110101100019030.0 Marinos (1 Season)1 League1.8100620423000 La Liga (5 Seasons)101.61611123234423546486400451509833.8 J1 League (3 Seasons)14.21002332257818000
Totals may not be complete for all senior-level play, see coverage note.Expected Goals (xG explained) and other Advanced Data provided by Opta, and is available for these competitions.
Player Club Summary
Leaderboard Appearances, Awards, and Honors
Expected Goals (xG explained) and other Advanced Data provided by Opta, and is available for these competitions.
Wages
Data via Capology.
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FBref.com launched (June 13, 2018) with domestic league coverage for England, France, Germany, Italy, Spain, and United States. Since then we have been steadily expanding our coverage to include domestic leagues from over 40 countries as well as domestic cup, super cup and youth leagues from top European countries. We have also added coverage for major international cups such as the UEFA Champions League and Copa Libertadores.
FBref is the most complete sources for women's football data on the internet. This includes the entire history of the FIFA Women's World Cup as well as recent domestic league seasons from nine countries, including advanced stats like xG for most of those nine.
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KUBO编程第四届全国青少年人工智能创新大赛完美收官_中华教育网
KUBO编程第四届全国青少年人工智能创新大赛完美收官_中华教育网
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KUBO编程第四届全国青少年人工智能创新大赛完美收官
中华教育网
2021-07-23 18:12:33
2021年7月18日,为期4天的中国·上海第四届青少年人工智能创新大赛暨全国邀请赛完美收官。本次大赛是2021年全国青少年人工智能创新大赛的重点赛事之一,…
2021年7月18日,为期4天的中国·上海第四届青少年人工智能创新大赛暨全国邀请赛完美收官。本次大赛是2021年全国青少年人工智能创新大赛的重点赛事之一,也是2021WAIC(世界人工智能大会)的重要组成部分。本次大赛得到了上海市委、上海市教育局、上海市经济和信息化委员会、上海市科委的支持。KUBO无屏编程受邀参加,并拥有独家TagTile®赛道,堪称今年比赛的一大亮点。
本次AI大赛的主题是通过无屏编程语言和编程技巧,将编程机器人装扮成小游客,在指定的时间内设计一天的上海城市之旅:拜访中国共产党的诞生地;在陈毅广场饱览浦江两岸;探索自然博物馆的秘密。在中国共产党砥砺前行的一百年中,上海,作为中国共产党的诞生地,红色文化是上海的城市底色,也是鲜明的城市标识。
作为改革开放的排头兵,上海主动服务“一带一路”建设、长江经济带发展等战略,成为创新之城、人文之城、生态之城,并且成为了卓越的全球城市和社会主义现代化国际大都市。
KUBO编程希望学生们通过此次比赛,利用所学无屏编程知识+主题综合探究的活动方式,去寻访、探索上海的过去、现在和未来,用特别的方式深入了解并学习城市的发展和变迁。
此次AI少儿无屏编程参赛选手为 4-10 岁学生,分为学前组(幼儿园)和低段学龄组(小学2年级及以上)。比赛要求参赛学生组队在现场编写、调试程序,并控制机器人完成比赛任务。参赛机器人必须由程序控制自主运行,且比赛任务通过现场出题的方式公布给所有参赛选手, 其目的是检验学生对编程思维和算法设计的应用水平,锻炼编程和计算思维能力。比赛得分由编程任务完成度、编程技巧分、主题表达、机器人装饰四部分组成。
在本次大赛中,参加KUBO无屏编程AI动手大赛共有175支队伍,每个团队由2-4名学生组成,学生总数为424名, 另外共有168名教师/辅导员加入“2021人工智能实操教师培训”微信群, 并有84名教师获得了KUBO教师培训师证书。
在AI少儿无屏编程赛场上还上演了一场小机器人“皮肤秀”,每个小机器人都有小朋友们自己设计的专属造型,“雏鹰展翅一队”设计的造型是战“疫”英雄——白衣天使。此外,还有中国智造的“北斗卫星”、“神舟”宇航员、建党百年主题等各具特色的造型。
KUBO无屏编程将充分利用自身优势,不断创新产品,帮助提高学生们的编程技巧,为培养人才提供智力支持。KUBO无屏编程教学活动不仅锻炼和培养孩子们的动手实践能力,还能在实践中提高与伙伴和老师的沟通能力及体验团队合作精神。此次活动旨在推动新一代信息技术与各学科的广泛应用和深度融合,实现产、学、研的相互转化。更多内容详见公众号KUBO编程。
免责声明:市场有风险,选择需谨慎!此文转自网络内容仅供参考,不作买卖依据。
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GitHub - ipfs/kubo: An IPFS implementation in Go
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An IPFS implementation in Go
docs.ipfs.tech/how-to/command-line-quick-start/
