Резольвентные пределы квантовой эволюции открытых систем (1104643)

Просмтор этого файла доступен только зарегистрированным пользователям. Но у нас супер быстрая регистрация: достаточно только электронной почты!

Текст из файла

 !"#$&%'$)( !"*+,$- ./0*# 12345768 9;:=<;>;:@?A:CBD>FEFGIH@<;JLKMJN#O=PRQTSUWVYXZ/[I\^]7Z_QF`acb,a/dcUWVWa8efRgihkjl( mn%ngRoqplo2r g stfRgvu wg ( r} %~jl(  €tt j‚plxtfYr ‚p r ƒxt%zytoqplj %{j2|„…†„~pqgY‡_ˆŠ‰Œ‹WŠŽW‘“’Š”–•˜—=‘F™;š;›œžš–ŸTœ š“¡_¢ £¥¤“¦ HA> ¦§¤ J;¨ ¦ KMG©:Cª¬«#J©­®J;G©:©¯° ±²´³*µ·¶3¸=¶·µ°²,¹ŠJLKMK ¦ > ¤ :º;JLJw9;:=KMH@J;K§G©:@9LJ ¦ EF¨L»M9;H@¼¬K ¤A¦ < ¦ 9;JG©:9©¹WJ©¹Š: ¤ :=«#JF­J;GIHC½¿¾À: ¤“¦ ¾·: ¤ J;¨ ¦ KMGLJ©BÁ9T:EFG œÂ H@KMGL?“: ¡šAš@ÃÄTÅÇƌȌÉÊÅ˘ÌÍCȘÎCÏCÐÑϝÅϝÅҥŘÓ/ÐÕԖÖCÐ3ÒC˧ÅÊÏCɘȌˌȌ×#ØÙɘÅÇɌږØÕɘÚCÒ¥Ú#ÚɌÐÑȌ֥ÚCÚÍCȘÎCÛÓ_ÚCÜÑÚCÝ¥ÐÞØÙҐȘßàÈÓÅÊÒCáâΖãÇɘÐÑÉÊÅäȧØÕÒMȌËMØÙҐȌßÑÈßàȧØÕáàÔAÅÇ֝ØÙɌ˘ÐàÏ¥ÏCȌßÑÈáÏ¥ÚCˌÐÑ֝ØÙÚCɘÐÑɘÅÚCåæCäçæ¿è/æ&éȌåWȌÏCȧØÕȘËMÅCæêÀÅàáÝCÏCÌ+×,ÖCáÒÈ˜ËŒÈâԝÚCɘÐÕΖãëԝȌÒCÉ˜ÈŒÖ Ó_Ú¥ÜàڥҐȘìíåÅÊɘÐÑåÅÊɘÚCÝCÐâØÙÒCÚ¥î ϝÅâáÒï æÙä=æÙð/ÐÑƌȌÉÊÅÊÖCñÑËò Ó/ÚCóCڝÅÞΖãŒÏCÌ+ÐÀȌÍCÍCȘÏCÐÑÏCɘ̷ëԝȌÒCÉ˜ÈŒÖ Ó_Ú¥ÜàڥҐȘìíåÅÊɘÐÑåÅÊɘÚCÝCÐâØÙÒCÚ¥î ϝÅâáÒò æÙô“æÕõöåWÈÊÎCÛCÏCȘËÒ¥ÅÊϮԖڮÔAÅÊÉÓ_Ú¥ÜàڥҐȘìíåÅÊɘÐÑåÅÊɘÚCÝCÐâØÙÒCÚ¥î_ϝÅâáÒ÷æÙÄ;æøéáÆŒÐÑÏCÐÑóèöÐÙԝáùÅÇÛȌÖCßÕÅÊÏ¥ÚCÜâÅÊóCÚ¥ÛIëäúÅÇɌÐÑåÅÊɘÚCÝ¥ÐÞØÙÒCÚ¥×,ÚCϝØÙɘÚCɘáÉ4Ä ï êÚCåæCè/æ ï æÑõöɘÐÑҥΖȘËMÅû ÅÊù3ÚCÉÊÅ=ØÙÈMØÙɘȌÚCɧØüÛiýþàÿ Ï¥ÈÞÛCƌ֧یÿ7ßÙæWËDþàÿ7ݝŌؘæåWڥϩæŠÏÅ7ÜâŌØÙÐÕÔ@ÅÊÏCÚCÚ Ô–ÚØ¿ìÙØ ÐÑÖCÉÊÅÊóCÚCȘÏCÏCȌßÑÈ ØÙȌˌÐÑÉÊÅCþ˜æ¥þŒæ þ äÈMØÙҐȘËMØÙҐȌßÑÈ ßÑÈMØÙáàÔAÅÊ֝ØÙɘˌÐÑÏCÏCȘßàÈ áÏ¥ÚCˌÐÑ֝ØÙÚCɘÐÑɘÅÚCåæFä=æÙè/æ&éȌåWȌϥÈMØÙȌËMÅ´ÍCÈ ÅÞԝ֥ÐÞØÙá“ëŠþŒþ,ô;õcì©äÈMØÙÒC˧ŠéÀÐÑÏCڥϝØÙÒCÚCÐßÑȌÖCÌ©äúôÓ/ÚCÜÑÚCÝCÐâØÙÒCÚC×ÓÀÅÇÒCáâΖãÇɘÐÑɖÅâáàÔLæ æõ ԝڝØÑØÙÐÑÖCÉÊÅÊóCÚCȘÏCÏCȌ׬֖ÅÊƌȌɘȌ×ÁåWÈ Ï¥È È˜ÜàϖÅÊҐȌåWÚCɧØüÛDË Æ˜ÚCƘΖÚCȘɌÐÑҐРÓ_ÚCÜÑÚCÝ¥ÐÞØÙҐȘßàÈÓÅÊÒCáâΖãÇɘÐÑÉÊÅäúô æï ˌɘȌÖCÐàÓ/Ðà֖ÅÊÉ֝ÅÊÜÑÈMØ¿Î@ÅÇÏ ýȌÒCÉâÛCƌ֧یÿ3ßÕæ8ÝCñÑÏCÌ×ØÙÐàÒ¥ÖCÐÑɘÅÇÖCãԝږØàØÙÐÑÖCÉÊÅÊóCڥȌÏCÏCȌßÑÈ ØÙȌˌÐÑÉÊÅCþŒæ CþŒæžþÀË ä#ô!ԝȘÒCɘȌÖÓ/ÚCÜÑÚCҐȘìíåÅÇɌÐÑåÅÊɘÚCÝ¥ÐÞØÙÒCÚ®îϝÅàáÒ"ÍC֥ȧÓ_ÐâØÑØÙȌÖæï æ#/ȘÎCۥҐȌË$%'&(*)+(-,.(-/10324,157680351/9(,7(-%;:;03<³ ¤ ;G >HJ ¤ :–ªlG;?A:@9 ¤ H@?“:CªqK§J;K ¤“¦ ¾·:n<L> ¦ ¹WK ¤ :?#K;ª ¦Œ¤K§HML@HA¼ G;?A:@9 ¤ H@?EAN KMJ;K ¤“¦ ¾/EPO ?–­¥:J;¾H¹ ¦ ¼LK ¤ ?EANRQ EAN KiGAKŠ:KMK§J;¨ ¦ KMGLJ;¾ JAKTJGL?“:9 ¤ HA?GJ¾ H@G;>©E!S ¦ 9;J ¦ ¾ T > ¦ ­ ¦ >L?E :>;H@¾VUWO4J;¾ ¦ NRQJL¾ L@H#KYXGZH ¦ JAKTJ[L ¦ K˜½GIH@9 ¦ ¨;9;H ¦ ¨;J;KKWHiK ¤“¦ < ¦ 9 ¦ ¼~KM?@GH LAHY¹ J ]œ \ >;J;¾ ¦ >T:¾ÀJ~H ¤ GL>^J ¤ JB~KMJLK ¤A¦ ¾2¾HC½_˜E ¤ KKLE!S J ¤ X=G;>LJ;K ¤ #: KHKWJ;¨ ¦ K§G©:–ª¬K ¤ >FEFG ¤ EF>TA: O;H ¤ ¹ ¦ KYX@^9 J¼¬: ¤ H@¾ "J KWJDJ;9 ¤A¦ >I½« ¦ >;H@¾ ¦§¤ >`O ?–­¥:J;¾H¹ ¦ ¼;K ¤ ?–AE N3Q7J ¦ bK aK ¦ G ¤ >;H@¾·c: _M9LJ ¤ ^9 J¾‚JFd­ KLEF¨ ¦ 9;J ¦ ¾ AJ KTJ¹W>FEA_MJL¾Ji?@9 ¦ Z9LJ;¾J <;#H K;ª;¾J O < ¦ > ¦ 9;H@KÞ^ª Q7J;¾eJ a9 ¦ H> _M^J N œ ² HA¨L9;H ¦ > ¦ Z ¦ 9;J ¦EF>;:@?@9 ¦ 9;JFª OHA<LJ;dK J?AG: NRQ ¦ _MfH aM?A#H KYN´º;^J N H ¤ G;H> J ¤ H@¼lK§J;K ¤“¦ g¾ JhOGH LMJ¨;9LHn9 ¦J©­®? ¦ K ¤ 9;HçJÁ<;cH a ¤ HA¾/E >T:KMK§¾À: ¤ >;JL?“: ¦§¤ KÞ1ª LA#H K ¦§¦ <;>;H@K ¤ :–iª a?@cH KjNºLJFª¬G;?A:9 ¤ H–½?@HA¼zKMJLK ¤A¦ ]¾ J E K§> ¦ ¹Š9;»§9;9;:–ªY<LHwKMH@K ¤ H®ª;9;HJ N H@G;>©!E S ¦ 9;JFkª T > ¦ ¹;EFº;JL>;H@?“:9;9;:–ªaM?A#H KYN´º;JFYª U œ± GL?“:9 ¤ H@?AH@¾RK K;EF¨;: ¦ O > ¦ ¹TEFº;JL>;H@?“:9;9;:–ªç¹WJ;9T:¾J;G©:#HA<LJ;dK J?A: ¦Œ¤ KÞª GL?“:9©½¤ HAG? J¾tGLJ;9 ¦§¤ J;¨ ¦ KMGLJ;¾tEF>;:@?@9 ¦ 9;J ¦ ¾ j¹ K;ª~¾À: ¤ >LJ;Hº J A< KTH ¤ 9;H@K ¤ J~"J KWJY¹W?AH@¼©½K ¤ ? ¦ 9L^9 J¾¬EF>T:?