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????瀹???涓??ㄩ???????洪????杈?灏?涓?涔?锛?Unruh灏辨敞???颁?涓???????????绫绘???[1]锛?杩??ㄦ?浣?涓?０娉㈢??琛?涓虹被浼间?寮???????腑???????虹???ㄥ??瀛︼??ㄥ０娉㈡尝??涓?娴?浣?娴??ㄧ????搴︾?澶у???????版?逛?瀛??ㄤ?涓??榛?娲?浜?浠惰????镐技???????€??Unruh璇???[1]瓒??抽??娴?浣?娴??ㄥ??互浜х??涓?涓?????娲?????杩????涓???榛?娲?????澹板?绫绘?锛????朵?????澹板?榛?娲?????娴???璺ㄨ?澹伴?????哄??琚?О浣???澹板?瑙?????锛?瀹????娲?瑙?????澹板?绫绘???杩?涓?被姣?琛ㄦ??锛?濡???榛?娲??锋??娓╁害骞跺??ㄩ????杈?灏???璇?锛?杩?涓?０瀛﹁???涔?浼??锋??娓╁害骞跺??澶?????杈?灏?澹板???杩?涓?涓?被姣?涓哄?楠???绌堕?娲???????杈?灏???寮?浜??扮????璺???2011骞达?Unruh??浠?????浜?棣?娆″?╃?ㄥ?????绀哄??婵?杈?灏?瀹?楠??规?灏?璇?娴???澹板?瑙?????娓╁害骞堕?璇?????杈?灏????︿负???灏?[6]???ㄥ?楠?涓??涓轰?褰㈡??涓?涓?０瀛﹁???锛?瀹?楠?浜哄???ㄤ?涓?ǔ瀹?娴??ㄧ??姘存Ы搴??ㄨ?缃??涓?涓???纰??┿??杩?涓???纰??╀?澧???娴?缁??朵??圭??姘存?娴???锛????跺??灏??朵??规按?㈢??娉㈤????濡????板??拌?璁℃按妲藉????纰??╋?骞堕??杩?姘存车??褰??版?у?舵?绘按娴???锛??ｄ??ㄦ按妲界??姘撮?㈠??涓?娓哥Щ?ㄧ??娉㈡氮灏????颁?涓??浠???娉?璺ㄨ???? ???? 涓?涓???????芥?瑙?????瀹?楠?浜哄?????扮郴缁?瀛??ㄥ??婵?杈?灏?锛?骞朵???????娉㈠か绯绘?扮??姣??奸??娉㈤?挎???伴???????╃?ㄧ?卞?????﹀??婵?杈?灏???????杈?灏?涔??寸???崇郴锛?瀹?楠?浜哄??寰??虹?璁猴?澹板?榛?娲?瀛??ㄨ?????????灏???涓?杩???绌朵汉??瀵硅?涓?缁??????﹁冻浠ョ‘璁ゅ０瀛﹁???浠ュ??楠?璇?????杈?灏?浠?瀛???寮?璁????朵腑涓?涓????????楠?涓?娇?ㄧ???╃?????板苟娌℃???ㄦ?????稿?抽?????缇ら??搴︿腑浜х??瓒?涓寸???哄????????6]??瀹?楠??界?舵?妤??拌〃???变?娴?????????瀛??ㄨ?妯¤浆???浣????绉?杞???技涔??ヨ???涓や釜涓?????浜?涓寸???哄??涔??寸???ｅ??????﹁?藉?灏?????6]?峰??????扮?瑰?瑙?涓洪????杈?灏?瀛??ㄧ??璇?????ㄤ?璁?7??9]??杩?涓?被姣?瀹?楠???绗??涓?己?瑰?ㄤ?锛?瀹?楠?骞舵病???存?ラ?璇?澹板?瑙?????????澹板?杈?灏????ㄨ?涓???哥被姣?绯荤?涓??瀹?楠?浜哄??蹇?椤讳富?ㄥ?颁骇??澹版尝?绘???瑙???澶????ｅ????界?跺?╃?ㄧ?卞?????﹁????杈?灏?????婵?杈?灏????崇郴??互??璁轰?璁＄?????杈?灏??????碉?浣???????存?ラ?璇?绫绘?瑙?????????杈?灏?浠??舵??涓?瀹?璺?绂汇??