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masterBranchesTagsGo to fileCodeFolders and filesNameNameLast commit messageLast commit dateLatest commit History15,036 Commits.github.github assetsassets binbin blocks/blockstoreutilblocks/blockstoreutil client/rpcclient/rpc cmdcmd commandscommands configconfig corecore coveragecoverage docsdocs fusefuse gcgc miscmisc mkmk p2pp2p pluginplugin profileprofile reporepo routingrouting testtest thirdpartythirdparty tracingtracing .codeclimate.yml.codeclimate.yml .dockerignore.dockerignore .gitattributes.gitattributes .gitignore.gitignore .golangci.yml.golangci.yml .mailmap.mailmap CHANGELOG.mdCHANGELOG.md CONTRIBUTING.mdCONTRIBUTING.md DockerfileDockerfile GNUmakefileGNUmakefile LICENSELICENSE LICENSE-APACHELICENSE-APACHE LICENSE-MITLICENSE-MIT MakefileMakefile README.mdREADME.md Rules.mkRules.mk SECURITY.mdSECURITY.md appveyor.ymlappveyor.yml codecov.ymlcodecov.yml doc.godoc.go docker-compose.yamldocker-compose.yaml go.modgo.mod go.sumgo.sum version.goversion.go View all filesRepository files navigationREADMELicenseLicenseMIT licenseSecurity
Kubo: IPFS Implementation in GO
The first implementation of IPFS.
What is Kubo?
Kubo was the first IPFS implementation and is the most widely used one today. Implementing the Interplanetary Filesystem - the Web3 standard for content-addressing, interoperable with HTTP. Thus powered by IPLD's data models and the libp2p for network communication. Kubo is written in Go.
Featureset
Runs an IPFS-Node as a network service that is part of LAN and WAN DHT
HTTP Gateway (/ipfs and /ipns) functionality for trusted and trustless content retrieval
HTTP Routing V1 (/routing/v1) client and server implementation for delegated routing lookups
HTTP Kubo RPC API (/api/v0) to access and control the daemon
Command Line Interface based on (/api/v0) RPC API
WebUI to manage the Kubo node
Content blocking support for operators of public nodes
Other implementations
See List
What is IPFS?
IPFS is a global, versioned, peer-to-peer filesystem. It combines good ideas from previous systems such as Git, BitTorrent, Kademlia, SFS, and the Web. It is like a single BitTorrent swarm, exchanging git objects. IPFS provides an interface as simple as the HTTP web, but with permanence built-in. You can also mount the world at /ipfs.
For more info see: https://docs.ipfs.tech/concepts/what-is-ipfs/
Before opening an issue, consider using one of the following locations to ensure you are opening your thread in the right place:
kubo (previously named go-ipfs) implementation bugs in this repo.
Documentation issues in ipfs/docs issues.
IPFS design in ipfs/specs issues.
Exploration of new ideas in ipfs/notes issues.
Ask questions and meet the rest of the community at the IPFS Forum.
Or chat with us.
Next milestones
Milestones on GitHub
Table of Contents
What is Kubo?
What is IPFS?
Next milestones
Table of Contents
Security Issues
Minimal System Requirements
Install
Docker
Official prebuilt binaries
Updating
Using ipfs-update
Downloading builds using IPFS
Unofficial Linux packages
ArchLinux
Nix
Solus
openSUSE
Guix
Snap
Unofficial Windows packages
Chocolatey
Scoop
Unofficial MacOS packages
MacPorts
Nix
Homebrew
Build from Source
Install Go
Download and Compile IPFS
Cross Compiling
Troubleshooting
Getting Started
Usage
Some things to try
Troubleshooting
Packages
Development
Map of Implemented Subsystems
CLI, HTTP-API, Architecture Diagram
Testing
Development Dependencies
Developer Notes
Maintainer Info
Contributing
License
Security Issues
Please follow SECURITY.md.