@9 ¦ 9LJ ¦ ¾Áj¹ KLªúHA< ¦ >T: ¤ HA>LHA?JF­: KY_ ¦ LA> ¦ 9Tc: LcKjN¹: ¦ ]¾ JB œ ± J ?@H¹¤ ldœ lnœ m MH _§cH KjN3L@H–½GL?“:9 ¤ HAG? JB G;J;9 ¦§¤ J;¨ ¦ KMGLJ©B EF>;:@?@9 ¦ 9;JL`¼ OF9T:®¨;J;9;:–ªkK>;G: L@H b?AH: O8J~JLKMK K ¦ ¹WHA?A:9;^9 JB~? >Tc: LAH ¤ :¥pB o œ µ nœ \ >;^J _§qH S J;9;H: O?r œ ?A:t9 s,HA?AA: O ¶ œ u aŒ½?@J;KMH: O ° dœ vœ s*#H K ¦ ?AHH O v´œ ± nœ w H–q­ J> ¦ ?“A: O^o œ ± œ ± cH KTHA?@J;¨;H: OFH ¤ 9LHAK§J ¤ KÞª Gk¨LJ;K KLE:G ¤ EI: KYX@^9 JBz­¥:¥¹:¥¨YKMH@?A> ¦ ¾ ¦ 9L9;H@¼{¾À: ¤“¦ ¾·: ¤ J;¨ ¦ KMGIH@¼^«#JF­J;GLJ œ ³ LMQ7J;¼Y?AJI¹aM?A#H KYN´º;J;H@9;9LMH _§HkEF>;:@?@9 ¦ 9;J©`ª O >T:C­®> ¦ ZG: NRQJL¼"HA< ¦ >T: ¤ HA>"GIH ¤ HA>LMH _§H ¢ GL?“:9©½¤ HA?A:Cª~¹ŠJ;9;:@¾JL¨ ¦ K§G©:–ª<;#H K;AE _M>©EF<;<;: ¢ >;:@?@9;H@¾ ¦ >;9LHR9 ¦ <L> ¦ ^> J? ¦ 9 J J;¾ ¦§¦§¤?@J©¹{?@<;#H KW9 ¦ <LcH KTqH S J ¤A¦ KjXA9LMH _§HwH ¤ MH L@>T: S ¦ 9;J©`ª OKMHBL>;:@9©^ª N3Q ¦ _§H ¦ ¹ŠJ;9LJ;¨L^9 J¼H@< ¦ >T: ¤ H@`> OLMJ8KHA<LJ;KM:@9 x œ r#J;9ID¹ L#KŠ:¥¹ŠH@¾"J OC9 ¦ ­®:@?@J;K§J;¾^H O ± œ xIH@>;JL9;`J O ° nœ w H@K˜½KM:@GIH@?AK§G;JL¾ J ¶ dœ yœ u S nœ v E®¹:^> Z:9;H@¾ œ± ¹WJ;KMK ¦ > ¤ :@ºLJ;J <;H@G©:–­®:@9L^H O ¨ ¤ H7> ¦ Z ¦ 9LJ ¦ >“ª©¹Š:#­¥:¥¹:¥¨ OIK§?ªF­®:@9L^9 JB K4G? J½?@H¹:¾JÁ> ¦ Z ¦ 9;JL¼wGL?“:9 ¤ H@M? JBÁGLJ;9 ¦Œ¤ JL¨ ¦ KMG;JIBÁEF>;:@?@9 ¦ 9;JL`¼ O ¤“¦ KM9LHçKM?–ªF­¥:9;HçK¹W>FAE _MJL¾w"G KŠ:KMK§HA¾¬?A: S ^9 JB*­®:C¹Š:¥¨KMH@?A> ¦ ¾ ¦ 9L9;H@¼#¾À: ¤A¦ ¾À: ¤ JL¨ ¦ KMGIH@¼#«JF­®JLG;J ¢<L> ¦ ¹ ¦ KjXAH9 J ¾ < ¦ > ¦ B H¹ŠH@¾ G ¤ H@¨ ¦ ¨;9;H@¾/E ?–­¥:J;¾H¹ ¦ ¼LK ¤ ?AHJ N;OJ©­MEF¨T:G? ZJL¾ÀKÞª? >Tc: LAH ¤ :¥B ¸ œ ° œ m¦ > ¦ ­J;9TA: O3r Wœ u œ ¸ :C¹ ¦M¦ ?“A: O v´œ ° KYXGL ¦ >;J;HH O vœ x nœ w > ¦ ¼;9TA: Oµ œ ° œ  JLA9 KTHAKM:YJ ¹Š> œ ± > ¦ ­ME KjX ¤ : ¤“¦w¤ :GIMH _§HY< ¦ > ¦ BIHY¹ J ?AH–­®9LJ;G©c: N ¤ GL?“:9©½¤ HAG? J ¦ K ¤ HBI:@K ¤ JL¨ ¦ KMG;J ¦ ¹ŠJL«#« ¦ > ¦ 9Lº;J;#: KjXAH9 J ¦ EF>T:?A9 ¦ 9LJFª œ o,KMK K ¦ ¹ŠH@?“:9;J ¦ ¾w3vu*z ­¥:9;JL¾·: KWJLdK XHO®?¨T:K ¤ 9;H@K ¤ `J O µ œ r œ s:¥¹ŠKMH@9#J wœ µ dœ \ :> ¤ :K:>T: ¤ J œ ³ 9LJ>;:–­?A"J KW;J L@H­HA9L9;H ¦ J7« ¦ >L¾J;H@9;9;H ¦ K ¤ HBI:@K ¤ JL¨ ¦ K§G;J ¦ J;K§¨;J;K K ¦ 9;JFª O<LcH KLEF¨;"J KWJ9 ¦ GIH@¾À¾/E ¤ : ¤ J;?@^9 J ¦ :@9;#: KTMH _§J «#H@>;¾/E KYJ{o ¤ H œ ± >Tc: L@H ¤ :¥B ° œ  nœ y,¦ L@H ¤ :>;»§?“:<LHAG©:C­¥:9;HH OÀ¨ ¤ HR> ¦ Z ¦ 9;J ¦ GL?“:9 ¤ H@?AGH _MHzK ¤ HBI:K ¤ J;¨ ¦ KMGIGH _MH"¹ŠJ;«« ¦ > ¦ 9;ºLJT: KYXC½¦ w GH ZJz^¹ K;ªYEF>;:@?@9 ¦ 9;J©ª9LMH _§HwEF>T:?A9 ¦ 9LJFªYEF9;J ¤ :@>L9;.H aG;?@J;?A: K ¦ 9 ¤ 9LHv­®:C¹Š:¥¨ |= ?S >A@öQTZ?BDCcUFEG>HB>;[Ib,O1I}>;»Ê¹ŠJL9^_ ¦ >T:vK_ ¦ 9 ¦ >T: ¤ H@>;H@¾€OcGIH ¤ HA>HJ ¼Y> ¦ :#KTJF­ME ¦§¤ KÞª^G©:@GYKMJL¾¾ ¦Œ¤ >LJ;¨L9T:CªGL>T: ¦ ?A:–ª*­¥:¥¹:¥¨;: œ ± ¹ŠJLKMK ¦ > ¤ :º;JLHA9L9;H@¼ >;:GL@H ¤A¦ ?MJ?AHM¹ŠJ ¤ KÞª#<;> ¦ ¹ ¦ KYX@9^J¼ >T:C­§½> ¦ ZG: NRQJL¼YHA< ¦ >;: ¤ HA>Y?wKKLEF¨T: ¦ 9 ¦ GIHA¾¾/E ¤ JL>FEANRQJIBYHM_§>T:9;JL¨ ¦ 9L9^JB^HA< ¦ ½>;: ¤ HA>L^9 JB¬GIcH a«#«#JLº;J ¦ 9 ¤ H@? J¬<LHAG©:C­qJ?“: ¦§¤ KÞªw? ªL?A9LHA¾ ?AJI¹ ¦ 9T:KWJL¨;J ¦ G;>;:C½¦ ?AGH _MHE K KWH@?AJ©ª j¹ KLª¬<;> ¦ ¹ ¦ KYX@9;GH _MH _ ¦ 9 ¦ >;: ¤ H@>T: œv > ¦ ¹ŠJ"«JF­®JL¨ ¦ KMG;JIB"<L>;"J KWqH S ¦ 9LJ;`¼ OW^¹ K;ª"HA<LJ;KM:@9LJFª"GIH ¤ H@>^JB ?@H–­®¾HqS 9;H<L>;J;¾ ¦ 9 ¦ 9LJ ¦ > ¦ ­ME KYX ¤ : ¤ H@?7¹WJ;K§K ¦ > ¤ :º;J;H@9;9LHA¼Á>;G: L@H ¤ JhOL¾qH S 9;H 9;:–­?“: ¤ X ¾HC½¹ ¦ KYX@9FAE N ­¥:¥¹:¥¨©Eç?–­¥:J;¾H¹ ¦ ¼;K ¤ ?@JFª GL?“:9 ¤ HA?