Конспект лекций по статистической физике. Коренблит С.Э - 26 стр.

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  2. ‘®£« á­® (2.10), á¬¥è ­­ë¥ á®áâ®ï­¨ï ¬®¦­® ¯à¨£®â®¢¨âì, \ᬥ-
è ¢" í⨠ç¨áâë¥ á®áâ®ï­¨ï á ᮮ⢥âáâ¢ãî騬¨ ¢¥á ¬¨ wk :
                          X           X
                      %b = wk %bc;k ;   wk = 1:              (2.22)
                                    k          k
’ ª, ¤«ï ¯ãçª , ïî饣®áï ᬥáìî á®áâ®ï­¨© 0; 5%c;x ¨ 0; 5%c;y , ¬ âà¨æ
¯«®â­®á⨠¥áâì:                                0         1
                                                 1 = 2 0
                  %b = 0; 5%bc;x + 0; 5%bc;y = @ 0 1=2 A :           (2.23)
®, ¤«ï ᬥᨠ%b = 0; 5%bc;=4 +0; 5%bc;3=4, ¯à¨å®¤¨¬ ª ⮩ ¦¥ á ¬®© ¬ âà¨æ¥
¯«®â­®áâ¨, ¨ í⨠¤¢ á¬¥è ­­ëå á®áâ®ï­¨ï ®ª §ë¢ îâáï 䨧¨ç¥áª¨ ­¥-
à §«¨ç¨¬ë: %b ¢ (2.23) ¯à¥¤áâ ¢«ï¥â ¥¤¨­ãî ᬥáì ç¨áâëå á®áâ®ï­¨© á
®â­®á¨â¥«ì­ë¬ 㣫®¬ ¯®«ïਧ 樨 =2 ¨ ¢¥á ¬¨ w1 = w2 = 0; 5. ’ ª¨¬
®¡à §®¬, ¢ í⮬ ¥¤¨­®¬ á¬¥è ­­®¬ á®áâ®ï­¨¨ ¯à®¨§®è« ¯®â¥àï ¨­ä®à-
¬ 樨 ® á¨á⥬¥ ¯® áà ¢­¥­¨î á «î¡ë¬ ¨§ ¥¥ ç¨áâëå á®áâ®ï­¨© (2.21).
    ‘ ¤à㣮© áâ®à®­ë, «î¡ ï ¬ âà¨æ 2  2 ¯à¥¤áâ ¢¨¬ ª ª á㬬 ¥¤¨-
­¨ç­®© ¬ âà¨æë 1 ¨ âà¥å íନ⮢ëå ¬ âà¨æ  㫨  ! (1;2;3) [30]x50:
        0     1          0        1           0       1         0        1
          1 0               0  1                0   i
  1 = @ 0 1 A ; 1 = @ 1 0 A ; 2 = @ i 0 A ; 3 = @ 0 1 A ; (2.24)1 0
                                                     0                   1
                                1                  1    1 +        i
  j2 = 1; Tr(j ) = 0; %b = 2 [1 + ( 
 )]  2 @  + i 1  A : (2.25)
                                                              3    1   2
                                                   1    2       3
Žç¥¢¨¤­®, Tr(%b) = 1. ’®£¤ ¤«ï «î¡®© â ª®© íନ⮢®© ¬ âà¨æë ¢¥ªâ®à
¯ à ¬¥â஢ ‘⮪á  ! (1;2;3) (â.¥. ®áâ «®áì 3 ¢¥é¥á⢥­­ëå ¯ à ¬¥âà
¨§ 8) ¯®«­®áâìî å à ªâ¥à¨§ã¥â á®áâ®ï­¨¥ á® á¬¥è ­­®© ¯®«ïਧ 樥©:
                                                     
                              b j ) ; det(%b) = 1 1 2 :
                  j = 21 Tr (%                4
                                                                    (2.26)
‚ ç¨á⮬ á®áâ®ï­¨¨ det(%b) = 0, â.¥. 2 = 1, á⥯¥­ì ¯®«ïਧ 樨
á¬¥è ­­®£® á®áâ®ï­¨ï 2 < 1. „¥©á⢨⥫쭮, â.ª. ᮡá⢥­­ë¥ §­ 祭¨ï
í⮩ ¬ âà¨æë %b: 0 < w1; w2 < 1, Tr(%b) = w1 + w2 = 1; det(%b) = w1w2; â®:
      2 = 1 4 det(%b) = (w1 + w2)2 4w1w2 = (w1 w2)2 < 1:           (2.27)
   ([6] x5, [7], [9], [39], [38])
   ‡ ¤ ç¨
8.1. ˆá¯®«ì§ãï (2.10), (2.11), ¯à¨ n  2, ¯®ª § âì, çâ® Tr (%b n)  1, £¤¥
à ¢¥­á⢮ ®â¢¥ç ¥â ⮫쪮 ç¨á⮬ã á®áâ®ï­¨î.
8.2.  ©â¨ ®¡é¨© ¢¨¤  ¨ j i, â ª¨å, çâ® ¤«ï ¬ âà¨æë (2.25) %bj i = 0: