STATISTICAL MECHANICS - gallavotti

Đây là bộ sách tiếng anh về chuyên ngành vật lý gồm các lý thuyết căn bản và lý liên quan đến công nghệ nano ,công nghệ vật liệu ,công nghệ vi điện tử,vật lý bán dẫn. Bộ sách này thích hợp cho những ai đam mê theo đuổi ngành vật lý và muốn tìm hiểu thế giới vũ trụ và hoạt độn ra sao.

[...]...1 Chapter I : Classical Statistical Mechanics 2 I: Classical Statistical Mechanics 3 x1.1 Introduction Statistical mechanics poses the problem of deducing macroscopic properties of matter from the atomic hypothesis According to the hypothesis matter consists of atoms or molecules that move subject to the laws of classical mechanics or of quantum mechanics Matter is therefore thought... (see x4.3) r0 = (3B=2 NA )1=3 " = 3A=8BNA = 81 kB Tc0 =64 Tctrue = experimental value of the critical temperature Tc0 12 I: Classical Statistical Mechanics In this book I will choose the attitude of not attempting to discuss which would be the structure of a statistical mechanics theory of phenomena below T0 if a strict, \axiomatic", classical viewpoint was taken assuming p = 0 q = 0: the theory would... classical statistical mechanics Given a mechanical system of N identical (for the sake of simplicity) particles consider the problem of studying a xed observable f (p q) de ned on phase space The rst important quantity that one can study, and often the only one that it is necessary to study, is the average value of f : 1:3:5 X 1 T ;1 f ( ) = Tlim T f (S k ) !1 k=0 (1:3:5) 15 I: Classical Statistical Mechanics. .. has to be taken as within the \majority" of the cells, where one can suppose that implies S 1 6= S 2 1 varies 6= 2 8 I: Classical Statistical Mechanics One should realize that if ' is a \reasonable" molecular potential (a typical model for ' is, for instance, the Lennard-Jones potential with intensity " and range r0 given by: '(r) = 4"(( rr0 )12 ; ( rr0 )6 )) it will generically be that: 1:2:7 lim... dimension of energy and the range r0 with the dimension of length It follows from the developments of the theory of equilibrium statistical mechanics, independently of the particular form of '(r) (as long as it is \reasonable", like for instance the above mentioned Lennard-Jones potential), that " = kB Tc0 where Tc0 is the critical liquefaction temperature and r0 is of the order of the molecular diameter... coordinates In fact in \recent" times the foundations of classical mechanics have been 1 N = 6:02 1023 particles per mole = \Avogadro's number": this implies, for instance, that 1 cm3 of Hydrogen, or of any other (perfect) gas, at normal conditions (1 atm at 0 C) contains about 2:7 1019 molecules 4 1:1:1 1:1:2 1:1:3 I: Classical Statistical Mechanics subject to intense critique and the indetermination... The optimistic viewpoint of orthodox statistical mechanics (which admits perfect simultaneous measurements of positions and momenta as possible) will be obtained by considering, in the more general theory with h > 0, the limit as h ! 0, which will mean p = p0 q = q0 , with p0 q0 xed and ! 0 Even if we wish to ignore (one should not!) the development of quantum mechanics, the real possibility of the... distribution on phase space (or, better, on phase space cells) The following de nition will be convenient (see x1.3): I: Classical Statistical Mechanics 19 1:5:3 De nition: Let be an invariant probability distribution on phase space cells If the dynamics map S acts as a one-cycle permutation of the set of cells for which ( ) > 0 then is called ergodic If one imagines covering phase space with a uid so... in other words, the statistical ensembles E in which it is possible to interpret the average kinetic energy per particle, T , as proportional to the absolute temperature T (via a proportionality constant, to be determined empirically and conventionally denoted (2=3kB );1 : 2 ( so that T = 3kB TN ) ) and furthermore it is possible to de ne via (1.5.6) a I: Classical Statistical Mechanics 21 function... could 22 I: Classical Statistical Mechanics reveal itself equivalent to the dynamical foundation of thermodynamics: the very problem that one is hoping to circumvent by deciding to \only" build a mechanical model of thermodynamics, i.e an orthodic ensemble x1.6 Models of Thermodynamics Microcanonical & Canonical Ensembles and the Ergodic Hypothesis The problem of the existence of statistical ensembles