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铜仁市2020年初中毕业生学业（升学）统一考试英语试题卷Ⅰ听力测试Ⅰ. 听五个句子，选择与所听句子内容相符的图画，并在答题卡的相应位置将其字母序号涂黑。
每个句子读两遍。
【此处可播放相关音频，请去附件查看】A. B. C. D. E.1. ______________2. ______________3. ______________4. ______________5. ______________Ⅱ. 听五个句子，分别选择其相应的应答语，并在答题卡的相应位置将其字母序号涂黑。
每个句子读两遍。
6.【此处可播放相关音频，请去附件查看】A. My pleasure.B. Never mind.C. Thank you all the same.7.【此处可播放相关音频，请去附件查看】A. Take care!B. Good idea!C. Thank you!8.【此处可播放相关音频，请去附件查看】A. I went to the Great Wall.B. I’m playing games.C. I want to visit Mount Fanjing.9.【此处可播放相关音频，请去附件查看】A. It’s Monday.B. It’s cloudy.C. It’s June 22nd.10.【此处可播放相关音频，请去附件查看】A. He is very kind.B. He likes reading.C. He is a cook.Ⅲ. 听五段对话，根据其内容及各小题的问题选择正确选项。
每段对话读两遍。
11.【此处可播放相关音频，请去附件查看】A. At 8:30.B. At 8:50.C. At 9:00.12.【此处可播放相关音频，请去附件查看】.A. Maria @126. com.B. Maria @163. com.C. Maria @qq. com.13.【此处可播放相关音频，请去附件查看】A. 3.B. 4.C. 5.14.【此处可播放相关音频，请去附件查看】A. A teacher.B. A doctorC. A nurse.15.【此处可播放相关音频，请去附件查看】A Interesting. B. Exciting C. Boring.听一篇短文，根据短文内容和所提问题选择正确答案。
许国璋英语第二册《第九课》（一）课文：1)课文原文：THE DEVOTED FRIENDOscar wild(adapted)Once upon a time there was an honest little fellow named Hans. He lived in a cottage all alone, and every day he worked in his garden. In all the village there wasno garden so lovely as his.Little Hans had many friends, but the most devoted friend was big Hugh the Miller. Indeed, the rich Miller was so devoted to little Hans that when he passed hisgarden he always picked a large bouquet of flowers, or if it was the fruit season, hewould fill his pockets with plums and cherries.“Real friends must share everything,” the Miller used to say, and little Hans nodded and smiled and was very proud that he had a friend with such noble ideas.Sometimes, indeed, the neighbors thought it was strange that the rich Miller never gave little Hans anything in return, but Hans never troubled his head aboutthese things.So little Hans worked and worked in his garden. During spring and summer and autumn he was very happy, but when winter came, he suffered from cold andhunger, and often went to bed without supper. Besides, in winter he was very lonely,as the Miller never came to see him.“It’s no use going to see little Hans in winter,” the Miller used to say to his wife, “ When people are in trouble we must leave them alone and not bother them. Thatis my idea of friendship, and I am sure I am right. So I shall wait till spring comes, andthen I shall visit him and he will give me a large bouquet of primroses, and that willmake him very happy.”“ You think so much about others,” said his wife, “ It is a pleasure to hear what you say about friendship. I am sure the priest himself cannot say such beautifulthings as you do, though he lives in a three-storeyed house, and wears a gold ring on his little finger.”“ But why don’t we ask little Hans to come here?” said the Miller’s youngest son. “ If poor Hans in trouble I shall give him half my porridge, and show him mywhite rabbits.”“ What a silly boy you are !” cried the Miller. “ I really don’t know what is the use of sending you to school. You do not learn anything. Why , if little Hans comes here, and sees our warm fire, and our good supper, and our red wine, he will envy us, and envy is a terrible thing. Besides, if Hans comes here, he will ask me to give him some flour on credit, and I cannot do that. Flour is one thing ,and friendship isanother. The words are spelt differently and they mean quite different things.”“How right you are!” said the Miller’s wife, “ Really, I feel quite sleepy. This is just like sitting in church.”(to be continued )2)译文：忠实的朋友奥斯卡·怀尔德(改编)从前有一个诚实的小家伙叫汉斯。
