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Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

A variational procedure for the statistical mechanics of a many-boson system

Marvin H. Friedman

Published Nov 1, 1965• 0 citations
Publisher
DOI
10.1007/bf02710765

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The density matrix of von Neumann can be used to formulate an exact variational principle for quantum statistics which embodies the principle of maximization of entropy. Using the formalism of second quantization, we can write this variational principle for fermions or bosons and can then derive from it an approximate variational procedure which yields the particle states of a system of interacting bosons or fermions as well as the distribution of particles in these states. These equations yield the generalization of the Hartree-Fock equations for nonzero temperature and the corresponding extension to bosons.
From the very beginning quantum statistical mechanics can be formulated in terms of a thermodynamic potential, which has the electron density as the basic variable. By employing a well-known procedure in quantum statistical mechanics for the construction of stationarity principles [T. D. Lee and C. N. Yang, Phys. Rev. 113, 1165 (1959); 117, 22 (1960)], the variational principles of Hohenberg, Kohn [P. Hohenberg and W. Kohn, Phys. Rev. B 136, 864 (1964)], and Mermin [N. D. Mermin, Phys. Rev. A 137, 1441 (1965)] are obtained as are generalizations thereof.