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????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??
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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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