人教版七年级下册英语英语七年级下册期末考试试卷一、单选题1．—I’ve just received a Wechat message—“ttyl”. Do you know ________?—It stands for “talk to you later”.A．how does it mean B．how it meansC．what does it mean D．what it means2．Lisa has been in China for only a few days. She can’t read ________ write in Chinese now. A．and B．so C．or D．but3．Mr. Smith_________to be one of the best teachers in our school.A．considers B．considering C．is considered D．considered4．They didn't go to bed_____ the work was finished.A．when B．while C．until D．after5．Mike likes playing ____ golf while I like playing _____ piano .A．the, the B．a , a C．/ , the D．the , /6．（2017年黑龙江哈尔滨）﹣______is it from your house to the bookstore？﹣It's about fifteen minutes' walk．A．How long B．How far C．How often7．—When shall we go on a picnic, Saturday or Sunday?—_________ is OK. I'm free the whole weekend.A．Neither B．All C．Either D．Both8．—What do you ______________ watch tonight?—I plan to watch I am a singer.A．plan B．to plan C．plan to9．There _______a big tree and some birds in the garden.A．is B．are C．have D．has10．Cindy eats __________, so she’s very healthy.A．good B．fine C．well D．great【详解】1．D【详解】句意：——我刚才收到一条微信“ttyl”，你知道它什么意思吗？——它代表“以后再谈”。
〖期末复习〗专项提升---动词填空1.Lucy, (not be )late for school again.2.(listen)to the music,and tell me the name of the music.3.(listen) to music brings him a lot of fun.4.Boys and girls ,now (read)the passage.5.I’m very happ y (see)you here6.It’s a sunny day tomorrow.What about (run)around the lake in the morning?7.Let me (buy)some food for you.8.Simon says he does well in (draw).9.Would you like (learn)to swim after school?10.The man has a big garden ,but he doesn’t know how (look)after the flowers there.11.. Do you really enjoy __________ (sit) here without doing anything?12. We __________ (not be) late for the meeting now, but we only have ten minutes left.13. One of our teachers __________ (be) from South America.14. It’s late at night. Don’t make your son __________ (do) the reading. It’s time to go to bed.15. Look! Almost every student in our class__________ (have) a mobile phone now.16. Maybe they want her __________ (give) a talk about how to take care of goldfish.17. Jenny doesn’t know how __________ (make) friends with his classmate.18. __________ the young man usually __________ (take) his dog for a walk in the evening?19.Are you hungry? What about______________(eat) something?20. Kitty doesn’t have much time____________(talk)with her friends.21. He_______ (not do) his homework sometimes.22. The poor students want_______ (go) to school like others.23. I'd like_______ (shop) with my friends this evening.24. We have great fun_______ (watch) the 3D film Titanic.25. Let us_______ (tell) her the good news, all right?26. Look, every one of them_______ (have)a new computer.27._______ the new teachers_______ (know)a lot about our school?28. One of you_______ (be) in the Football Club.29.