On a method in quantum statistical mechanics and its applications

Anatoliy K. Prykarpatsky, Ihor V. Mykytiuk

M. P. Nightingale, Cyrus J. Umrigar

In this review we discuss, from a unified point of view, a variety of Monte Carlo methods used to solve eigenvalue problems in statistical mechanics and quantum mechanics. Although the applications of these methods differ widely, the underlying mathematics is quite similar in that they are stochastic implementations of the power method. In all cases, optimized trial states can be used to reduce the errors of Monte Carlo estimates.

Kenneth Watson

A Laplace transform relation between the distribution function $\mathrm{exp}{\ensuremath{-}\ensuremath{\beta}H}$ in quantum statistical mechanics and the Green's function of the wave equation has been noted by Koppe. This relationship may be extended to the stationary-state scattering equation. General properties of the transformation are discussed. Applications to the evaluation of the virial coefficients are considered. A further application of the perturbation methods of Brueckner and his collaborators is described.

Min Liang

The degeneration conditions for quantum gas system were analyzed based on statistical mechanics method.We point out the coincidence among these methods and the dependent properties of quantum gas system to its degeneration by comparing and analyzing these methods.The application of degeneration Fermi gas model in astrophysics proves that quantum statistical theory plays a vitally important role in study area of modern physics.