Minimal System Requirements
IPFS can run on most Linux, macOS, and Windows systems. We recommend running it on a machine with at least 4 GB of RAM and 2 CPU cores (kubo is highly parallel). On systems with less memory, it may not be completely stable, and you run on your own risk.
Install
The canonical download instructions for IPFS are over at: https://docs.ipfs.tech/install/. It is highly recommended you follow those instructions if you are not interested in working on IPFS development.
Docker
Official images are published at https://hub.docker.com/r/ipfs/kubo/:
More info on how to run Kubo (go-ipfs) inside Docker can be found here.
Official prebuilt binaries
The official binaries are published at https://dist.ipfs.tech#kubo:
From there:
Click the blue "Download Kubo" on the right side of the page.
Open/extract the archive.
Move kubo (ipfs) to your path (install.sh can do it for you).
If you are unable to access dist.ipfs.tech, you can also download kubo (go-ipfs) from:
this project's GitHub releases page
/ipns/dist.ipfs.tech at dweb.link gateway
Updating
Using ipfs-update
IPFS has an updating tool that can be accessed through ipfs update. The tool is
not installed alongside IPFS in order to keep that logic independent of the main
codebase. To install ipfs-update tool, download it here.
Downloading builds using IPFS
List the available versions of Kubo (go-ipfs) implementation:
$ ipfs cat /ipns/dist.ipfs.tech/kubo/versions
Then, to view available builds for a version from the previous command ($VERSION):
$ ipfs ls /ipns/dist.ipfs.tech/kubo/$VERSION
To download a given build of a version:
$ ipfs get /ipns/dist.ipfs.tech/kubo/$VERSION/kubo_$VERSION_darwin-386.tar.gz # darwin 32-bit build
$ ipfs get /ipns/dist.ipfs.tech/kubo/$VERSION/kubo_$VERSION_darwin-amd64.tar.gz # darwin 64-bit build
$ ipfs get /ipns/dist.ipfs.tech/kubo/$VERSION/kubo_$VERSION_freebsd-amd64.tar.gz # freebsd 64-bit build
$ ipfs get /ipns/dist.ipfs.tech/kubo/$VERSION/kubo_$VERSION_linux-386.tar.gz # linux 32-bit build
$ ipfs get /ipns/dist.ipfs.tech/kubo/$VERSION/kubo_$VERSION_linux-amd64.tar.gz # linux 64-bit build
$ ipfs get /ipns/dist.ipfs.tech/kubo/$VERSION/kubo_$VERSION_linux-arm.tar.gz # linux arm build
$ ipfs get /ipns/dist.ipfs.tech/kubo/$VERSION/kubo_$VERSION_windows-amd64.zip # windows 64-bit build
Unofficial Linux packages
ArchLinux
Nix
Solus
openSUSE
Guix
Snap
Arch Linux
# pacman -S kubo
Nix
With the purely functional package manager Nix you can install kubo (go-ipfs) like this:
$ nix-env -i kubo
You can also install the Package by using its attribute name, which is also kubo.
Solus
Package for Solus
$ sudo eopkg install kubo
You can also install it through the Solus software center.
openSUSE
Community Package for go-ipfs
Guix
Community Package for go-ipfs is no out-of-date.
Snap
No longer supported, see rationale in kubo#8688.
Unofficial Windows packages
Chocolatey
Scoop
Chocolatey
No longer supported, see rationale in kubo#9341.
Scoop
Scoop provides kubo as kubo in its 'extras' bucket.
PS> scoop bucket add extras
PS> scoop install kubo
Unofficial macOS packages
MacPorts
Nix
Homebrew
MacPorts
The package ipfs currently points to kubo (go-ipfs) and is being maintained.
$ sudo port install ipfs
Nix
In macOS you can use the purely functional package manager Nix:
$ nix-env -i kubo
You can also install the Package by using its attribute name, which is also kubo.
Homebrew
A Homebrew formula ipfs is maintained too.
$ brew install --formula ipfs
Build from Source
kubo's build system requires Go and some standard POSIX build tools:
GNU make
Git
GCC (or some other go compatible C Compiler) (optional)
To build without GCC, build with CGO_ENABLED=0 (e.g., make build CGO_ENABLED=0).