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????Unruh 绛?浜哄?浜?澹板?瑙?????绌剁???﹀?涓?涓???瑕?璐＄????????浜轰滑??娓???瑙ｄ?????杈?灏?涓??涓???????trans-Planckian??(??璺ㄦ????????)????瑕???????????ㄩ?娲?杈?灏???璁鸿?涓??????杈?灏?琚?В????涓洪?娲??????????杩???绌烘定?藉舰????姝ｅ??绮?瀛?瀵逛腑????绮?瀛?锛?浣垮?姝ｇ?瀛?寰?浠ラ???辨巩??????杩???????瀹?绮?瀛????拌薄???变?杩?浜?绮?瀛??ㄩ?娲?瑙?????澶??????姝ゅ?浠??????介??????绌疯?锛?褰㈡???遍?娲???澶?杈?灏???绮?瀛?娴???杩?涓?瑙ｉ????涓?涓??伴?句?澶??ㄤ?锛??变?榛?娲???寮???绾㈢Щ??搴?锛??ㄦ??绌疯?澶????惰?介????杈?灏?绮?瀛?锛?褰?浜轰滑娌跨??瀹???杞ㄨ抗????婧??? ?讹?瀹????介??浼?涓????板?????褰???婧??伴?娲?瑙????讹?绮?瀛????介??浼?杩?杩?澶т????????芥??????姝わ??ㄦ??绌疯?澶?瑙?娴??扮???介??寰?浣???????杈?灏?绮?瀛?涔????ヨ???榛?娲???杩?杩?楂?浜????????芥????绮?瀛???杩?绉?楂??芥???╃??娑????版???ョ????瀛?寮?????杩?浣垮?浜轰滑????????杈?灏?浼?瀹?璐ㄦ?у?颁?璧?浜????ョ????瀛?寮?????缁?????杩??ㄦ?╂???炬????浜?瀵归????杈?灏???涓?涓?弗??????[10]??瑙ｅ?宠?涓??????????????骞朵????ヨ???寮?????绌剁????韩???稿??锛?瀹??存???ヨ??? Unruh 瀵瑰０瀛﹂?娲?????绌?11]??Unruh ??杩?澹板?榛?娲????板?兼ā????绌讹????伴?娲???杩?楂??芥?????╃??骞朵?浼?褰卞??杈?灏?杩?绋?锛?杩?缁?榛?娲??稿??杩?绋?????瀹??у???浜????????ㄨ?涓?宸ヤ???????涓?锛?????12]杈?涓轰弗?煎???????拌???浜?????杈?灏?涓?榛?娲?瑙?????杩???楂??芥???╃?????炽??杩?涓??蜂?浜?渚?琛ㄦ??锛?????被姣?寮????ㄥ??????绫绘?????绌朵?浠?浠???互浣?涓衡??婕?绀哄?楠???灏?涓?浜??伴?剧???╃???拌薄灞??板?ㄤ汉浠??㈠??锛?瀹?涔???府?╀汉浠??㈢储琚?ā????绯荤?涓????ョ?╃??瑙?寰???涓?绉??规???