@GH _MH#HAK§º;AJ KHK;ª ¤ H@>T:úKHAGL>F!E S ¦ 9;JI½¦4¾ OC<;> ¦ ¹ŠK ¤ :c? KL^ª N3Q7J;¾ KMGH L@HA¼7<FEF¨LHAG«#H ¤ H@9;H@? œ ² :@GLJ ¦ ­¥:¥¹:®¨;J?@H­9;J;G©c: N ¤ O–G<L>;J;¾ ¦ >FPE OŠ<;>LJv<;H@K ¤ >;H ¦ 9;JLJ ¾À: ¤A¦ ¾À: ¤ JL¨ ¦ KMGIH@¼v¾H¹ ¦ KWJD¹ ¦§¤A¦ G ¤ H@>T: _M>;:@?@J ¤ :C½ºLJ;H@9;^9 JB ?@cH KT9 Gœ u :9;9T:Cª ¾H¹ ¦ KYXúJF­MEF¨;#: KW:@nK X zœ r*NJLK ¦ K^KWH@€¾ O ± dœ m4dœ m >Tc: _MJ;9I½K§G;J;€¾ O ¸ nœ  œ s*#: KTAJ KT`J O wdœ m >;JL«#HA€¾ O ° œ  :9;H@4¾ O \ œ r nœ l :@¼ ¤ H@€¾ O ° œ ¸ nœ \*¦ ¼©½K§HA€¾ O  œ u S nœ w #H K^K ¦§¤ HA¾ wœ ± œ x©:>A¹ŠJ;9 ¦ >LHA¾Jk¹Š> œ‚w[“ƒZ BdcQW\ŠjU >L1O I o­§EF¨ ¦ 9;J ¦ ¾H¹ ¦ KYX@9^JBn«#J©­®J;¨ ¦ K§G;J©B{­®:C¹Š:¥¨`O_K§?ªF­®:@9L9^JBK ¤ H@¨ ¦ ¨L^9 J¾ ?–­¥:J;¾H¹ ¦ ¼LK ¤ ?AJ ¦ ¾ KMJ;K ¤“¦ ]¾ J J ¦ »¬H@G;>©!E S ¦ 9;JFª œ µ :@K§KM¾H ¤ > ¦ 9©½9 J ¦ ?i¹ŠJLKMK ¦ > ¤ :@ºLJ;J…­¥:¥¹:®¨;J ª;#? K;^ª N ¤ KÞª ¹WHAK ¤ : ¤ H@¨;9;HYK KTqH S ^9 J¾J K ¤ H@¨;GLJH­> ¦ 9LJFªD¾À: ¤A¦ ¾À: ¤ JLG;J <LHAK§GIcH KjXAG©E ?> ¦ ­ME KYX ¤ : ¤A¦ <;> ¦ ¹ ¦ KYX@^9 JBÁ< ¦ > ¦ B H¹ŠH@?7­®:C½¹Š:¥¨T: w GH ZJ†^¹ K;ªtEF>;:@?@9 ¦ 9;J©ª ~ >;»Ê¹ŠJL^9 _ ¦ >T:l<L> ¦ ?@>Tc: Q: ¦Œ¤ KÞª ? 9T:¥¨;#: KjXA9LH–½GL>T: ¦ ?–AE N­®:C¹Š:¥¨FEDK#H@< ¦ >T: ¤ H@>;H9 J ¾JwGIcH a«#«#JLº;J ¦ 9 ¤ :@¾J¬„? _M>T:9;JL¨;H9 JBÁE“K KTH–½?@JFª©B œ ± ¹ŠJLKMK ¦ > ¤ :@ºLJ;`J O ¤ :@bG S ¦ O <L>;H®ª;#? K;ª ¦§¤ KÞªkK§?ª©q­ X ¾ ¦ S=¹TE ¤ :G;J;¾J <;> ¦ ¹ ¦ ½KW:@¾J JkG;?A:9 ¤ HAG? J ¾J K ¤ HMB©:K ¤ J;¨ ¦ KMGLJ;¾J ¹ŠJ;«« ¦ > ¦ 9;ºLJT: KYX@^9 J¾JkEF>T:?A9 ¦ 9;JI½ª;¾J O;GIH ¤ H@^> J ¦ O;?=KM?@MH N†HA¨ ¦ > ¦ D¹ XHO;<;H–­®?@cH KL^ª N ¤ < ¦ > ¦ ¼ ¤ JÁGÁG;?A:9 ¤ HAG? J ¾ GLJ;9 ¦ ½¤ J;¨ ¦ KMGLJ;¾ EF>T:?@9 ¦ 9LJFª;€¾ OH@<;JLdK J?“c: N3Q7J ¦ E“KM> ¦ ¹W9;»M9L9FAE N…<;HKMH@K ¤ H®ª;9;HJ NH@G;>©E ½S ¦ 9LJFªÁ9 ¦ GH L@>T: ¤ JL¾_AE Na?@cH KjNº;HJ NKMJ;K ¤“¦ ]¾ J œ…[ >;U `_O ƒa EPE@Z/[@`ÀUWVŠYQ C8‡a †gI ± ¹ŠJLKMK ¦ > ¤ :º;JLJ~J;K§<;H#KYX–­MEAN ¤ KÞª{K ¤ >;HG_MJ ¦ ¾ ¦ ½¤ HD¹ Jq¾À: ¤“¦ ¾À: ¤ J;¨ ¦ KMGIH@¼Á«#JF­J;GLJ œˆw"Q @+?e CcjQ †‰C/UŠVT?a ŠPC/‹Q I µ ¦ ­§EKYX ¤ : ¤ Jn¹WJ;KMK ¦ > ¤ :@ºLJ;JçªL?cKLª^N ¤ KÞª 9;H@?GJ ¾J J K§H–½K ¤ H®ª ¤ ?çK K ¦ ¹;AE N3Q ¦ €¾ Œ›@3œ l :¼©¹ ¦ 9T:D:@K§J;¾< ¤ H ¤ J;G©: <LH K ¦ ¾ ¦ ¼LK ¤ ?“: >;:–­> ¦ Z:cN3Q7J©B H@< ¦ >T: ¤ H@>;H@?tEF>;:@?@9 ¦ 9;JFª ~ >;»˜¹WJ;H9 _ ¦ >;:´K _˜:@¾AJ KjX ¤ HA9LJT:9;H@¾ K39 ¦ GIH@¾À¾/E ¤ J;>©AE N3Q7J;¾JH _M>;:@9LJ;¨ ¦ 9;H9 J ¾JkGIGH aM«#«#JLº;J ¦ 9 ¤ :¾`J O@¹ ¦ ¼LK ¤ ?AE NRQ ¦ ¾^? <L>;H@JF­®? ¦ ¹ ¦ 9LJ;JG_§AJ KYXGL ¦ > ¤ H@M? JB <;>LHAK ¤ >;:@9LK ¤ ^? O Jç­¥:?@J;KÞ^ª Q7J;¾YH ¤ ¹ ¦ ¼;K ¤ ?@J ¤A¦ KYX@9;GH _MH <;:C½>;:@¾ ¦§¤ >T: α œ ± J ¨LJ;K K ¦ 9…K ¤ HBI:K ¤ J;¨ ¦ KMGLJ;¼…<L> ¦ ¹ ¦ K α → 0 O·GIH ¤ H@^> J¼«#J©­®JL¨ ¦ K§G;JúK§HAH ¤ ? ¦§¤ K ¤ ?–E ¦Œ¤ < ¦ > ¦ BIHM¹TEG ¤ H@¨ ¦ ¨L9;H@¾/E?–­¥:J;¾H¹ ¦ ¼LK ¤ ?AHJ N œ~Ÿ¡Fœ3\ H#K;EF¨ ¦ 9 ? ª;?@9;H@¾ ?@J©¹ ¦ <L> ¦ ¹ ¦ KjXA9HJ ¼;_ ¦ 9 ¦ >;: ¤ H@>7>;:–­> ¦ Z :cN3Q ¦ _§H4HA< ¦ ½>;: ¤ HA>;:HO+?GJ ? ¦ ¹ ¦ 9LHw<L> ¦ ¹ ¦ KjXA9LH ¦ EF>T:?@9 ¦ 9LJ ¦ OGIH ¤ H@>;H@¾/EiH@9z<;HM¹Š¨;JL9Fª©½¦Œ¤ KÞªÁJÁ<L> ¦ ¹ ¦ KjXA9LH ¦ GL?“:9 ¤ H@?AH ¦ K ¤ HBI:K ¤ J;¨ ¦ KMGIH ¦ ¹WJ;«#« ¦ > ¦ 9;º;J;:#KjXA9LH ¦EF>;:@?@9 ¦ 9;J ¦ ?=«#HA>L¾ ¦ s:¥¹ŠK§HA9;: ¢„\ :> ¤ :@KM:@>;: ¤ J œœ l :wH@KM9LHA? ¦ <;H#K;EF¨ ¦ 9;9LHA¼{:KMJL¾< ¤ H ¤ J;GLJ^<L> ¦ ¹ ¦ KjXA9LHM_§H HA< ¦ >;: ¤ HA>;:w<LH–½} 3K ¤ >LH ¦ 9;H ¤ H@¨;9;H ¦ > ¦ Z ¦ 9;J ¦œŸTœ ³ KM9LHA?GJ?“:Cª;KdXÁ9T: ª;?@9;H@¾q?@J©¹ ¦ <L> ¦ ¹ ¦ KjXA9LHM_§Hw>T:C­®> ¦ Z:GNRQ ¦ _MHÁHA< ¦ >;:C½¤ HA>;:*JF­MEF¨ ¦ 9;h: a?@cH KjNºLJFªç>;:–n­ KWJL¨;^9 JB H ¤ G;^> J ¤ JB=GL?