--Where _______ the Green family_______ (live)? --They live in Beijing.30. My cousin enjoys_______ (run) with his father every morning.31.One of us _________( be not )in the Football Club.32.Simon _________(not fly)kites on Sunday sometimes.33.Where _______the Smiths ________(live)now?34.Kitty,________(not look)out of the window in class please.35.My friend Jack,together with some boys usually _______(carry)water in his class.36.Mr.Wu hopes his students ________(get)good results in the exam next week.37.Jim always lets me _______(make)model planes for him.38.He doesn’t enjoy_________(get)up early on Saturdays.39.I’d like ________(shop)with my friends this evening.40.The poor student wants ________(go)to school like others41. I enjoy ______________(listen) to light music after supper.42. She spends much time _______________(read) English every day.43. The little boy ______________(not eat) bananas, but I do.44. This pair of trousers ________________(look) very nice.45. My cousin with his parents ________________(begin) to eat lunch at 11:30 a.m..46. He has no time ______________(talk) to his sister.47. He goes to the shop _____________(buy) some food.48. It is so hot today. Why not ___________(swim) in the lake.49. Let the lovely girl ______________(go) home now.50. Lily _____________(not be) happy today because she is ill.51. -May I________(use) the mobike here?-Of course, it’s easy and cheap.52. It’s very interesting for me________(play) cards with you.53. Adam comes to China with his parents. He wants to know how________(have) fun here.54. Mrs Black doesn’t let little Jack________(ride) his bike in the street. He’s too young.55. It often________(rain) cats and dogs in summer here.56. ________(make) chocolate by yourself is great fun.57. His mother goes to the nearest Family Mart________(buy) something to eat twice a week.58. Zoe’s father________(not do) the housework at home. Her mother does.59. Jimes,________(do) some morning exercises every week.It keeps you strong.60. Don't let me________(stay) at home alone.61. Thank you for (bring) us new clothes.62. It’s interesting (be) a doctor for animals.63. Who (get) up earlier every day, you or your sister?64. Are the children good at (speak) English?65. My brother can (play) basketball very well.66. Would Jason and his parents like (go) fishing tomorrow?67. Let the little boy (sing) a song for me.68. How long does it take the parents (watch) the lessons?69. (not take) the books away. I’m reading them.70. The bookshops (not be) open on Sunday mornings.71. Jimes,________(do) some morning exercises every week.It keeps you strong.72. Don't let me________(stay) at home alone.73. Who often________(help) you with your English?74. The teacher makes them_______________(not talk)when she's talking.75. How long does it take Lucy's father ________(drive) to work?76. __________(eat) healthy food everyday helps us keep healthy.77. Are the children talking about ___________ (have) a picnic at the weekend?78. Would you please______(take) me to Hang Lung Plaza this weekend?79. Who's ready ____________(show) his drawing first?80. Mum tells Jim ____________(not play) computer games on weekdays.81. I spend an hour ____________ (do) my homework in the evening.82. We need a lot of energy (play) games.83. Would you like (have) supper with us?84. Jim is good at (cook). What about you?85. Millie can (eat) a lot of fruit now.86. There are some (knife) on the desk.87. Millie goes to the Reading Club (two) a day.88. He often buys chocolate to eat without (tell) his mother.89.It is my first time _______(visit) the Great Wall. It’s wonderful.90.A good breakfast helps Amy ______ fit and health. (keep)91 .Are you hungry? What