A thermodynamically self-consistent quantum statistical theory of the crystalline state

V.A. Golovko

Physica A: Statistical Mechanics and its Applications, 2002, vol. 310, issue 1, 39-66

Abstract: The quantum hierarchy of equations for equilibrium density matrices obtained earlier by the author is extended to studies of the crystalline state. The thermodynamics of a crystal is constructed consistently with periodic solutions of the hierarchy. The structure of the pair correlation function is assumed to be the same as in a previous paper by the author on the classical case. The equations obtained are analysed in the quasiclassical approximation and in the low-temperature limit. The quasiclassical approximation gives quantum corrections to the classical formulae of the previous paper. The low-temperature limit leads to Debye's and Grüneisen's laws without using the concept of phonons. The results obtained in this limit are compared with experimental data for rare gas solids. A method for solving the quantum equations based upon bifurcation theory is considered too. Results given by this method agree with the Landau theory of phase transitions.

Keywords: Quantum statistical thermodynamics; Thermodynamic properties of solids; Quantum crystals (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:310:y:2002:i:1:p:39-66

DOI: 10.1016/S0378-4371(02)00617-9

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