“:9 ¤ H@M? JB=KMJLK ¤A¦ €¾ O?7¨;:@K ¤ 9LHAK ¤ J O©G;?A:9 ¤ HA?@MH _§H HAK§º;AJ KHK;ª ¤ H@>T:7K ¹ŠJLKMK§J;<T:º;J ¦ ¼ OL?–­¥:J;¾H¹ ¦ ¼©½K ¤ ?–AE N3Q ¦ _§HúK JFd­ KLEF¨ ¦ 9;J ¦ ¾^<;>LJ 9T: KWJL¨;J;J KM"J KYJhO@¹ ¦ ¼;K ¤ ?–AE N3Q ¦ ¼ 9;:#H@K˜½ºLAJ K^KLª ¤ HA> ?œ w a ¤ H@¼ S ¦ ­¥:¥¹:¥¨ ¦ <;>LJ;¾ ¦ 9L»M9 ¹Š>©AE _MH@¼R<;H¹LBIH¹ ¢ > ¦ Z ¦ 9;HK ¤ HBI:K ¤ J;¨ ¦ KMGIH ¦ ¹ŠJL«#« ¦ > ¦ 9Lº;J;#: KjXA9LH ¦ EF>T:?A9 ¦ 9LJ ¦ j¹ K;ª¬> ¦ ¹TEFº;JL>;H@?“:9©½9LHA¼¬¾À: ¤ >;JL^º J "< KWH ¤ 9LHAK ¤ J¬HAK§º;"J K^K;ª ¤ H@>T: ?çGIHAH@>A¹ŠJL9T: ¤ 9LHA¾<;> ¦ ¹ŠK ¤ :?–½K ¦ 9;JLJ œœ \ H#K;EF¨ ¦ 9;H GL?“:9 ¤ H@?AH ¦ GLJ;9 ¦§¤ J;¨ ¦ KMGIH ¦ EF>;:@?@9 ¦ 9;J ¦ ¹^K;ª"<;>LHAJ©­®?@HcKjXA9LHA¼Ž 39;G: L#KYN¹Š: ¦ ¾ÀH@¼wK#J;KM<LcH KjX­HA?A:9;J ¦ ¾ ª;?A9LMH _§H ?@J©¹:ç<;> ¦ ¹ ¦ KYX@9;GH _MH >T:C­®> ¦ ½ZG: NRQ ¦ _MH=H@< ¦ >T: ¤ H@>T: œ[IUWdc[ >Lacec"[ E@S^Q †va cdcQT?S >Lacec"[ E@S^Q †’‘/[ C‡C/DU EM>HBI µ :cLAH ¤ :49LHAK§J ¤¤“¦ HA> ¦§¤ J©½¨ ¦ KMGLJ;¼zB©:>T:G ¤A¦ > œ µ ¦ ­ME KjX ¤ : ¤ J ¹ŠJLKMK ¦ > ¤ :@ºLJ;J{¾GH _ŒE ¤ LMJ ¤ XvJLKM<;#H KYX–­®H@?A:@H9 JK§< ¦ ºLJT: KWJLK ¤ :¾`J OA>Tc: LAH ¤ c: N3Q7J;¾J ?*MH L#KŠ:K ¤ J=J;KMK K ¦ ¹ŠH@?“:9;J©ª K ¤ HMB©:K ¤ J;¨ ¦ KMGLJ©B¹WJ;«#« ¦ > ¦ 9;º;J;#: KjXAH9 JB EF>T:?A9 ¦ 9LJ;`¼ O“H ¤ GL^> J ¤ JBçK§J;K ¤“¦ ¾Y?«#J©­®JLG ¦ bJ anK ¦ G ¤ >;HC½9LJ;G ¦@œ= /d8UŠ\ŠjQ ‘ca †"`_“a EPEA[I‡d >IjQ ‘ca88a I µ ¦ ­MEKYX ¤ : ¤ J^¹ŠJLKMK ¦ > ¤ :@ºLJ;J ¹WHAG"KŠ:¥¹DJ?“:KWJLKdX9;:=K K ¦ ¹TAE NRQJIB¬GIH@9;« ¦ > ¦ 9;ºLJFª©B Œl :EF¨L9T:Cª¬GIHA9L« ¦ > ¦ 9Lº;JFª £ r#HA¾H@9;H@KMH@?AK§G;J ¦ ¨ ¤A¦ 9;J©ª©½ ¡š@šAš ¯O••••¦ 9Lº;JFª £ r#HA¾H@9;H@KMH@?–½ ¡@š@š;› ¯ Ol¦ 9Lº;JFª £ r#HA¾H@9;H@KMH@?AK§G;J ¦ ¨ A¤ ¦ ;9 J©ª©½ ¡š@šŸ ¯ œl :EF¨L9T:Cª¬GIHA9L« ¦ > ¦ 9Lº;JFª q£ u ¦ ?–ª ¤ 9T:¥¹Šº;: ¤ J ¦ ¾ ¦ S=¹TEF9T:>;HM¹Š9^J '¦ \ K ¦ IB :C½9LHA?@KMGLJ ¦ ¨ ¤“¦ 9;JFªö¯ œl:EF¨L9T:Cª¬GIHA9L« ¦ >:EF¨L9T:Cª¬GIHA9L« ¦ >Žµ ¦ ­§EKjX ¤ : ¤ J ¹ŠJLKMK ¦ > ¤ :@ºLJ;J ¹ŠH@GAKŠ:¥¹DJ?A:#KTJ;KdX JkHGLAK˜E!S=¹:KWJ;KnX9T:7K ¦ ¾J;9;:@>;:CBG©:« ¦ ¹W>^J G;?A:@9 ¤ H@?@HA¼çK ¤ : ¤ JLK ¤ J;GLJ J ¤A¦ H@>;JLJ <LHcKLª «JF­®JL¨ ¦ KMGIHG_MHú«ú:GFEKYX ¤“¦ ½¤ :  x z O;>FEFGIH@?AHM¹ŠJ ¤A¦ KjX ¢ :G©:¥¹ ¦ ¾JLG ± œY\œ  :@KKWH@? œ”@\;Z/acS+YQ ‘8acVa I ³ K§9;H@?A9HJ ¦ > ¦ ­MEKYX ¤ : ¤ Jq¹WJ;K§K ¦ > ¤ :º;J;JvHA<©EALcKTJ;GIH@?“:9^J ?9•>;G: L@H ¤ :CBÁ:? ¤ H@>TA: O;KM<LJ;KMH@G¬GIH ¤ HA>HJBD<;>LJ;? ¦ ¹Š»§9w?çGIH@9;º ¦ :? ¤ HA> ¦ « ¦ >T: ¤ : œ– >;‹d @‡S >A@d8Q~a UŠj\ —V˜Ib `ƒa EPE“[Id >IYQ ‘8acVa I u JLKMK ¦ > ¤ :@ºLJFª"JF­nKWHqS ¦ 9;: 9T: › }M™K ¤ >;:@9LJ;ºT:¥B~J~KMH@K ¤ HAJ ¤ JF­Á?A? ¦ ¹ ¦ 9LJFªnJ ¤ >;»˜fB _KW:@? ]œ m HJ LcKTJ;GH _M>T:«#J©ª K§H¹ ¦ >©½Ã š 9T:J;¾ ¦ 9LHA?A:9;J;¼ œS J ¤ ›,.(-03/:;26V:4œe24,„(-ž1512œe5.66V24,104(-Ÿ15:;ž1ž1:; ,.(-%;:'0¡<]=UzVWVŠ[@`[Ccaca ¹:» ¤ KÞªDHGL–­®H@>DJLKMKK ¦ ¹WHA?A:@9LJ;¼O;KM?–ªF­¥:9;9HJBDK ¤A¦ ¾HA¼ ¹ŠJ;KʽK ¦ > ¤ :@ºLJ;`J OA<;>;JL?AHM¹Tª ¤ KÞªçHA<L> ¦ ¹ ¦ K ¦ 9;J©ª H@KM9LHA?@9^JBç<;H@9Fª ¤ JL¼`O¹Š:@» ¤ KÞª=G;>T: ¤ G;J;¼HGL­HA>ÁH@KM9LHA?@^9 JBÁ> ¦ ­MEKjX ¤ : ¤ H@?¹ŠJLKMK ¦ > ¤ :º;JLJ œv K ¦ ¹TE ¦§¤ H ¤ ¾ ¦Œ¤ J ¤ XHO´¨ ¤ H­¥:¥¹:®¨T:AO>T:KMK§¾·: ¤ >;J;?A: ¦ ¾À:–ª†? ¹ŠJLKMK ¦ > ¤ :º;JLJ`O?lK KLEF¨T: ¦ EF>;:@?@9 ¦ 9;J©ª K GIH@¾¾/E ¤ JL>FEAN3Q7J;¾J H@< ¦ >;: ¤ H@>;9^J¾J GIHca«#«#JLº;JI½¦ 9 ¤ :¾`J O>T:KMK§¾À: ¤ >;JL?“: KŠ:dK Xv?w>Tc: L@H ¤ :¥B ° œ  nœ y,¦ L@H ¤ :@>L»M?A:HO u œ ± œ ± J;G ¤ H@>;HC½?AH: O  œ x > ¦ _MH@>T: ¤@¤ JRJ ¹W> œ ³ LAGH LMQ ¦ 9LJ ¦ a ¤ J©Bz> ¦ ­ME KYX ¤ : ¤ H@?