about______________(eat) something?92. Kitty doesn’t have much time____________(talk)with her friends.93. It takes my grandpa half an hour __ __ (get) home by bus from the hospital .94. We often practise______________(play) football after school95. Shall we go ______________(walk) after supper?96. It’s time______________(have) breakfast now97. ____________(wake) up! It’s time for breakfast.98. Thank you very much for ______ (write)to me.99. Some students don’t know how________________( lea rn) English well.100. Millie often helps her mother _______________(do) housework...。
2019中考英语必备习题精编专题11 听力试题及录音材料（含解析）编辑整理：尊敬的读者朋友们：这里是精品文档编辑中心，本文档内容是由我和我的同事精心编辑整理后发布的，发布之前我们对文中内容进行仔细校对，但是难免会有疏漏的地方，但是任然希望（2019中考英语必备习题精编专题11 听力试题及录音材料（含解析））的内容能够给您的工作和学习带来便利。
同时也真诚的希望收到您的建议和反馈，这将是我们进步的源泉，前进的动力。
本文可编辑可修改，如果觉得对您有帮助请收藏以便随时查阅，最后祝您生活愉快业绩进步，以下为2019中考英语必备习题精编专题11 听力试题及录音材料（含解析）的全部内容。
听力I。
(2018. 贵州铜仁) 听五个句子，选择与所听内容相符的图片，并在答题卡的相应位置将其字母序号涂黑。
每个句子读两遍。
（5分）II. （2018. 贵州铜仁) 听五个句子，分别选择其相应的应答语，并在答题卡的相应位置将其字母序号涂黑。
每个句子读两遍.（5分)6。
（2018. 贵州铜仁）A。
Sorry to hear that. B。
Well done。
C.I'm afraid you can't.7. （2018. 贵州铜仁）A。
Good idea. B. Sorry, I cant。
C。
Yes。
please。
8。
（2018. 贵州铜仁）A。
Two hours。
B。
Once a week. C. In an hour.9. (2018。
贵州铜仁） A. How are you? B. Yes, I’m Ann. C. Speaking，please.10. （2018. 贵州铜仁）A。
Not yet. B。
No，I don’t。
C. All right。
III。
（2018。
贵州铜仁）听五段对话。
根据其内容及各题的问题选择正确选项。
每段对话读两遍。
（5分）11. (2018。
贵州铜仁) How is the weather the day after tomorrow？A。
翻译补全句子一．填空题（共39小题）1．（2018•广州）你沿丝绸之路旅游过吗？Have you ever travelled along the Silk Road？【解答】根据句意，要用现在完成时，其构成是have/ has + done．旅游travel．一般疑问句把助动词have 提前．故答案为Have you；travelled．2．（2018•广州）参观广州博物馆对我们很有教育意义．It is very educational for us to visit Guangzhou Museum．【解答】考查It is + adj + for sb．to do sth．作某事花费某人多少时间，参观visit，根据句意"参观广州博物馆对我们很有教育意义"可知，要用一般现在时．故答案为It is；to visit．3．（2018•广州）明天的大雨可能会阻碍我们外出．The heavy rain may keep/stop/prevent us from going out tomorrow．【解答】考查动词短语，阻止某人做某事keep/stop/prevent sb．from doing sth．；放在情态动词may 后面用动词原形．出去go out．故答案为keep/stop/prevent；going．4．（2018•广州）广州的公园每年都种很多树．Every year，a lot of trees are planted in the parks in Guangzhou．【解答】种植plant，根据句意"广州的公园每年都种很多树"可知，要用一般现在时的被动语态，其构成为am/ is/ are done．故答案为are planted．5．（2018•广州）我昨晚看的那场电影真好笑!What a funny movie I saw last night!【解答】考查感叹句，what+a/an +形容词+名词，是感叹句的句型，根据句意"我昨晚看的那场电影真好笑!"可知，要用一般过去时．故答案为What a funny．6．（2018•广州）我想知道明天我们在哪里见面．I wonder where we will meet tomorrow．第1页（共9页）。
how long的用法归纳嘿，同学们！今天咱们来聊聊“how long”的用法。
先来说说“how long”常见的第一个用法，那就是用来询问时间的长短。
比如说，“How long have you been learning English?”（你学英语多久啦？）这里的“how long”就是在问学习英语这个动作持续的时间长度。
咱们再来看个例子，假设你正在参加一场跑步比赛，比赛结束后，小伙伴问你“How long did it take you to finish the race?”（你跑完这场比赛花了多长时间？）这也是用“how long”来询问做某件事所花费的具体时长。
“how long”还能用来询问物体的长度呢！像“ How long is the rope?”（这根绳子有多长？）这时候就是在关心绳子的长度啦。
还记得有一次我坐火车旅行，旁边的小朋友好奇地问我：“Howlong is this train?”（这列火车有多长？）我当时就耐心地给他解释，告诉他可以通过看列车的参数或者询问工作人员来得到准确的答案。
有时候呀，“how long”还会出现在一些比较复杂的句子里。
比如说，“I wonder how long it will take for us to reach the destination”（我想知道我们到达目的地要多久。
）这就是在表达一种对未来所需时间的疑惑和猜测。
还有哦，如果有人问你“How long does it take to fly from Beijing to Shanghai?”（从北京坐飞机到上海要多久？）你可别答错啦，要根据实际的飞行时间来回答哟。
另外，咱们在使用“how long”的时候，要注意和“how often”（多久一次，询问频率）还有“how soon”（多久之后，常用于将来时）区分开来。
比如说“How often do you exercise?”是在问你锻炼的频率，而“How soon will you come back?”则是在问你回来的时间点。
how long does it take句型
'Howlongdoesittake'是一个常见的句型，表示询问某件事情需要多长时间才能完成。
以下是该句型的常见用法及应用场景：
1. 询问时间：How long does it take to drive to the airport?