Install Go
If you need to update: Download latest version of Go.
You'll need to add Go's bin directories to your $PATH environment variable e.g., by adding these lines to your /etc/profile (for a system-wide installation) or $HOME/.profile:
export PATH=$PATH:/usr/local/go/bin
export PATH=$PATH:$GOPATH/bin
(If you run into trouble, see the Go install instructions).
Download and Compile IPFS
$ git clone https://github.com/ipfs/kubo.git
$ cd kubo
$ make install
Alternatively, you can run make build to build the go-ipfs binary (storing it in cmd/ipfs/ipfs) without installing it.
NOTE: If you get an error along the lines of "fatal error: stdlib.h: No such file or directory", you're missing a C compiler. Either re-run make with CGO_ENABLED=0 or install GCC.
Cross Compiling
Compiling for a different platform is as simple as running:
make build GOOS=myTargetOS GOARCH=myTargetArchitecture
Troubleshooting
Separate instructions are available for building on Windows.
git is required in order for go get to fetch all dependencies.
Package managers often contain out-of-date golang packages.
Ensure that go version reports at least 1.10. See above for how to install go.
If you are interested in development, please install the development
dependencies as well.
Shell command completions can be generated with one of the ipfs commands completion subcommands. Read docs/command-completion.md to learn more.
See the misc folder for how to connect IPFS to systemd or whatever init system your distro uses.
Getting Started
Usage
To start using IPFS, you must first initialize IPFS's config files on your
system, this is done with ipfs init. See ipfs init --help for information on
the optional arguments it takes. After initialization is complete, you can use
ipfs mount, ipfs add and any of the other commands to explore!
Some things to try
Basic proof of 'ipfs working' locally:
echo "hello world" > hello
ipfs add hello
# This should output a hash string that looks something like:
# QmT78zSuBmuS4z925WZfrqQ1qHaJ56DQaTfyMUF7F8ff5o
ipfs cat
HTTP/RPC clients
For programmatic interaction with Kubo, see our list of HTTP/RPC clients.
Troubleshooting
If you have previously installed IPFS before and you are running into problems getting a newer version to work, try deleting (or backing up somewhere else) your IPFS config directory (~/.ipfs by default) and rerunning ipfs init. This will reinitialize the config file to its defaults and clear out the local datastore of any bad entries.
Please direct general questions and help requests to our forums.
If you believe you've found a bug, check the issues list and, if you don't see your problem there, either come talk to us on Matrix chat, or file an issue of your own!
Packages
See IPFS in GO documentation.
Development
Some places to get you started on the codebase:
Main file: ./cmd/ipfs/main.go
CLI Commands: ./core/commands/
Bitswap (the data trading engine): go-bitswap
libp2p
libp2p: https://github.com/libp2p/go-libp2p
DHT: https://github.com/libp2p/go-libp2p-kad-dht
IPFS : The Add command demystified
Map of Implemented Subsystems
WIP: This is a high-level architecture diagram of the various sub-systems of this specific implementation. To be updated with how they interact. Anyone who has suggestions is welcome to comment here on how we can improve this!
CLI, HTTP-API, Architecture Diagram
Origin
Description: Dotted means "likely going away". The "Legacy" parts are thin wrappers around some commands to translate between the new system and the old system. The grayed-out parts on the "daemon" diagram are there to show that the code is all the same, it's just that we turn some pieces on and some pieces off depending on whether we're running on the client or the server.
Testing
make test
Development Dependencies
If you make changes to the protocol buffers, you will need to install the protoc compiler.
Developer Notes
Find more documentation for developers on docs
Maintainer Info
Project Board for active and upcoming work
Release Process
Additional PL EngRes Kubo maintainer info
Contributing
We ❤️ all our contributors; this project wouldn’t be what it is without you! If you want to help out, please see CONTRIBUTING.md.
This repository falls under the IPFS Code of Conduct.
Please reach out to us in one chat rooms.
License
This project is dual-licensed under Apache 2.0 and MIT terms:
Apache License, Version 2.0, (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
MIT license (LICENSE-MIT or http://opensource.org/licenses/MIT)
About
An IPFS implementation in Go
docs.ipfs.tech/how-to/command-line-quick-start/
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