¬9T: EF>T:?A9 ¦ 9LJ ¦ K9 ¦ GIH@¾À¾/E ¤ J;>©AE N3Q7J;¾J GIGH aM«#«#J;ºLJ ¦ 9 ¤ :¾`J O“?A#: S 9LH ¦ j¹ KLª <L>;AJ KTqH S ¦ 9;JL¼ ?#«#JI½­J;¨ ¦ KMGLJ©B ­®:C¹Š:¥¨T:¥B OIªLc? KLª ¦§¤ KÞª K KTqH S 9;H@¼kK ¤ H@¨;G;J ­®> ¦ 9;J©ªD¾À: ¤A¦ ¾À: ¤ JL¨ ¦ KMGIGH _MH:9T: KWJ©­¥: “œ \ H¹;B H¹~G^> ¦ Z ¦ 9L^J N a ¤ HA¼R­®:C¹Š:¥¨;J Oc>T:C­®?@J;?A: ¦ ]¾ J ¼^?¬¹Š:@9L9;H@¼{>;:C½L@H ¤A¦ OöK§HAK ¤ H@J ¤ ? K K ¦ ¹;AE N3Q ¦ ¾ ‹œ v 9T:¥¨;#: KW: J©­MEF¨;: ¦Œ¤ KÞª 9 ¦ GH LB H¹ŠJL¾ÀH ¦ E K KWH@?AJ ¦ OGIH ¤ H@>;H@¾/E~¹Š#H K^S ¦ 9 E®¹ŠH@c? K ¦§¤ ?AH@>“ª ¤ X^«#H@>;¾À#: KjXAH9 J ¢¼ _ ¦ 9 ¦ >T: ¤ H@>EF>;:@?@9 ¦ 9;JFª OK§HAH ¤ ? ¦§¤ K ¤ ?–AE N3Q ¦ ¾/E7<;> ¦ ¹ ¦ K;E ¤ H@¨ ¦ ¨;9LMH _§H#?–­¥:J;¾H¹ ¦ ¼LK ¤ ?AJ©ª œ £ : ¤A¦ €¾ O@K ¤ >LHAJ ¤ ½KÞª#<LcH KLAE _M>FEF<L<T:EF9LJ ¤ :>;H9 JB#H@< ¦ >;: ¤ H@>;H@^? OJ;¾ ¦ NRQ :Cª#9T:¼©¹ ¦ 9;H9 J ¼ _ ¦ 9 ¦ >;: ¤ H@`> OJzE“K ¤ :@9;:@#? KWJL?“: ¦§¤ KÞªYHM¹Š9;H–­®9;:¥¨;9;:–ªYKM?–ªFq­ Xw¾ ¦ S=¹TEz<L> ¦ ¹ ¦ KjXAH9 J ¾tJ _ ¦ 9 ¦ >T: ¤ HC½>;:@¾J=J w3vu*z O–^¹ K;ªçGIH ¤ H@>;GH _MHJF­? ¦ K ¤ ^9 J ¤A¦ H@> ¦ g¾ J K˜AE Q ¦ K ¤ ?AH@?“:9;J©ªçJ ¦ ¹ŠJ;9I½K ¤ ? ¦ 9L9;H@K ¤ J†> ¦ Z ¦ 9;J©ª œ ² :@GLJ;¾ MH L@>T:C­®H@€¾ O4MH L@HAK§9;H@M? J?A: ¦Œ¤ KÞª K˜AE Q ¦ K ¤ ? ¦ 9;9T:CªKM:@¾H@KMH@<;>“Aª S »M9L9;H@K ¤ XR>T:9 ¦§¦ 9;:@¼I¹ ¦ 9;^9 J¤B _ ¦ 9 ¦ >;: ¤ HA>LHA? œ ± #: S 9LHRH ¤ ¾ ¦Œ¤ J ¤ XHO¨ ¤ H KM?–ªF¥­ Xi¾ ¦ S=¹TE{H@< ¦ >T: ¤ H@>;H9 J ¾J GIcH a««#J;ºLJ ¦ 9 ¤ :¾ÀJ{J;KâB H¹Š9LMH _§H"EF>;:@?@9 ¦ ½9LJFª¬JÁ<;> ¦ ¹ ¦ KYX@9;H@¼Á­¥:¥¹:¥¨LJ ª;c? KLª ¦§¤ KÞª¬KŒAE Q ¦ K ¤ ? ¦ 9L9;Hç9 ¦ KWJL9 ¦ ¼;9;H@¼ œ] c[IdcVWYU ¦ §Z/QŠVŠ[ >;:@K§KM¾À: ¤ >;JL?“: ¦§¤ KÞª2:KMJ;¾< ¤ H ¤ JLG©: <;H K ¦ ¾ ¦ ¼;K ¤ ?A:t>;:–­> ¦ Zc: N3Q7J©B=H@< ¦ >T: ¤ H@>;H@?,EF>T:?A9 ¦ 9;J©ª ~ >L»˜¹ŠJL^9 _ ¦ >TA: O­¥:?AJLKÞ^ª Q ¦ _MHH ¤ ¹ ¦ ¼I½ÃK ¤ ?@J ¤A¦ KjXA9LHM_§HD<T:>T:¾ ¦Œ¤ >;: α J >T:KMK§¾À: ¤ >;JL?“: ¦§¤ KÞªiK ¤ HMB©:K ¤ J;¨ ¦ KMGLJ;¼i<L> ¦ ¹ ¦ Kœ z ¤j¤¦ ¤¦~ >;»Ê¹ŠJL9©½α → 0 ¨LJ J ?A:Cª`O¨ H GIHca«#«#JLº;J 9 J†J;KâB H¹W9;HG_MH EF>T:?@9 9LJFª_ ¦ >T:9 ¦ ­¥:?AJLKÞª ¤ H ¤ ?@> ¦ ¾ ¦ 9;J`O¥<;H#K;EF¨ ¦ 9L9^JB7H@º ¦ 9;H@G¹ŠH@K ¤ : ¤ H@¨;9LH¹jKLª7?GJ¨;J;KʽK ¦ 9;J©ª ?#ª;?@9;H@¾^?@J©¹ ¦ <L> ¦ ¹ ¦ KjXA9LHM_§H¨_ ¦ 9 ¦ >T: ¤ HA>;: >;:–­> ¦ Z :cN3Q ¦ _§H H@< ¦ >;: ¤ H@>T:J'G? J ?@H¹Š:{<L> ¦ ¹ ¦ KjXA9LMH _§H{EF>;:@?@9 ¦ 9;J©`ª OGIH ¤ HA>LHA¾/E…H@9'<LH¹Š¨LJ;9©ª ¦§¤ KÞª œ ² :GAS ¦? J ?@H¹WJ ¤ KÞª <L> ¦ ¹ ¦ KjXA9LH ¦ GL?“:9 ¤ HA?@H ¦ K ¤ HB©:K ¤ J;¨ ¦ K§GIH ¦ ¹WJ;«#« ¦ > ¦ 9;º;J;:#KjXA9LH ¦G¢ \ :@> ¤ :@KM:@>;: ¤ J Aœ £ : ¤“¦ €EF>;:@?@9 ¦ 9;J ¦ ?7«#H@>;¾ ¦ s*:C¹WKMH@9T: ¾ O©9T: HAK§9;H@? ¦ <;#H K;EF¨ ¦ 9©½9LH ¦ :KMJ;¾< ¤ H ¤ JLG;J¬<L> ¦ ¹ ¦ KjXA9LMH _§H HA< ¦ >T: ¤ HA>;:çK ¤ >;H@J ¤ KÞª ¤ H@¨;9LH ¦ > ¦ Z ¦ 9;J ¦@œ\ E“K ¤ X¢¦ J KYXGL ¦ > ¤ H@?AH#<L>;H@K ¤ >T:9;K ¤ ?@^H O¢¦H <;>LHAJ©­®?@cH KjXA9LH _§AB(H) : KY_ LC½>;: MH _§>T:9;JL¨ ¦ 9L^9 JB H@< ¦ >;: ¤ H@>;H@?=¹ ¦ ¼;K ¤ ?–AE N3Q7J©Bw? H O ΓS (L2(R)) ¢ K§J;¾¾ ¦§¤ ½>LJ;¨;9LH ¦ «#H@GIHA?@KMGIH ¦ <;>LHAK ¤ >;:@9LK ¤ ?AH œ µ :KMKM¾H ¤ >LJ;¾ EF>T:?@9 ¦ 9LJ ¦ j¹ KLªúH@< ¦ >;: ¤ H@>T:aM?A#H KYN´º;J;J UtdUtT › U= iHUt , U (0) = IdtK1_˜:@¾J"KYX ¤ HA9LJT:9;H@¾ H O_¹ ¦ ¼;K ¤ ?–EAN3Q ¦ ¾ ? ¤A¦ 9F­HA>L9;H@¾ <;>LHAJ©­®? ¦ ¹ ¦ 9;JLJ H =¦= H ⊗ ΓS (L2 (R)) Oj_â¹T¡ UH = H0 ⊗ I − I ⊗ i∇ + H©ª¬« ,<L>;J;¨ ¦ ¾H©­ª®« = K ⊗ Λ(g) + R ⊗ A† (g) + R∗ ⊗ A(g),¢¦¦¦¤K ∗ = K O H0∗ = H0 J R HM_§>T:9;JL¨ 9L9^J HA< >;: HA>HJOZZ†Λ(g) =dx g(x) a (x)a(x), A(g) =dx g(x) a(x),A†(g) = A∗ (g) O g ∈ L1 (R) ∩ L2 (R) ∩ C(R) O a(x)Ja† (x)¢ <AKTH ¤ 9;H@K ¤ JH@< ¦ >T: ¤ H@>;H@? EF9;JL¨ ¤ HqS ¦ 9;J©ª¬J¬>;HqS=¹ ¦ 9LJFª œ± ¾ ¦ K ¤ H «J;GIKMJL>;H@?