2. 询问学习任务所需时间：How long does it take to learn a new language?
3. 询问完成某项工作所需时间：How long does it take to finish the project?
4. 询问运动所需时间：How long does it take to run a 5K race?
5. 询问等待时间：How long does it take to get a table at this restaurant?
6. 询问完成某个过程所需时间：How long does it take for bread to bake in the oven?
7. 询问完成某项任务所需时间：How long does it take to write
a book?
以上是《how long does it take句型》的常见用法及应用场景，希望能够帮助大家更好地理解和应用这个句型。
- 1 -。
一、根据句意及汉语提示完成单词1．My grandfather is __________(九十)now, but he is very healthy. 2．The students take the __________(地铁)to school from Monday to Friday. 3．Jane has a __________(新的)bike.4．Lisa's home isn't far. It's only one________(公里)．5．Tom and Jerry __________(骑)their bikes to school.二、根据汉语意思完成课文原句或原句改编6．你怎样到达学校？________ do you ________ ________ school?7．从你家到学校有多远？_______ _______ is it _______ your home _______ school? 8．骑自行车大约六十到七十分钟。
It's about______ to ________ minutes ________ ________．9．你到达那儿要花费多长时间？_______ ________ does it ________ you________ get there? 10．他们乘火车去上学吗？Do they ________ ________ ________ to school?三、根据首字母或汉语提示完成句子11．Tom is from the US, but now he __________(居住)in Beijing. 12．(中考•滨州)There are nearly four __________(百)students in our school. 13．Hurry up! We have few __________(分钟)left.14．There are lots of cars and b________ at the station.15．My home isn't f________from the school. It is only ten minutes' walk.四、用所给词的适当形式填空16．Tom's father is a good ________(drive). He likes ________ (drive) and he wants________ (drive) every day.17．My sister usually ________ (go) to school by train.18．Yang Lei needs about ten minutes ________ (get) to school. 19．—Does Li Juan ________ (walk) to school every day?—Yes，she does.20．How long does it take you ________ (clean) your bedroom?五、单项选择21．(中考•广东)Eric is not going to Nanjing by ________ plane.Instead，he is taking ________ train.A．/；a B．a；/ C．a；the D．the；a22．(2015•武威)—________does Bob usually go to work?—He usually rides his bike.A．What B．WhoC．Where D．How23．It usually ________ Mum about half an hour to cook supper.A．pays B．takes C．spends D．costs24．(2015•克拉玛依)________ is it from your home to school?A．How far B．How longC．How soon D．How often25．The library is not far from here. We can ________ our bikes there.A．by B．on C．drive D．ride26．(2016•安徽)—Nice to meet you, Mr.Green.I'm Sandy and this is Brad, Ken and Emily.—________.A．See you late B．You're welcomeC．Pleased to meet you allD．You have a point there27．—Do you know when his birthday is?—________. Maybe it's on April 24th.A．Sorry B．I'm not sureC．You, too D．Yes, please28. —Who was the first to ________ school yesterday?—Tom was.A．reach B．get C．arrive29．There are ________ apple trees on the farm.A．three hundredfiveB．three hundred and fiveC．three hundred fiveD．threehundredandfive30．—How is your father going to Beijing?—He's going to Beijing ________.A．by his car B．drive his carC．in his car D．by cars六、用特殊疑问词或词组填空31．—________do the children go to school?—By bus or on foot.32．—____________does it take you to get home from work every day?—About twenty minutes.33．—____________is it from your uncle's home to your grandma's?—It's about three kilometers.34．—________is twenty and fifty?—It's seventy.35．—I walk to school.________about you，Jane?—I ride my bike.七、语法专练：按要求改写句子36．Does Lisa walk to school？(作否定回答)________，________ ________.37．I often go to school by bike．(对画线部分提问)________ ________ ________ often ________ to school?38．It takes about 15 minutes to get to the park.(对画线部分提问) ________ ________ ________ it ________ ________ ________ to the park?39．It is five kilometers from the school to the park.(对画线部分提问) _______ _______ _______ _______ from the school to the park?40. Mr. Green goes to work by car every day.(改为同义句)Mr. Green ________ his car ________ work every day.八、根据汉语意思完成句子41．因为北京离这儿远，所以我们不得不乘火车去那儿。
