Конспект лекций по статистической физике. Коренблит С.Э - 25 стр.

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4   à¨¬¥àë ¬ âà¨æë ¯«®â­®áâ¨
    áᬮâਬ, ­ ¯à¨¬¥à, ¬ âà¨æã ¯«®â­®á⨠¤«ï ¯®«ïਧ®¢ ­­®£® ᢥâ .
„«ï ¯ãçª , à á¯à®áâà ­ïî饣®áï ¢¤®«ì ®á¨ Z , ¢¢¥¤¥¬ ¢¥ªâ®àë á®áâ®ï-
­¨©: j'1i, á ¯®«ïਧ 樥© ¢¤®«ì ®á¨ X ¨ j'2i, { ¢¤®«ì ®á¨ Y :
                              0 1              0 1
                       j'1i = @ 1 A ;
                                0       j'2i = @ 0 A :
                                                 1                     (2.20)

‹î¡®¥ ç¨á⮥ á®áâ®ï­¨¥ ji ¥áâì ®¤­®§­ ç­ ï «¨­¥©­ ï á㯥௮§¨æ¨ï
íâ¨å ®à⮣®­ «ì­ëå ¤à㣠¤àã£ã ¢¥ªâ®à®¢ j'1i ¨ j'2i, h'i j'j i = ij :
                                               0 1
                ji = C1j'1i + C2j'2i = @ CC12 A ; hj = (C1; C2) ;  (2.21)

á ¬¯«¨â㤠¬¨ C1 = h'1ji, C2 = h'2ji, ¯à¨ h j i = jC1j2 + jC2j2 = 1.
     1.  ©¤¥¬ ¬ âà¨ç­ë¥ í«¥¬¥­âë %b ¢ ç¨á⮬ á®áâ®ï­¨¨ %bc = jihj:
(%bc)il = h'i j%bcj'l i =) h'ijihj'l i, â® ¥áâì:
                                0 1                0         C1 C  1
                                  C 1              C  1 C
                      %bc =!!!) @ C A (C1 ; C2 ) = @ C C1 C C2 A :
                                    2                   2 1 2 2
‘¢¥âã, ¯®«ïਧ®¢ ­­®¬ã ¢¤®«ì ®á¨ X (C1 = 1; C2 = 0), ®â¢¥ç ¥â ¬ âà¨æ
¯«®â­®áâ¨:                                    0     1
                                                1 0
                                      %bc;x = @ 0 0 A ;
á®áâ®ï­¨î ¯®«ïਧ 樨 ¢¤®«ì ®á¨ Y (C1 = 0; C2 = 1), {
                                      0     1
                              %bc;y = @ 0 0 A;
                                        0 1
                                                                 p
á®áâ®ï­¨î ¯®«ïਧ 樨 ¯®¤ 㣫®¬ =4 ª ®á¨ X (C1 = C2 = 1= 2), {
                                 0             1
                                   1 = 2 1 = 2
                       %bc;=4 = @ 1=2 1=2 A ;
                                                                      p
á®áâ®ï­¨î ¯®«ïਧ 樨 ¯®¤ 㣫®¬ 3=4 ª ®á¨ X (C1 = C2 = 1= 2), {
                                0             1
                                  1 = 2 1 = 2
                     %bc;3=4 = @ 1=2 1=2 A :