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?????ㄧ????????绌剁????瀛?绯荤?涓???昏?测???卞?????﹀????浣?(BEC)??????????绯荤???BEC?ㄥ?堕??澹板?榛?娲??归?㈡??璁稿?浼??裤??瀹?涓?浠???互灏?娓╁害?峰?村? 10-12 K???虫?翠?锛???涓???杩?EC??????ross??Pitaevskii ?圭???互琚??瑰????涓?缁?娴?浣???瀛︽?圭????﹀?锛?BEC涓???澹版尝?ㄦ尝?垮ぇ浜?涓?涓??绉颁?涓?ealing length (?????垮害)???瑰?灏哄害?讹??舵尝??杩?浼间?娉㈤?挎???炽??2010骞达?Jeff Steinhauer绛?浜?13]???轰?涓?涓???EC涓???板０瀛﹂?娲????规????ㄤ?浠????规?涓??澶х害10涓?涓???87??瀛???杩?婵????峰?村?版?ヨ?缁?瀵归?跺害褰㈡??BEC???????讹?浠?浠?负BEC娴?浣?璁捐?浜?涓?涓??伴?剁?跺??灏????胯?斤?浠????藉?娴?浣??????拌?杩?BEC涓???澹伴??锛?杩??蜂?浠???EC涓?????浜?涓?涓?０瀛﹁??????╃?ㄨ?涓?ā??锛?Jeff Steinhauer绛?浜哄?ㄦ????13]涓????轰?濡?浣?娴???骞堕?璇?????杈?灏???璺?嚎?俱??涓?杩??ㄦ??绔?涓??浠?浠???????浜??板?兼ā???ヨ???杩??风??瀹?楠?璁捐???互琚??ㄦ?ラ?璇?澹板?榛?娲???????杈?灏???
????2016骞达?Jeff Steinhauer棰?瀵肩??灏?缁?棣?娆″??颁???EC涓??澹板?瑙???????杈?灏???瑙?娴?[14]??杩?涓?瀹?楠????抽???澶??や???瑕?浠??????瀹??版????13]??璁捐???BEC绯荤?涔?澶?锛?浠?浠?????ㄦ???澹板?瑙???涓や晶????瀵?搴︹??瀵?搴︹???宠???芥?版?ユ?㈡?????杈?灏???杩?涓??规????辨??澶у?╁??娲?灏间?澶у???Roberto Balbinot ??浠?????浜?浠???008骞寸??涓?绡???绔?[15]涓????烘?ョ?????ㄩ????杈?灏????╃???惧??涓??????杈?灏????变?榛?娲????????绌烘定?藉??寸??姝ｅ??绮?瀛?瀵逛腑????绮?瀛???褰㈡???????规????瀛???瀛︼?杩?绉???绌烘定?界??绮?瀛?瀵瑰?瀹????瀵圭?缂?绮?瀛???杩?瀵逛?浠讳???浠?绾挎?ф?圭?????渚?濡?BEC涓???澹版尝??澶╀??╃??榛?娲??ㄥ?寸???╄川???芥????绔???????姝わ?姣?涓?涓?????杈?灏?绮?瀛?蹇?瀹???瑙????????﹀?涓?涓???绮?瀛?澶?浜?绾?缂?????????15]???猴?娴???瑙???涓や晶瀵?搴︽尝?ㄧ???稿?虫?у??互?惧?伴????杈?灏?瀛??ㄧ??璇?????缁?杩??板??娆＄????澶?娴???锛?Jeff Steinhauer ?峰?浜?浠?浠??璁＄??BEC绯荤?涓?０瀛﹁???涓や晶???宠???芥?般??瀵逛???尝??浣??告?浜?绯荤??? healing length 浠??惰冻澶???锛?浠?浠??峰?浜?姝ｉ?㈢??娴???缁???锛??筹?澹板?瑙???涓や晶??瀵?搴︽定?藉??ㄧ?变???瀛?绾?缂?寮?璧风???宠??锛?骞跺???扮???涓????灏?涓???灏界??版???纭??搴﹁?姣?杈?澶?????(a)? Jeff Steinhauer 棰?瀵肩??灏?缁??ㄦ????14]涓??ラ????娴???缁??????句腑瑙?????涓や晶(???茬??甫??)??互???颁袱?℃ā绯?浣?????互杈ㄨ?????甯︼?杩??剧ず浜?澹板?瑙?????杩???瀵?搴︽定?藉??ㄩ??瀛?绾?缂???杩?涓?瀹?楠?缁???琚??涓烘??????????杈?灏?瀛??ㄧ??淇″?枫??