a r X i v :c o n d -m a t /9903240v 1 [c o n d -m a t .m e s -h a l l ] 15 M a r 1999How long does it take for the Kondo effect to develop?Peter NordlanderDepartment of Physics and Rice Quantum Institute,Rice University,Houston,Texas 77251-1892Michael Pustilnik and Yigal MeirPhysics Department,Ben Gurion University,Beer Sheva,84105,IsraelNed S.WingreenNEC Research Institute,4Independence Way,Princeton,NJ 08540David ngrethDepartment of Physics and Astronomy,Rutgers University,Piscataway,NJ 08854-8019The time-development of the Kondo effect is theoretically investigated by studying a quantum dot suddenly shifted into the Kondo regime by a change of voltage on a nearby ing time-dependent versions of both the Anderson and Kondo Hamiltonians,it is shown that after a time t following the voltage shift,the form of the Kondo resonance matches the time-independent resonance at an effective temperature T eff=T /tanh(πT t/2).Relevance of the buildup of the Kondo resonance to the transport current through a quantum dot is demonstrated.PACS numbers:72.15.Qm,85.30.Vw,73.50.MxThe Kondo effect in quantum dots has been observed in several recent experiments [1].Beyond verifying the-oretical predictions [2,3],these experiments demonstrate that quantum dots can serve as an important new tool to study strongly correlated electron systems.Unlike magnetic impurities in metals,the physical parameters of the quantum dot can be varied continuously,which allows,for example,systematic experimental study of the crossover between the Kondo,the mixed-valence,and the non-Kondo regimes.Moreover,the quantum dot sys-tem opens the possibility of directly observing the time-dependent response of a Kondo system,as there is a well developed technology for applying time-dependent per-turbations to dots [4].Along these lines,several theoret-ical works have addressed the behavior of a Kondo impu-rity subject to ac driving [5].However,a clearer picture of the temporal development of many-body correlations is obtained if the impurity is subject to a sudden shift in energy.Specifically,by applying a step-like impulse to a nearby gate,the dot can be suddenly shifted into the Kondo regime,and the buildup of the correlated state observed in the transport current.In this Letter,we analyze the behavior of a quan-tum dot following a sudden shift into the Kondo regime.The time-dependent spectral function is evaluated within the non-crossing approximation (NCA)[3,6–8],as is the transport current in response to a pulse train.The latter provides an experimental window on the development of the Kondo resonance.Employing the Kondo Hamilto-nian,we show that a finite development time t is pertur-batively equivalent to an increase in the effective tem-perature.We treat a quantum dot coupled by tunnel barriers to two leads (inset to Fig.2).Only one spin-degenerate level on the dot is considered,which is a good approximation at low temperatures.A time-dependent voltage V g (t )is applied to a nearby gate,causing a proportionate shift in the energy of the level ǫdot (t ).If the Coulomb inter-action between electrons prevents double occupancy of the dot,the system is described by the U =∞Anderson Hamiltonian for a magnetic impurity,σǫdot (t )n σ+ kσǫkσn kσ+(V k c †kσc σ+H .c .) ,(1)with the constraint that the occupation of the dot cannot exceed one electron.Here c †σcreates an electron of spin σin the quantum dot,with n σthe corresponding number operator;c †kσcreates an electron in the leads,with k rep-resenting all quantum numbers other than spin,including the labels,left and right,for the leads.V k is the tunnel-ing matrix element through the appropriate barrier.The quantum dot is occupied by a single electron provided the level energy ǫdot lies at least a resonance width Γdot [9]below the chemical potential of the leads.At low temper-atures,the resulting free spin on the dot forms a singlet with a spin drawn from the electrons in the leads –this is the Kondo effect.The Kondo temperature,beneath which the strongly correlated state is established,is given by T K ≃D ′exp(−π|ǫdot |/Γdot ),where D ′is a high en-ergy cutoff[10].The