Computer Simulation of Polaron and Bipolaron Systems

Abstract

Thermodynamic behavior of classical many-particle systems such as Ising models, hard sphere gases, fluids etc. can be studied by means of analytical, e.g. high-temperature series, perturbation expansions and renormalization group methods, and computer simulation techniques. There is no doubt that the latter have contributed a lot to the present understanding of the behavior of classical many-body systems [1,2]. Extending the techniques, originally developed for classical-mechanical models, to quantum systems is not straightforward. In this paper a Monte Carlo approach for quantum models at non-zero temperatures (T≠0) is discussed. The technique is complementary to the T = 0 Monte Carlo methods, see for instance CEPERLEY and KALOS [3]. In the following section an outline of the basic concepts and mathematical justification of the method are given. The general methodology is illustrated in subsequent sections by considering explicit examples. Topics treated include the one-, two- and three-dimensional Molecular Crystal Model, a two-level system with non-linear coupling and bipolaron formation.