?? (a)?句腑?????茬??甫?? [14] 浠ュ??(b)?剧豢?叉?规?????????甯??ㄥ?瑙?绾夸袱渚х????甯︽?剧ず浜?????绮?瀛?涓??跺??绮?瀛?涔??寸???宠??? [16] ???句腑x浠ｈ〃绌洪?翠?缃??x' 浠ｈ〃?堕?淬??澹板?瑙???浣?浜?x=0??浣?缃??(c)绾?缂?璋遍??娉㈤?跨?????????朵腑妯???????尝?㈢??澶у?锛?绾靛??????０瀛﹁???涓や晶??绾?缂?搴︺???句腑??绾挎???规?????灏?璁＄???绾?缂?璋憋?榛??插?绾夸互??璇?樊妫????楠?娴?????缁??? [16]
??????瑕????虹?????涔???浜哄? Jeff Steinhauer 灏?缁???016骞寸??瀹?楠?缁??????轰?璐ㄧ?????瑰????????﹀??互灏?涓?杩?EC涓???缁???浣?涓虹被姣?寮???绯荤?涓?????杈?灏???纭??胯?????惰???浜?璁??姣?濡?????17锛?18]浠ュ?? Jeff Steinhauer ??汉????搴?[19]???ㄧ??????ワ?Jeff Steinhauer 灏?缁???016骞寸??缁????充究???纭???锛?涔???涓や釜涓?瀹?缇????版?广??涓??归?㈡???楠??版????绮惧害杩?涓?澶?锛?涓?纭???ц?寰?澶э???姝ゆ??寰?缁???娌℃??瓒冲???淇℃???????︿??归???瀹?楠??界?跺?绀哄??ㄨ????杈?灏???璇?????存??娉?璇???杩?涓?????杈?灏??????灏?锛???姝や?灏辨??娉?楠?璇?澹板?瑙?????娓╁害???﹀??澹板?瑙?????????娓╁害涓??淬??2019骞翠?浠??涔?????瀹?楠??????琛?浜???澶ф?硅?[16]????(b)涓????涓や晶澹板???瀵?搴﹀?宠???芥?帮?????(a)?告?锛??扮??缁?????浣?浜???????０锛??村??娓??板?板?绀轰?涓や晶绾?缂?绮?瀛???瀛??ㄣ??姝ゅ?锛?浠?浠??ㄥ?楠?涓??娆℃???浜?澹板?瑙?????杩?????杈?灏???澹板?绾?缂?璋卞?芥????(c))锛?浠????峰?浜?澹板?杈?灏???娓╁害锛?骞跺???板??澹板?瑙?????????娓╁害?诲????瀵逛?杩?涓?瀹?楠?缁???锛?绗???????灏??????版????绔?瀵瑰?舵???鸿川????濡???????16]??缁???琚?‘璁ゆ????纭???璇???璇?锛?杩?灏????娆″?ㄧ被姣?寮???绯荤?涓??存?ヨ?娴??伴????杈?灏?骞舵???浜??稿???娓╁害??
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??????澹板?榛?娲????????镐技锛?浜轰滑涔???互?ㄧ?规?????瀛︽????涓????娉㈠????涓?涓?????瀛﹁????????ㄧ?规?????瀛︿?璐ㄤ腑瀹??颁?涓??????瑙?????澶?绉???璺???涓?绉?甯歌?????璺???澹板?榛?娲?绫讳技??杩?????????澹板?浠?璐ㄦ?㈡????瀛︿?璐??澹版尝?㈡???电?娉€??????涓???互灏?浠?璐ㄧ????灏???璁捐?寰?寰?澶э??ㄥ??ㄤ娇寰?浠?璐ㄨ??ㄩ??搴﹁?杩?浠?璐ㄤ腑??????锛?浠???涓轰?璐ㄤ腑???电?娉㈡??渚?涓?涓??????瑙?????涓?杩??ㄥ?璺典腑锛?璁╀?璐ㄤ???杈?楂?????搴﹁??ㄦ??涓?瀹??伴?俱??杩???浠?缁???eonhardt?ㄦ????20]涓????虹??涓?涓???甯稿阀濡????ㄩ??姝㈢??浠?璐ㄤ腑瀹??扮???瑙??????规???
