Конспект лекций по статистической физике. Коренблит С.Э - 31 стр.

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‚ ª¢ §¨ª« áá¨ç¥áª®¬ ¯à¨¡«¨¦¥­¨¨ í⮬㠨­â¥à¢ «ã ®â¢¥ç ¥â ­¥ª®â®àë©
á«®© á ⮫騭®© / 
E ¢ ä §®¢®¬ ¯à®áâà ­á⢥, ¢ ª®â®à®¬, ᮣ« á­® á®-
®â­®è¥­¨î ­¥®¯à¥¤¥«¥­­®á⥩ ƒ¥©§¥­¡¥à£ , 
q
p  h, ª ¦¤®¥ ¤®áâã¯-
­®¥ á¨á⥬¥ ª¢ ­â®¢®¥ á®áâ®ï­¨¥ jmi á í­¥à£¨¥© Em  E § ­¨¬ ¥â ï祩ªã
®¡ê¥¬®¬ hs = (2h )s. ®í⮬ã, ç¨á«® ª¢ ­â®¢ëå ¬ˆªà®á®áâ®ï­¨© ¢ «î-
¡®¬ ¬€ªà®áª®¯¨ç¥áª¨ ¬ «®¬ í«¥¬¥­â¥ ®¡ê¥¬ ª« áá¨ç¥áª®£® ä §®¢®£®
¯à®áâà ­á⢠, ª ª ¨ ¨å ¯®«­ãî í­¥à£¥â¨ç¥áªãî ¯«®â­®áâì ¤«ï í­¥à£¨¨
E , ¬®¦­® ­ ©â¨ ¯® ä®à¬ã« ¬ (á¬ë᫠ᮮ⢥âá⢨ï *  ) ãâ®ç­¥­ ¢ (3.32)):
     2s
             s
             Y         d 2s X
    d X = dqidpi ; hs  d  dE       d dE *
                                          ) (E; dE ); ¢ á¬ëá«¥: (3.16)
        0   i=1     1
  d *     @   ( E )                             O (E )    Z
        @
  dE ) @E
                    A  D(E; V; N ); £¤¥: (E ) = hs =       d ; (3.17)
                 V;N                                      H(X)E
{ ¥áâì ¯®«­®¥ ç¨á«® ª¢ ­â®¢ëå á®áâ®ï­¨© ¢ ®¡ê¥¬¥ O(E ) (á¬. (3.33))
ä §®¢®£® ¯à®áâà ­á⢠, § ­ï⮬ ª« áá¨ç¥áª¨¬ ­á ¬¡«¥¬ ¨§®«¨à®¢ ­­®©
á¨á⥬ë, ®£à ­¨ç¥­­®¬ ¯®¢¥àå­®áâìî ¯®áâ®ï­­®© í­¥à£¨¨ H (X ) = E .
ˆá¯®«ì§ãï (3.15){(3.17), ¬®¦­® ⥯¥àì ¯¥à¥©â¨ ®â (3.3) ª ª¢ §¨ª« áá¨ç¥-
᪮© ¤¨ää¥à¥­æ¨ «ì­®© ¢¥à®ïâ­®á⨠⨯ (1.11), ⮣® çâ® á¨á⥬ ®ª -
¦¥âáï ¢ í«¥¬¥­â¥ ®¡ê¥¬ ä §®¢®£® ¯à®áâà ­á⢠¢¡«¨§¨ â®çª¨ X = fxig2s1 ,
®â¢¥ç î饩 §­ 祭¨î í­¥à£¨¨ ¬ˆªà®á®áâ®ï­¨ï Em  E 2 (E; E + 
E ),
¢ á«®¥ ¯à¨ £¨¯¥à¯®¢¥àå­®áâ¨ á ¤ ­­®© í­¥à£¨¥© H (X ) = E = const:
                                           ) w
(H )d = %(X ) d hsX ; (3.18)
 dW (E ) = aE (Em ) 
dEE = w
(E ) (E; dE ) *
                                                              2s


£¤¥ %(X ) = w
(H ) =) w
(E ), ¡¥§à §¬¥à­ ï áâ â¨áâ¨ç¥áª ï äã­ªæ¨ï
à á¯à¥¤¥«¥­¨ï ¢ ª¢ §¨ª« áá¨ç¥áª®¬ ¯à¨¡«¨¦¥­¨¨, ¯®áâ®ï­­ ¯® ¢á¥¬ã
á«®î. à¨ 
E ! 0 ¢á¥ á®áâ®ï­¨ï á®á।®â®ç¥­ë ­ á ¬®© í⮩ £¨¯¥à¯®-
¢¥àå­®áâ¨, â.¥. ­ ¬­®£®®¡à §¨¨ á ç¨á«®¬ ¨§¬¥à¥­¨© 2s 1, ­ ¥¤¨­¨æã
¬¥­ì訬 à §¬¥à­®áâ¨ ä §®¢®£® ¯à®áâà ­á⢠, ¨ ¤«ï ¢ë¯®«­¥­¨ï ãá«®¢¨ï
­®à¬¨à®¢ª¨ (1.12) ­¥®¡å®¤¨¬® ®¡à 饭¨¥ í⮩ ä㭪樨 ¢ ¡¥áª®­¥ç­®áâì   
­ í⮩ £¨¯¥à¯®¢¥àå­®áâ¨, â.¥.: %(X ) =) w(H (X )) = C H (X ) E , ¢
ᮮ⢥âá⢨¨ á (1.40). ‘ ãç¥â®¬ (3.16){(3.18), íâ® ¤ ¥â ¯®áâ®ï­­ãî C :
    Z          Z           Z     @ (E ) dE = C Z (E E )D(E; V )dE; (3.19)
1= dW (E )= %(X )d = w(E )
                                  @E
                                                     
                  1
 ¢ ¢¨¤¥: C = D(E; V ) ; %(X ) = D(E;1 V )  H (X ) E ; ¯à¨ç¥¬, (3.20)