signature of this correlated state is a peak at the Fermi energy in the spectral density of the dot electrons.This peak,in turn,dramatically enhances transport through the dot,allowing perfect transmission−6.0−4.0−2.00.0ε0.00.51.01.52.02.5ρd o t (ε,t )−0.10.00.1εt<0t=13.8t=27.6t=82.8t=193t=759FIG.1.Spectral density ρdot (ǫ,t )vs.energy ǫat various times following a step-function change in the level energy ǫdot (t )=−5+3θ(t ).The ordinates for positive times are successively offset by 0.5units.For t <0,ρdot (ǫ,t )is iden-tical to the equilibrium spectral density at ǫdot =−5while for the largest time shown it is indistinguishable on this scale from the equilibrium spectral density at ǫdot =−2.Through-out this work energies are given in units of Γdot ,and times in units of 1/Γdot ,with ¯h =1.Here T =0.0025.at zero temperature [2].We employ the non-crossing approximation (NCA)to analyze the spectral density and transport through the dot in the presence of a time-dependent level energy ǫdot (t ).The NCA is based on an exact transformation of the U =∞Anderson model in Eq.(1)into a slave-boson Hamiltonian [6].The latter is then solved self-consistently to second order in the tunneling matrix el-ements V k .The NCA approximation gives reliable re-sults for temperatures down to T <T K ,and its time-dependent formulation has been discussed at length in previous works [7,8].We define a time-dependent spec-tral density for the dot electrons as [11]ρdot (ǫ,t )≡Re∞dτ2ψα′,S =ββ′c †βσββ′t t’t t’t=0-t=0+t=0+t=0-FIG.3.Contributions of order J 2to the renormalized con-duction electron scattering vertex,from the Kondo Hamilto-nian in Eq.(3).Solid lines are conduction electron propaga-tors and dashed lines are pseudofermion propagators.Sum-mation over internal spins is implied.pseudofermion number is conserved by H K +λn c ,and wehave n c =0for t <0because of the large pseudofermion energy λ→∞,we obtain an abrupt turn on of the Kondo coupling at t =0and all later expectations are taken in the physical subspace n c =1.The analytical signature of the Kondo effect is the log-arithmic divergence of perturbation theory in the dimen-sionless coupling Jρ,where ρis the density of conduction electron states per spin direction at the Fermi level.In-deed,for T <T K perturbation theory in Jρfails,even for small Jρ.For T >T K ,temperature cuts offthe logarith-mic divergencesand perturbationtheoryis reliable [14].We find that a finite time t following a sudden switching on of the Kondo coupling also results in a convergent per-turbation theory.To demonstrate this,we focus on the simplest quantity that diverges in perturbation theory.Specifically,we calculate the scattering vertex γpp (t,t ′)to order J 2.Physically,this quantity represents the low-est order change in J due to multiple scattering from the Kondo impurity.Since abruptly turning on the Kondo coupling creates a nonequilibrium state of the system,we use Keldysh Green functions with p =±1for the out-ward/backward branches.In time,the Keldysh contour runs from −∞to ∞(p =+1)and then from ∞to −∞(p =−1).As shown in Fig.(3),there are two contri-butions at order J 2,one with the conduction electron line and the pseudofermion line parallel and one with the lines antiparallel.Evaluating the diagrams in Fig.(3),and keeping only logarithmically divergent contributions in addition to the bare vertex,we find γpp ′(t,t ′)=pδpp ′J2G pp 0(t −t ′)sgn (t −t ′).(4)(Note that in this order there is no logarithmic contri-bution that is off-diagonal in the Keldysh indices.)HereG pp 0(t −t ′)is the bare time-ordered (for p =+1)or anti-time-ordered (for p =−1)Green function for conduc-tion electrons at the site of the Kondo impurity.For|t −t ′|≫1/D (D is a high-energy cutoff)it takes the form [15]G pp 0(t −t ′)→−πρT2ρJ lnD2.