Effective Forces for Application of Classical Methods to Quantum Systems

James Dufty
University of Florida

Many body methods of classical statistical mechanics are quite well-developed and accurate for strongly coupled conditions (e.g., liquid state theory, molecular dynamics simulation). Exploitation of such methods for application to quantum systems is not straightforward, but significant progress has been made by defining effective classical systems corresponding to a chosen quantum problem of interest. Most commonly this is accomplished by defining pair potentials or forces for the classical system in which selected quantum properties (e.g., diffraction, exchange) have been imbedded. One approach for equilibrium states, generalizing earlier methods, is based on equating classical and quantum pair correlation functions. Here, attention is focused on possible applications to non-equilibrium states. A reformulation of the Liouville – von Neumann equation in Wigner representation is given, resulting in a semi-classical form with effective forces that are non-local in momentum space. A local form is defined, resulting in a classical description for non-conservative dynamics. The price is state-dependent
effective forces. The correspondence with earlier results for equilibrium states is described and simplified results for mean field non-equilibrium states are discussed.
Implementation via molecular dynamics simulation and by classical kinetic theory are considered. This research was supported in part by US DOE Grant DE-SC0002139.

Back to Workshop IV: Computational Challenges in Warm Dense Matter