????杩?涓??虫???互?卞?? 涓???绀烘???炬?ヨВ????瀹?楠?浜哄???ㄩ??绾挎?х???典?璐ㄥ??绾や腑棣???娉ㄥ?ヤ?娈佃??????茬传澶?(杈?楂?棰???)??婵??????变???灏???绾挎?т??????绾や腑???????蹭????㈣??捐?杩?瀹???绾㈠?(杈?浣?棰?)?㈡???????搴︺??绾㈠??㈡???????灏???浼?????绱?????插????寮哄害??甯???涓?????????20]??涓?涓?阀濡?涔?澶??ㄤ?锛?浣???灏?????绯婚???╀负?㈡??????卞?ㄥ????绯汇???变???绾や腑??????瀹???涓?灏?浜???绌轰腑??????锛???姝ら???╄??风???卞?ㄥ????绯诲?ㄧ?╃??涓?????璁哥?????ㄥ?卞?ㄥ????绯讳腑锛??ュ??????茬??浣?缃??????涓?????锛?浣????璐ㄥ?村?ㄤ互?稿??????搴﹁??ㄣ??浠ョ传澶????茬??涓??涓哄?绉拌酱锛?绱?????茬??寮哄害??娓???灏?锛???姝ょ孩澶??㈡???????灏???涔???娓???灏???杩?瀵艰?翠?璐ㄤ腑??绾㈠??㈡?????缇ら??搴︾?辩传澶?????涓????涓や晶澧?澶с??濡???(b)??绀猴??卞?ㄥ????绯讳腑??浠?璐ㄦ???浜???涓???娴?浣?锛???绱?????插???????浜???涓?????纰??╋?骞跺??灏?浜???杩???绾㈠?????缇ら??搴︺???板??拌?璁″?楠????板氨??互涓虹孩澶??㈡????堕??涓?涓??????????瀛﹁????? ???? ?? 姘存Ы瀹?楠?涓?０瀛﹁?????????瀛︾????????????20]?ㄥ?楠?涓??娴??颁???瀛﹁?????杩???绾㈢Щ????绉汇????杩???璁鸿?绠?琛ㄦ??杩??风??绯荤?瀛??ㄩ????杈?灏?????杩?Leonhardt?ㄦ????21]涓??ラ??浜??ㄨ?涓?ā??灏?璇?瀵归????杈?灏???楠?璇???娴?????缁????????颁?????杈?灏?瀛??ㄧ??璇????涓?杩?瀹?楠?缁??????借?峰?绫讳技浜?????杈?灏???榛?浣??借氨??
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????寮??????ㄦ????跺???????╁??互杩芥函?版?╂??瀵归?娲??电????绌躲????0涓?绾?0骞翠唬浜轰滑??绌堕?娲??跺???伴?娲?涔????涓?????瀛︾郴缁?锛???杩伴?娲??电??璐??????︹???????靛???琛ㄦ??榛?娲????垫?姣?浜?榛?娲?瑙??????㈢Н[24]???变??╃??绯荤????典唬琛ㄧ郴缁???寰?????卞害锛???姝よ??????︹???????靛???琛ㄦ??榛?娲???寰?????卞害骞朵???????甯哥???╃??绯荤??ｆ?锋?姣?浜?浣?绉???????姣?浜?绯荤????㈢Н??杩?涓???瑕????圭?归????辫?璐?灏??╃??濂??峰??? ??t Hooft ??993骞存敞????25]锛?骞惰?Susskind??994骞磋?涓?姝ュ??灞?涓衡??寮??????ㄦ????跺??????[26]????缁?杩?涓?????缁???aldacena??Steven Gubser??Igor Klebanov??Alexander Polyakov??Edward Witten 绛?浜鸿?涓?姝ュ??灞???涓轰?????骞夸负??绌剁????AdS/CFT瀵瑰?垛??????27??29]??? AdS/CFT 瀵瑰?剁???充腑锛?涓?涓??杩???寰疯タ?规?剁┖(涓?绫昏?甯告?茬???剁┖)涓?????瀛?寮?????涓?涓??ㄥ??寰疯タ?规?剁┖杈圭??涓???寮鸿?﹀????瀛??鸿????浠风?????╃?ㄥ????ㄦ????讹?浜轰滑瀵逛?寮???浠ュ??榛?娲???????瀛????归?㈡??浜?璁稿??扮??璁よ???棰?瑷???杩?浜??扮??缁?????????杈?灏?涓??凤???ず浜?榛?娲?涓?浜?瓒?瓒?缁??哥??璁虹???ц川锛?姣?濡???瀛?娣锋???绾?缂??点??????绮?婊?姣?绛????惰????????杩?瀹?楠?瀹ゆ??娈垫?ユā??榛?娲???杩?浜??ц川????绌惰????????锛?瀹?楠?????璁洪?借?涓???????涓?缁??稿箍涔??稿?璁轰互??璇稿?????杈?灏?绛?榛?娲?????瀛??拌薄涓???锛??ヨ??????ㄦ????朵腑??璁稿???璁洪?瑷?杩?澶?浜??㈣??舵?????杩?绫绘?寮???绯荤?????绌舵?????戒负杩?浜???璁虹????绌舵??渚??扮????ず??