(6)For T t ≫1this reduces to the usual equilibrium form,γ∝J 1+1T ,with the logarithmic divergence cut offonly by temperature.However,since in our case the Kondo coupling exists only for times t >0,the re-sult contains an additional cutoffdue to the finite time allowed for spin-flip scattering.Formally,the finite time t since the onset of the Kondo coupling can be absorbed into an increase in the effective temperature,T eff=T¯h Γdot ∂ǫ,(8)where f (ǫ)is the Fermi function,and ¯h is explicitly in-cluded for clarity.If a periodic gate voltage is applied tothe dot,formula (8)is still valid if G is replaced by the time-averaged conductance G ,and ρdot (ǫ)is replaced by the average of the time-dependent spectral density ρdot (ǫ,t ) .Consider a periodic signal consisting of an “on”pulse of duration τon which brings the dot into the Kondo regime followed by an “off”pulse which moves it back out of the Kondo regime.During each on pulse,ρdot (ǫF ,t )will build up to a maximum at time τon and then rapidly decrease back to a low value during the offpulse.The differential increase of conductance as the duration of the on100200300400τon [1/Γdot ]0.00.51.01.5d G i n t /d τo n [e 2/h ]T=0.04T=0.02T=0.01T=0.005T=0.0025ττon V (t)goffFIG.4.Solid curves:derivative of G int (in units of e 2/h )with respect to duration τon of “on”gate-voltage pulses,at various temperatures.G int is the conductance inte-grated over a full cycle of gate voltage.Dashed curve:−π dǫΓdot f ′(ǫ)ρdot (ǫ,t =τon )for T =0.0025.Inset:schematic periodic gate-voltage pulse train.The level energy is ǫdot =−2in the on state and ǫdot =−5in the offstate.The duration of the offperiod,τoffis long enough to allow transients from each on pulse to die out.pulse is increased will therefore reflect the magnitude of the spectral density near or at the Fermi energy at a timeτon following the shift into the Kondo regime.In Fig.(4),we have plotted the differential with respect to τon of the conductance,with a fixed off-pulse duration τoff.The conductance is integrated over the period,rather than time-averaged,to remove effects due to the changing du-ration of the period,i.e.G int =(τon +τoff) G .This measurable transport quantity provides a probe of the time-development of the Kondo resonance [18].In conclusion,we have analyzed the response of a quan-tum dot to a sudden shift of gate voltage which takes the dot into the regime of the Kondo effect.The buildup of many-body correlations between the dot and the leads follows an uncertainty principle:at time t the Kondo res-onance is cut offby an energy ∼1/t .Within perturba-tion theory in the Kondo coupling,we find that the finite time t plays the role of an increased effective tempera-ture T eff=T/tanh(πT t/2).To experimentally probe the buildup of the Kondo resonance,we propose applying a train of square gate-voltage pulses to the dot.The deriva-tive of current with respect to duration of the “on”pulse accurately reproduces the time-dependent amplitude of the Kondo resonance.The work was supported in part by NSF grants DMR 95-21444(Rice)and DMR 97-08499(Rutgers).Work at BGU was supported by the The Israel Science Founda-tion -Centers of Excellence Program.One of us (MP)acknowledges the support of a Kreitman Fellowship.D Γdot /4,where 2D is the effectivebandwidth.The calculations here used a parabolic band of total width 40Γdot .[11]A.-P.Jauho,N.S.Wingreen,and Y.Meir,Phys.Rev.B 50,5528(1994).[12]Our calculations are based on the approximation that the switching time,τs ,is exactly zero.In reality,τs is always a finite time.Our results are valid for finite τs as well,provided that t ≫τs .[13]J.R.Schrieffer and P.A.Wolff,Phys.Rev.149,491(1966).[14]A.A.Abrikosov,Physics 2,5(1965).[15]G.Yuval,and P.W.Anderson,Phys.Rev.B 1,1522(1970).[16]By evaluating the conduction electron self-energy to or-der J 3,we have directly confirmed the ∼1/t cutofffor the Kondo peak in the spectral density.[17]Y.Meir and N.S.Wingreen,Phys.Rev.Lett.68,2512(1992).[18]The difference between the dashed and solid curves at small τon reflects the finite decay -time of the Kondo res-onance after the pulse is switched off.。
