A semiclassical approach to quantum Brownian motion in Wigner's phase space

Abstract

In this thesis, the recent semiclassical approach to quantum Brownian motion of Coffey et al. [Phys. Chem. Chem. Phys. 9, 3361 (2007)] is studied in detail. This approach is based on a semiclassical extension of Wigner's method of obtaining corrections to the classical equilibrium Maxwell-Boltzmann distribution, yielding a master equation for the reduced Wigner function in quasi-phase space valid in the weak coupling and high temperature limits. In the non-inertial or high damping limit, this master equation reduces to a quantum Smoluchowksi equation (QSE), where the drift coefficient remains as in the classical case, while the diffusion coefficient is altered to include the quantum parameter and derivatives of the potential.