Multidimensional Classical Liouville Dynamics with Quantum Initial Conditions

Abstract

A simple and numerically efficient approach to Wigner transforms and classical Liouville dynamics in phase-space is presented. The Wigner transform can be obtained with a given accuracy by optimal decomposition of an initial quantum-mechanical wavefunction in terms of a minimal set of Gaussian wavepackets. The solution of the classical Liouville equation within the locally quadratic approximation of the potential energy function requires a representation of the density in terms of an ensemble of narrow Gaussian phase-space packets. The corresponding equations of motion can be efficiently solved by a modified Leap-Frog integrator. For both problems the use of Monte-Carlo based techniques allows numerical calculation in multidimensional cases where grid-based methods such as fast Fourier transforms are prohibitive. In total, the proposed strategy provides a practical and efficient tool for classical Liouville dynamics with quantum-mechanical initial states.