“:9;9LHA¼q«,EF9;G;ºLJ;J O?–B H¹;ª^Q ¦ ¼q? HA<L> ¦ ¹ ¦ K ¦ 9;J ¦ _˜:¥½g¾AJ KjX ¤ HA9LJT:9T: H©­ª®« OgL–E®¹ ¦ ¾ >;:@K§KM¾À: ¤ >;JL?“: ¤ XzK ¦ ¾ ¦ ¼;K ¤ ?@Hz9 ¦ H ¤ >;J;º;: ¤A¦ KjXA9HJB«#JL9;J ¤ H9 JBi«*EF9;GLº;JL¼ gα(x) ∈ C ∞(R) O α ∈ (0, 1] O+GIH ¤ HA>LH ¦ J;¾ ¦M¦Œ¤ <;> ¦ ¹ ¦ ½0KTHA¾~¹ ¦ KjX ¤ :¥½¿«*EF9LG;º;HJ N;Œlimα→0Zf (x)gα (x) dx = f (0)¹^K;ª KYNRLAH@¼ 9 ¦ <;> ¦ >^J?A9LHA¼ HG_M>;:@9LJ;¨ ¦ 9;9LHA¼ «*EF9LG;º;JLJ f Oz<L>;J;¨ ¦ ¾ ¹ŠJ;:C½¾ ¦§¤ > dg (α) 9LHAK§J ¤A¦ KLª¬«*EF9LG;ºLJ;J gα K ¤ > ¦ ¾J ¤ KÞªÁGD9FEKYN<;>LJ α → 0 œYv «#JI½­J;¨ ¦ MK GIH@¼ ¤ H@¨;G;J ­®> ¦ 9;J©ª`O ¤ :@GIH@¼k<;> ¦ ¹ ¦ K¬K§HAH ¤ ? ¦Œ¤ K ¤ ?–E ¦Œ¤ ¾H¹ ¦ KTJ ¤ H@¨ ¦ ¨;9LHM_§Hš?–­¥:J;¾H¹ ¦ ¼;K ¤ ?@J ¦ ¾'K§J;K ¤“¦ ¾gJ†K7H@G;>FE!S ¦ 9LJ ¦ ¾ œ ¸ HA>L¾À:#KjXA9HJ ¼ <;> ¦ ¹ ¦ KiK ¦ ¾ ¦ ¼©½K ¤ ?A: _˜:¾JAKYX ¤ H@9;J;:@9LHA? lim H©­αª®« ª;?#K;ª ¦Œ¤ KÞª1¯°^±^²³G´Hµ!¶D±F·*¸!·#¹º‡³j»„¼±H±^½€º¾·¿DÀÁα→0¶Â!Ã#·d¶`·º€O ¤ :G=G©:Gç> ¦ ­§EKjX ¤ : ¤#¦ _MH¹ ¦ ¼;K ¤ ?@JFªç9T:,? ¦ G ¤ HA>HJ ?@J©¹Š: ψ(v) ⊗ r OG_â¹ ¦¢¦ ¦ ¤¦ ¤¦ψ(v) ∈ ΓS (L2 (R)) GIMH _ > 9 9^J¼D? G H@>`O v(0) = 0 O r ∈ H OF>T:? 9 9FEKjN;O: KWJL9 ¦ ¼L9T:CªwMH L@cH KTHA¨LG©: ¤ :G;J©BD? ¦ G ¤ HA>LHA?ç<"KWH ¤ 9;:=? H œ;± ¹Š#: KjXA9 ¦ H¼ Z ¦ 4¾ OG_â¹ ¦ a ¤ H,9 ¦ <L>;J;?@H¹WJ ¤ G <FE ¤ :9;JLº ¦ OGL–E®¹ ¦ ¾zH@<FE“KMG©: ¤ X,J;9I½¹ ¦ GIK α Mœ v KLEF¨T:`¼ OGIMH _⹊:,H@< ¦ >T: ¤ H@^> J K O R J H0 GIH@¾¾/E ¤ JL>FAE N ¤ O–>;:@K§KM¾H ¤ > ¦ 9? Ä ŽÅ œ ± ¹ŠJLKMK ¦ > ¤ :@ºLJ;H@9;9;H@¼=>Tc: LAH ¤“¦ >;:@K§KM¾À: ¤ >LJ;?A: ¦Œ¤ KÞª GH L@MH LGQ ¦ 9;J ¦ 9T:K KLEF¨T:¼b9 ¦ GIH@¾À¾/E ¤ J;>©AE N3Q7J©BÁH@< ¦ >T: ¤ H@>;H@? œµ :KMK§¾ÀH ¤ >;J;¾ EF>T:?@9 ¦ 9LJ ¦ T › UÁ?…<L> ¦ ¹ŠK ¤ :@#? K ¦ 9;J ¦ ?–­¥:J;¾H¹ ¦ ¼LK ¤ ?AJ©`ª O´<LH–½>LqH S=¹: ¦ ¾H ¦ H@< ¦ >;: ¤ H@>;H@¾ Hb0 = H0 ⊗ I − I ⊗ i∇ O;9 ¦ ­¥:?AJLKÞ^ª Q7J;¾ H ¤ g ŒK_˜:¾ÀJ"KYX ¤ H@9;JT:9;H@¾e (t)dUe (t),= iH(t)UdtbT} Ue (t) = e−iHb0 t UtUbH(t) = e−iH0 t H©­ª®« eiH0 t_⹦TŸ U= K(t) ⊗ Λt (g) + R(t) ⊗ A†t (g) + R∗ (t) ⊗ At (g),K(t) J R(t)>;: ¤ HA>LHA?:*H@< ¦ >;: ¤ H@>^J¢ 9 ¦ <;> ¦ >^J?@9^J ¦ <LH*9;H@>;¾ ¦ K ¦ ¾ ¦ ¼LK ¤ ?“:,HG_M>;:@9LJ;¨ ¦ 9;9HJB=H@< ¦ ½K(t) = e−iH0 t KeiH0 t ,R(t) = e−iH0 t ReiH0 t ,¤¦Λt (g) O At(g) J A†t (g) = A∗t (g) ª;?#K;ª^N KÞªç9 HM_§>T:9;JL¨Z−t∇t∇Λt (g) = e Λ(g)e =dx g(x − t) a† (x)a(x),Z−t∇t∇At (g) = e A(g)e =dx g(x − t) a(x).¦ 9L9^J¾J`Œ± G©:¥¨ ¦ K ¤ ? ¦R¤ H ¤ :KYX@9;HG_MH¾9;H¥S ¦ K ¤ ?“:AO­¥:¥¹:cN3Q ¦ _§HHML#KŠ:K ¤ XH@<;> ¦ ¹ ¦ K ¦ L9 JFªŠ¹ :@9L9^JB¬H@< ¦ >T: ¤ H@>;H@?HOT?AH–­qX@¾»M¾pKWJL9 ¦ ¼L9FEANtHML@H#KWH@¨;GFE Lε ¾À9LHqS ¦ K ¤ ?A:EεS = φ(f ) : φ(f ) ∈ E S ,kf kB(H) 6 ε, kf kB(H)⊗L2 < 1, f ∈ W21(B(H), R) ,¦ S ¢ ¾9;HqS ¦ K ¤ ?@H GIHG_ ¦ > ¦ 9EKTHA¨LG©: ¤ :@GIHG_MHú¾À9LHqS ¦ K ¤ ?A:#<AKWH¤ HAH> J ¢ K§JAKjXA9LH 9 ¦ <;> ¦ >^J?A9LH ¦_⹤ ^9 JBv? ¦ G ¤ H@>;H@?^Oœ¦0 < ε 6 1 r#J;9 ¼;9;:–ªvHGLAHC½¤ 9T:ú? S¤¦ ¦ ¦Γ (L2 (R)) Æ >T:KMKM¾À: >LJ;?A: ¾]J H@< >T:¥½<;H t K ¦ ¾ ¦ ¼LK ¤ ?AHkH@< ¦ >;: ¤ H@>;H@?^OT¹ ¦ ¼LK ¤ ?EANRQJ ¦™J©­EεS?ΓS (L2 (R))œDv <;H@¾HMQ;XMN†9 ¦ M_ Hç?@? ¦ Š¹ »M¾ KK ¦ ¹TEANRQ EANt9LHA>L¾/ED?_â¹ ¦Sp(X) = sup kXh ⊗ ψkH ,ψ,h<L>;JL¨;»M¾ψ ∈ Eε , h ∈ H,HŒTŽ UkψkΓS = khkH = 1.?AH@¼;K ¤ ?A:v<;> ¦ ¹Š9LHA>L¾gJ ¹jKLª p(X) <L>;H@? ¦ >“ª^N ¤ KÞª{9 ¦ <;H@KM> ¦ ¹WK ¤ ? ¦ 9;9;H œv ?@HA¼I½K ¤ ?