Statistical mechanics of the isothermal lane-emden equation |
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Authors: | Joachim Messer Herbert Spohn |
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Institution: | (1) Fachbereich Physik der Universität München, Theresienstr. 37, 8, München 2, West Germany |
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Abstract: | For classical point particles in a box with potential energy H(N)=N
–1(1/2)
i j=1
N
V(x
i,x
j) we investigate the canonical ensemble for largeN. We prove that asN![rarr](/content/mmu4208041704878/xxlarge8594.gif) the correlation functions are determined by the global minima of a certain free energy functional. Locally the distribution of particles is given by a superposition of Poisson fields. We study the particular case =– L, L] andV(x, y)=}- cos(x–y),L}>0, }>0.References |
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Keywords: | Classical point particles Lane-Emden equation canonical ensemble instable interactions mean field limit equilibrium states |
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