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????2019 骞磋??归???涓???瓒ｇ??杩?灞??ヨ???????42]锛?瀹?涓?榛?娲???淇℃??蒋璋????炽???挎??浠ユ?ワ?绉?瀛﹀?浠???村?ㄦ??????褰??╀??藉?ラ?娲??朵?????浠?涔???杩?涓????锛??瑰?????瀹????涓???瀛?绮?瀛??躲????瀛??╃??瀛︾???烘?????琛ㄦ??锛???璁洪?娲?瀵归??瀛?绮?瀛???浜?浠?涔???浣?锛?瀹??藉?璇ユ??????????杩????变???瀛???瀛︿腑锛?涓?涓??绔?绯荤???婕???蹇?瀹???购姝ｇ????杩?涓??圭?逛?璇?浜?瀛ょ?绯荤???淇℃???????杩?涓?棰?娴?浼间?涓?榛?娲?灏??╀???????绌峰????瑰苟???峰?衡??????杈?灏???????濂解???告??锛???涓洪????杈?灏????????俊???????灏???杩?涓??????锯??琚?О浣???榛?娲???淇℃??蒋璋???[43锛?44]??杩???箍涔??稿?璁哄????瀛???瀛︿??稿???涓?涓???瑕?浣??般??涓?涓?????????瀛?寮?????璁哄?椤诲?杩?涓????缁??鸿??唇????绛???寮????ㄦ????跺????????绛?????冲??ㄦ?杩???寰疯タ?规?剁┖涓??榛?娲???婕???婊¤冻骞烘??э???姝よ?藉?ラ?娲???淇℃????互琚???????涓?杩?寮????ㄦ????跺苟娌℃???存?ュ??绛??藉?ラ?娲???淇℃?????浣??????糕???洪?娲?????????宸茬???澶?绉?涓??????????糕???哄?惰??哥户???恒???朵腑涓?绉???璁烘ā??璁や负[45??47]锛?濡?????瀛?淇℃???ㄩ?娲???琚??????缃?贡(scrambling)??锛??ｄ???杩??堕??榛?娲??稿???板???ュぇ灏???涓????朵?????????杈?灏?绮?瀛?锛?灏卞??互?㈠??烘???ラ?娲?涓?????瀛?淇℃????????涓?骞哥?????瀵逛?涓?涓?????璐ㄩ????榛?娲?锛?姣?濡?涓?澶??宠川??涓??峰ぇ??榛?娲?锛?瀹???璐ㄩ????杩??稿????灏??颁?????瑕?1067骞粹????杩?瀵逛?浜虹被?ヨ?瀹??ㄦ??お?夸?锛???姝わ?浜轰滑??娉??ㄧ??瀹???榛?娲?涓??楠?涓?杩拌??圭??姝ｇ‘?с??????42]??019骞磋?璁′???绫绘???瀹?楠??ユ?楠?杩?绉?瑙??癸?璁捐?濡???(b)??绀虹??7姣??归??瀛??佃矾妯℃????┛瓒??????浠?浠???瀹?楠?琛ㄦ??锛?绯荤?涓???????瀛?缃?贡瓒???交搴?锛?瓒??藉???纭??????鸿?浼?杈???淇℃????杩?灞?绀轰?杩??蜂?涓??瀹?锛??变???瀛?缃?贡锛?涓?涓??瀛???淇℃????涓鸿?娣峰?????╂?ｅ?版?翠釜绯荤?涓?????璧锋?ュ????涪澶变?锛?浣?瀹???涓?浠??堕?????ㄤ???绮?瀛?涔??寸???镐??宠??涓???