@H 9;H@>;¾]J p(X) = 0 ⇒ X = 0 KK ¦ ¹TE ¦§¤ J©­'KWJL9 ¦ ¼;9;H@K ¤ J >T:KMKM¾À: ¤ >LJ;?A: ¦ ½¾]JB H@< ¦ >;: ¤ H@>;H@?J ¤ H ¤ :#KjXA9LHAK ¤ J ¾9;HqS ¦ K ¤ ?A: E S œcl H@>;¾À: p(X) HA<L> ¦ ¹ ¦ KLª ¦§¤εKTHAG©: KYX@9;HçG? J <©EFAG KLEAN ¤ HA<LHcKTHM_§J^N? H œRtRt\ E“K ¤ XœKΛ (t) = 0 K(s)Λs (g) ds J Kg (t, u) = 0 K(s)g(u − s) ds\ #H KWqH S JL¾vR(t, u) = e−iKg (t,u) e−iKΛ (t) R(t)eiKΛ (t)JÁ>T:KMK§¾H ¤ >;JL¾K ¦ ¾ ¦ ¼LK ¤ ?AHçH@< ¦ >T: ¤ H@>;H@?( ZtZτZiK(t)Λeα (t) = ef∗ (τ, u)R(s,e u)Uexp − dτ ds du R00× g(u − τ )g(u − s)v¦)Zt Z†e× exp i dw a (w) dτ g(w − τ )R(τ, w)0Zt Z∗f (τ, w) a(w)g(w − τ ) .× exp i dw dτ R0¾ ¦ ¼LK ¤ ?AH´HA< ¦ >;: ¤ HA>LHA? Uα(t) GIH@>;> ¦ G ¤ 9;HH@<;> ¦ ¹ ¦ K ¦ 9;H,9;: Lε(H) = Lε ⊗H O¦ _MHY­®:@?@J;K§J;¾H@K ¤ X{H ¤¦¦ ¦ ¤œl :@¼I¹Š»M¾α HGLE“KKTHA?#K 9T:^K ¾ ¼;K ?@H@¾ «*EF9LG;ºLJ;¼ gα:KMJL¾À< ¤ H ¤ J;GFE~>;:–­> ¦ Z :cN3Q ¦ _§HiHA< ¦ >;: ¤ HA>;:"EF>;:@?@9 ¦ 9;J©ª ~ >L»˜¹WJ;9^_ ¦ >;:iK_˜:¥½¾AJ KjX ¤ HA9LJT:9;H@[¾ TŸ U œ”¥ˆc͉nΖ‰Õ‰˜’”Ï9ÐÒÑ#ÓPÔÖÕL”#×Ǝ;ΌAØ YÙÛÚqÜ?ÝÁ‰dލT’WjÞAߏ[IUWdc[Ib*ÈQ ÇDIÊÉ`I‡Ë-Ì •Œ— ‘H(t)•’jÜ?ݍÏ@‰à“— ”Í”Ïψ ∈ EεS á h ∈ H•ŒˆcÍFŽGÏ@‰dΌWDÏ@Ž •Œ©W‘“’Ž¥Ø ”¥‹‰˜’YàIŽt+∆tZoneα (t + ∆t) − expeα (t) h ⊗ ψ UH(τ)dτUtH√3/2= O ∆tC1 (ψ) + O( t ∆t) C2 (ψ)√ √ √+ O(min( α, t, ∆t))C3 (ψ),×Ζ‰’‰à©”®—ç”ÍDÜ·‰úˆ”ޏ”qろT—ç‰ÕW‘“’YÜ·‰-ä Ì ’Yà“‹WŠ”¥’ŠŽYÜCj (ψ) á j = 1, 2, 3 âµ : KMK§¾·: ¤ >;J;?A:Cª “¤ ¦ < ¦ >^X{H@< ¦ >T: ¤ H@>¦¦b eU (t) = eiH t U(t) O3<LHcKLEF¨T: ¾ KK ¹;½K ¤ ?@J ¦ ¹:9;9LHA¼ ¤“¦ HA> ¦ ¾]J œ”®ˆGÍö‰dÎC‰Õ‰Œ’Š”9ύÐçænÓÔ3ÕL”#×ΖŽÎŒAØ YÙÛÚÜ?ÝY‰dލW’TYÞ"ߏ[IUWdc[Ib*{Q ÇDIÊå`IÖË*Ì •Œ— ‘Hα’ Ü?ݍÏ@‰ à“— ” ͔ Ïj•Œcˆ ÍFGŽ Ï@d‰ ΌWD Ï@Ž •Œ©W‘“’¥Ž Ø ”¥‹‰˜’YàIŽS0ψ ∈ Eε á h ∈ H×Ζ‰k(Uα (t) − exp{iHα t}) h ⊗ ϕkH = C1 (ϕ)O t3/2 ,’‰à©”®—ç”ÍDÜ]è ˆ”ޏ”qろT—ç‰ÕW‘“’YÜ]èC1 âÔSΓ (L2 (R))ä Ì Y’ à“‹WŠ”¥’ŠŽµ :KMK§¾ÀH ¤ >;J;¾ <;> ¦ ¹ ¦ vK K ¦ ¾ ¦ ¼;K ¤ ?A:=HA< ¦ >;: ¤ HA>LHA?UαáΖ‰è•˜—Ï Ì Ù4é Y èÏ<;>LJlim gα = δ(x).±_α→0>;:#S ¦ L9 J ¦ ¹jKLª7¹ ¦ ¼;K ¤ ?@JFª <;> ¦ ¹ ¦ KYX@9;HG_MH*H@< ¦ T> : ¤ H@>T:9T:<;>LHAJ©­®?@HcKjXA9HJ ¼ GIH–½¦ > ¦ 9 ¤ 9^Jw¼ ? ¦ G ¤ H@> ψ(f ) ¾HqS 9LH ­®:@<L;J K: ¤ X ª;?AL9 H^ŒJψ t (f ) êW=ëíì lim Uα (t)ψ(f ) = exp{i(H0 )5 t}α→0 × exp − R∗ (exp{iK} − iK − 1) (iK)−2 R 3 t t Z∗iK−1× exp i dτ R e − 1 (iK) 1 f (τ ) , ψ f t<L> ¦ ¹ ¦ KjXA9;:–ª¬«*EF9;GLº;JFª0f t (x)>T:?A9;:f t (x) = r(x) (f (x + t) + h(x)) ,›šTà U<L>;J;¨L»M¾h(x) = iI(−t,0) (x) 1 − e−iK (iK)−1 R 2 ,r(x) = exp i (K)4 I(−t,0) (x) .¦ IG KnJlEDH@< ¦ >T: ¤ H@>;H@? H@<;> ¦ ¹ ¦ K;ªHN ¤ <LHA>“ªI¹ŠH@G¬J©Bk¹ ¦ ¼;K ¤ ?@JFª œ± J¨;J;KKWJL¾ G;>;: ¦ ?AH ¦ E KKWH@?AJ ¦ O_GIH ¤ H@>;H@¾/EYE®¹ŠH@?cK ¦§¤ ?AH@>“ª ¦§¤ <;> ¦ ¹ ¦ KYX@9^J¼? ¦ G ¤ H@> K§HAK ¤ H®ªL9;JFªOI: ¤ :GAS ¦ <;> ¦ ¹ ¦ KYX@9^J¼9_ ¦ 9 ¦ >T: ¤ H@> K ¦ ¾ ¦ ¼;K ¤ ?A:*_§>FEF<L< Uα œz ¨;J ¤ J?“:Cª ¤A¦ H@> ¦ ¾/E › J ¤ H ¤ «ú:@G ¤ O®¨ ¤ HR_ ¦ 9 ¦ >T: ¤ H@>îT ¡ U+9 ¦ ­¥:?@J;KMJ ¤ H ¤ ?A> ¦ ¾ ¦ ½9LJ`OŠG;>T: ¦ ?@H ¦ E K KWH@?AJ ¦ J <L> ¦ ¹ ¦ KjXA9HJ ¼ï_ ¦ 9 ¦ >T: ¤ HA>v¾HqS 9;H 9T:¼ ¤ J JLKM<;H#KYX–­ME@ªK ¦ ¾ ¦ ¼LK ¤ ?AH Uα(t) œ ³ <;> ¦ ¹ ¦ KWJL¾…K K ¦ ¹;EAN3Q7J ¦ KM< ¦ º;J;:#KjXA9HJ ¦ H@< ¦ >T: ¤ H@>^JlEF9LJ©½¨ ¤ qH S ¦ 9LJF`ª Œo,9©¹o´­9T à U KKv ∈ W21 (R \ {0}).A± ψ(v) êW=ëíì v(±0)ψ(v) ,¦ ¹;E Œ¦ ¤ OT¨ ¤ HA− ψ t (f ) =eiKf (t) + i eiK4A+ ψ t (f ) = f (t)ψ t(f ),4H ¤ G©E®¹:=<;H#K;EF¨;: ¦ ¾GL>T: ¦ ?@H ¦ E KKWH@?AJ ¦ ¹^K;ªu KLª¬?MJ?@H¹:(1 − e−iK )(iK)−1 R2ψ t (f )ψt ŒA− − eiK A+ − i(eiK − 1)(iK)−1 R ψ t = 0.Tš U<;> ¦ ¹ ¦ KYX@9;HG_MH=EF>T:?