Constant-temperature dynamics in the Wigner representation of quantum mechanics.

Abstract

This dissertation deals with theory and algorithms for computer simulations of classical and quantum systems in the canonical ensemble. First, the approach of Nos e-Hoover and its generalization, known as the Nos e- Hoover chain dynamics, are introduced. Such methods are used in classical molecular dynamics simulations to control the temperature of particle systems through a coupling to a few additional fictitious variables, mimicking an in nite thermal reservoir. In order to introduce the extension of the Nos e-Hoover method to quantum systems, the features of the Wigner representation of quantum mechanics are reviewed. Finally, a recent approach [A. Sergi and F. Petruccione, J. Phys. A 41 355304 (2008)], which extends the Nos e-Hoover and Nos e-Hoover chain equations in quantum phase space, is described. Such a method is applied to a single harmonic mode, and the conditions for quantum-to-classical transitions as a function of the thermodynamical temperature are studied by means of numerical simulations. It is shown that, in the case of strong coupling, the open system dynamics simulated by Nos e-Hoover chain equations leads to quantum-classical transition of the Wigner function of the harmonic mode. Agreement between the numerical and analytical results is also found. The algorithms and results illustrated are of interest to the numerical simulation of the quantum dissipative dynamics of more general systems.