By D. Ter Haar
Lectures on chosen themes in Statistical Mechanics is a suite of lectures given on the 1971 Simla summer time university of Statistical Mechanics held in India. The lectures discover a variety of issues relating to statistical mechanics, together with career quantity illustration; the golf green functionality strategy; the pair Hamiltonian version of a less than perfect Bose fuel; fluctuations in an ideal Bose gasoline; and the equation of country of a less than excellent fuel. an easy derivation of the Bloch equation can be offered, besides the statistical mechanics of stellar systems.
Comprised of 8 chapters, this quantity starts with a dialogue at the career quantity illustration via contemplating a few correct formulae from ensemble idea. Classical petit and grand ensembles are defined, including quanta1 petit and grand ensembles. next chapters concentrate on the golf green functionality process in statistical mechanics; the pair Hamiltonian version of the imperfect Bose fuel and its resolution within the absence of Bose-Einstein condensation utilizing eco-friendly functionality equipment and diagrammatic thoughts; fluctuations in an ideal Bose gasoline; the equation of country of a less than excellent gasoline; and an easy derivation of the Bloch equation. eventually, the statistical mechanics of stellar platforms and an method of equilibrium are described.
This publication may be of curiosity to physicists.
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Extra resources for Lectures on Selected Topics in Statistical Mechanics
Example text
E. condensation. E. 4. E. transition temperature. 7 an exact solution to the problem using a method close in spirit to Luban's own. 1) THE PAIR HAMILTONIAN MODEL OF AN IMPERFECT BOSE GAS 39 The time Fourier transforms of the Green functions may he used to define a function analytic in the whole of the complex energy plane, apart from a cut along the real axis. For details of the Green functions we refer to the arti- cles by Zuharev (i960) and ter Haar (1962) (see also Chapter 1 of the present lecture notes).
A pâ M 7 P+q ^ + j ^ £ k2 = — -μ, m T is the mass of a boson, is the Fourier transform of the two-body poten- and a are boson creation and annihilation operators. l) model liamiltonians which, one hopes will still reflect some of the properties of the original Hamiltonian while being amenable to analytical studies. l) by omitting all interaction terms containing less than two operators a and a . zero-momentum state has a macroscopic occupation number (a a )/V 0 Bogolyubov then replaced the operators aQ and aQ If the is finite.
0 = 0 Similarly . 7) we see that « ώ , Η ρ ] . ^ ; a+»° = 0 . 1), therefore, reduce to those for G. and Γ. multiplied by °. " " In summary, the whole chain of equations of motion of Green functions generated from G. and Γ. has been shown to be satisfied to within terms of order l/V by our decoupling procedure, if averages are evaluated using the Hamiltonian H° . -condensation. -condensation the Green function equation of motion may not he neglected. ((aQ a Q a Q ; aQ)) in the However, a consistent decoupling procedure may be found provided it gives correctly the leading-order term in the expansion of ((aQ a a ; a )) in powers of V .