@9 ¦ 9LJFªDEF¨ ¤ »M¾€OT¨ ¤ H∂∂I(−t, 0) (x) = 0−∂x ∂t<L>;J x 6= 0 OöH ¤ GFE®¹Š:kKK ¦ ¹TE ¦§¤ Oö¨¹^K;ªw:>^_ŒEF¾ ¦ 9 ¤ :=GIHG_ ¦ > ¦ 9 ¤ 9LHM_§H² :@GLJ;¾ HGLA>;:–­HA¾€O;<LHcKLEF¨T: ¦ ¾¤ H ¤ : GIH ¦ S ¦ MK H@H ¤ 9;HGZ ¦ 9;J ¦ ?MJ<;H#KW9©ª §¦ ¤ ÞK ªiJ? ¦ G ¤ H@>T:AŒ∂∂f t (x) = 0.−∂x ∂td t ψ = ∇ + i R∗ (eiK − 1)(iK)−1 1 f (t) − i(H0 )5dt− R∗ (exp{iK} − iK − 1) (iK)−2 R 3 ψ t .›A›K ¤ > ¦ ¾ƒK;ªFªztGÁ9FEKjNtJDEF¨;J ¤ J ?A:–ª¬GL>T: ¦ ?@H ¦ E“KKWH@?@J ¦ TO JL¾ M¦ ¦ ¾dU (t)ψ(f ) = −i∇ + R∗ (eiK − 1)(iK)−1 A+ + H0−idtt=0+ iR∗ (exp{iK} − iK − 1) (iK)−2 R ψ(f ) .² :G;J;¾ HML@>T:C­®H@¾€O;KM<L>T:? ¦ ¹jKWJL?AH KK ¦ ¹;EAN3Q ¦M¦ E ¤ ? ¦ >PS=¹ ¦ 9LJ ¦œ[IUWdc[Ib*QðÇYIÊñòI ‡/FW‘“’j܇ó ͉ô@”ǏW‘!Ï@‰Œ’T— ’Y܇ó ˆGÍö‰dÎC‰Õ”Wó •M‰®óú‰è•˜—ϝŽ ”¥ˆŠ‰õÍFŽ#ß—ç” Í” Ï.ÐçænÓ Gˆ ͊ØFϐ"؉Œ—ç•Øz”®ˆŠ‰õÍFŽ–—ç”Ígα → δH = −i∇ + H0 + R∗ (eiK − 1)(iK)−1 A++ iR∗ (exp{iK} − iK − 1) (iK)−2 R,"óú‰Ù4é=jèÈÏ9àIŽ#Þ;‰M•˜—„Ï@‰ ”ÚǏŽ@•˜— Y”®ˆGÍö‰dÎC‰Õ‰Œ’T"ØzˆŠ”În󒊔qㆉ§•Œ—„Ï@”Ï@‰à —ç”͔ύAô” ÏM‰Œ„— Ï@” Í^ØYÙ4é HݒànÍFŽ@‰dϝ”Wó Ì|Ì •Õ”Ï–YÙ ÐWö®ÓÔÌ ÎC#Lε (H) áo*KâB H¹;ªJF­ª;?@9;HG_MH?@J©¹:´<L> ¦ ¹ ¦ KjXA9LHM_§H*>;:–­> ¦ Z:cN3Q ¦ _MH´HA< ¦ >;: ¤ HA>;:´¾ÀH¥S=½9LHnM? J? ¦ K ¤ J K ¤ HB©:K ¤ J;¨ ¦ K§GIH ¦ ¹ŠJL«#« ¦ > ¦ 9Lº;J;#: KjXA9LH ¦ EF>;:@?@9 ¦ 9;J ¦ OGIH ¤ H@>;H@¾/EH@9;Hç<LH¹Š¨LJ;9Fª ¦§¤ KÞª œ µ :@K§KM¾H ¤ >LJ;¾ <;> ¦ ¹ ¦ Klim ψ(w), U (t + dt) − U (t) ψ(v) ΓS = ψ(w), M (dt)ψ(v) ΓS ,t→+0¦ K ¤ HB©:K ¤ J;¨ ¦ K§G;J;¼*¹WJ;«#« ¦ > ¦ 9;ºLJT:K¦¦ 9 ­¥:?AJLK ¦Œ¤ XH ¤ ?GJ€LAH@>T:M (t) 9 ¹WHcKHS GIH@9;GL> ¦§¤ 9^JBGIHG_ ¦ > ¦ 9 ¤ 9HJB7? ¦ G ¤ HA>LHA? ψ(w) J ψ(v) œ ³ F< E“KMG©:Cª<;>;H@¾ ¦ SçE ¤ HA¨I½9HJ ¦ M? JGAKW:C¹WG;J`O­¥:<;JHZ ¦ ¾?GJ >;:#S ¦ 9LJ ¦ ¹^K;ª{K ¤ HBI:K ¤ J;¨ ¦ MK GIHG_MH¬¹WJ;«#« ¦ > ¦ 9©½ºLJT: KŠ: M (dt) ?ç«#H@>;¾ ¦ s*:C¹WKMH@9T: ¢\ :@> ¤ :@KM:@>;: ¤ J`Œ_â¹M (dt) = eiK − 1 dΛt+ eiK − 1 (iK)−1 iR dA†t + iR∗ eiK − 1 (iK)−1 dAt+ H0 + R∗ (eiK − iK − 1)(iK)−2 R dt.u KLª «#H@>;¾/EKWJL>;H@?AGLJ H@KM9;H@?@9;HG_MHl> ¦ ­MEKjX ¤ : ¤ :'< ¦ >L?AH@¼ _KW:@?GJhO?@? ¦ ¹Š»§¾?@KM<LHA¾HG_˜: ¤A¦ KjXA9LH ¦ <LHA9©ª ¤ J ¦ ³j¿F·n¶AµM÷‡·AøPÀW±^±F·²· ·¿FÀ¬¶`ÂÃc·n¶ò·¹n±YÂ!ø#±D·²· ù^·²ÀÁ¶`À±Ã¥±F·²·ú¸!ÀùÃc·n¶` ψ (J) œ\ H†HA<L> ¦ ¹ ¦ K ¦ 9;JHN;O¨a ¤ H†? ¦ G ¤ H@> «#H@GIH@?AK§GIHM_§H<L>;H@K ¤ >T:9;K ¤ ?A:HO‡anK ¦ ¾ ¦ 9 N¤ :@¾J^GIH ¤ HA>LHM_§HvªL?cKLª^N ¤ KÞª{H@< ¦ >;: ¤ H@>^J 9 ¦ GIH ¤ H@>;HG_MH§_ JAKYXGL ¦ > ¤ H@?“:=<L>;H@K ¤ >T:9;K ¤ ?A: H TO JL¾ ¦ N37Q J;¼Á?@J©¹‹Œ−ψN (H) = ←expZ†dx a (x)J(x) |0i,›®¡J ∈ L2 (B(H), R).<;H@>“ª©¹ŠH@¨ ¦ 9;J ¦ v? BL>LHA9LHcKTHM_§J;¨ ¦ KMGIH@¼paGIK§<;H@9 ¦ 9 ¤A¦ ? ¦ ¹W» ¤ KÞª~<LHi:>^_ŒEF¾ ¦ 9 ¤ :¾¦ ¤ >:œ ²¦ ¤¦ ¤x ∈ R HA< >T: HA;J(x) :@GLJ;¾ HGLA>;:–­HA¾€O4<;>;Jq¹ ¼LK ?AJLJGIH@¾À<LHA9 9 J¦¦ ¦ ¤φn(x1 .

Характеристики

Тип файла PDF

PDF-формат наиболее широко используется для просмотра любого типа файлов на любом устройстве. В него можно сохранить документ, таблицы, презентацию, текст, чертежи, вычисления, графики и всё остальное, что можно показать на экране любого устройства. Именно его лучше всего использовать для печати.

Например, если Вам нужно распечатать чертёж из автокада, Вы сохраните чертёж на флешку, но будет ли автокад в пункте печати? А если будет, то нужная версия с нужными библиотеками? Именно для этого и нужен формат PDF - в нём точно будет показано верно вне зависимости от того, в какой программе создали PDF-файл и есть ли нужная программа для его просмотра.

Список файлов диссертации