?? (a)榛?娲?????????俊?????╄川?????朵互????杈?灏???褰㈠???澶?杈?灏?绮?瀛?锛?(b)?ㄩ??瀛???褰????妫?娴?淇℃??疆涔辩??7??瀛?姣??圭???????俱????瀛?姣???琛ㄧず瑕?浼??????舵??锛??朵?6涓???瀛?姣??逛互EPR瀵圭??褰㈠??跺? [42]
?????ㄦ???抽?娲?????绌朵腑锛?浜轰滑缁?甯稿???伴?娲??锋????浜???绔????ц川??寮????ㄦ????跺??涓洪?娲???杩?浜???绔??ц川澧???浜?涓?灏??板??瀹广???朵腑涓?涓?氨???娲????涓???涓烘贩娌?????瀛?绯荤?[38]???ㄦ??杩扮??告贩娌?绯荤??讹?浜轰滑寮??ヤ????????澶????帮?瀹?????杩扮郴缁?瀵瑰???肩??????绋?搴︾??????涓?涓?郴缁??????????澶????拌?澶э?琛ㄦ??绯荤?瀵瑰???艰?????锛?涔?灏辫〃?板?瓒??句互棰?娴????ㄩ??瀛?绯荤?涓??浜轰滑??互??杩? ?????跺??宠???芥??out-time-order-corr elation锛?OTOC)??瀹?涔?涓?涓???瀛??????????????澶????般??涓?涓???瀛?绯荤??????????澶????拌?澶э?杩?涓?郴缁?灏辫〃?板?瓒?娣锋???????38]?ㄤ?浜??????у??璁句?锛??规??????ㄦ????惰???浜??ㄧ?瀹?娓╁害????瀛?绯荤?涓??榛?娲??锋????澶х?????????澶????般????姝わ?浠?杩?涓???涔?涓?璁诧?榛?娲????涓???涓烘贩娌?????瀛?绯荤???涓轰??ㄧ被姣?寮???绯荤?涓???绌堕?娲???娣锋?琛?涓猴???杩??ㄦ????48]涓???浠????轰?涓?涓??轰???瀛?澶?浣?绯荤???绫绘?寮???妯″????杩?涓?ā??涓?浠???互瀹??颁?浜?浼?缁???绫绘?寮????拌薄(姣?濡?????杈?灏?)锛?杩???互?ㄦ?ュ??伴?璇?寮????ㄦ????剁????浜?缁?璁恒??????48]璇???浜?浠绘??浜?缁撮?????剁┖涓?????璐ㄩ???????烘?绘???浠蜂?浣?缃??稿?崇?? bosonic hopping 妯 ??锛?????璐ㄩ?????????哄??绛?浠蜂?涓?浣?缃??稿?崇??Hubbard妯″??????????????Y妯″????杩?涓?被姣?妯″?????抽???ㄤ?灏?1+1缁村集?叉?剁┖????璐ㄩ???????烘???????????哄???舵?间腑绱ф??缂?妯″????绯昏捣?ャ??寮??叉?剁┖??搴﹁???琚?????扮揣??缂?妯″??涓????昏??肩?圭???﹀??绯绘?颁腑锛?濡???(a)??绀恒??浣?涓轰?涓?被姣?寮???妯″????搴????????48]璇???浜?瀹?浠???互?ㄦ?ユā??榛?娲???????杈?灏?锛?骞惰???杈?灏?璋辨弧瓒抽?浣?璋便???翠负??瑕??????杩?涓?ā????互?ㄦ?ユā??娓?杩???寰疯タ?规?剁┖涓???榛?娲???濡???(c)??绀猴?????48]璇???浜?绫绘?榛?娲??????????澶????扮‘瀹?婊¤冻????38]???虹??涓???锛?浠???楠?璇?浜?榛?娲??????剁??涓???娣锋???绯荤???
?? (a)涓?涓?????榛?娲???寮??叉?剁┖??浣?琚?????版?舵?肩?????昏??﹀??绯绘?颁腑锛??﹀??绯绘?颁?姝ｅ?拌?????????唬琛ㄤ?涓?涓?被姣???榛?娲?瑙???锛?(b)?板?兼ā??寰??扮??榛?娲?杈?灏??借氨??妯?????浠ｈ〃绮?瀛????介??锛?绾靛????浠ｈ〃浜х??姒?????瀵规?帮?绾㈣?茬?寸嚎???浣?杈?灏?????璁烘?茬嚎锛?(c)绫绘?榛?娲???OTOC澧??跨????妯????????堕?达?绾靛??????TOC??瀵规?般???句腑涓??????茬嚎浠ｈ〃?肩?圭???磋?锛?缁胯?茬?寸嚎????澶ф贩娌??剁????璁烘?茬嚎????互???帮??ㄨ?缁?????涓?(涔?灏辨???肩?归?磋?瓒?浜?0)锛?绫绘?榛?娲???OTOC澧??挎?板ソ婊¤冻??澶ф贩娌?????? [48]
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?????╃?ㄧ被姣?绯荤???绌堕?娲?锛?骞朵???姹??㈤??勘?板?板?绀洪?娲????????ц川锛???????句互??瀛?绯荤????蜂??板?妯″??涓烘??瀵间???????榛?娲????ㄥ????瀛??ц川??杩?涓???绌舵???????ㄥ?????ㄥ?楠?瀹ょ郴缁?涓???炬ā???洪????杈?灏?绛?寮??叉?剁┖????瀛??拌薄??缁?杩?澶?骞寸????灞?锛?浜轰滑???轰?璁稿?绫绘?寮???妯″??锛?骞朵?宸茬???EC绯荤?涓????颁???纭???绫婚????杈?灏???瀹?楠?璇?????杩?浜?绫绘?寮???????绌朵?浠???娣变?浜轰滑瀵瑰?????韩????瑙ｏ????朵?涓烘?????╃???????????╃??绛?瀹?楠?绉?瀛﹀甫?绘?扮?????????ㄥ?????︿??归???寮?????璁虹????绌跺?ㄨ?浜?骞翠???寰?浜?涓?浜??扮??杩?灞?锛??瑰????????ㄦ????剁?????轰互??涓???瀛?淇℃?????缁?????杩?浜?缁?绫绘?寮???????绌舵???轰??扮??????锛?涔?娉ㄥ?ヤ??伴?琛?娑层???翠负??瑕????????杩?瀵硅?浜?妯℃??绯荤?????绌讹???浠?????藉???缁???绛?渚?濡???寮??????虹?版??澶?????锛??? ??褰???瀛?淇???稿???瑕??讹??剁┖浼?????浠?涔?锛???杩??风???烘?????[49]??????浠ュ??涓?ā??涓轰?锛?绠?瑕??颁?缁?浠ヤ??归?㈢??涓?浜????茶??????杩?灞???绫绘?寮??????????瀛??鸿???骞夸??稿?璁恒??娴?浣???瀛︺????绾挎?х?╃??????瀛?淇℃???????????╃??绛?棰?????浜ゅ??璇鹃???杩??朵腑浠讳?涓?涓??归?㈢??杩?姝ラ?芥?????戒负杩?涓??瑰??????绌跺甫?ユ?扮??绐??淬?????凤?绫绘?寮???????绌朵?浼?瀵逛?杩扮?稿?抽???甯︽?ヤ?杩?浣??ㄣ???镐俊杩?涓???绌朵??ㄥ??ヤ????扮???浠?甫?ユ??????
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