Quantum hydrodynamics for mixed states.

Irène Burghardt, Klaus B. Møller, Keith H. Hughes +1 more

R. Eisenschitz

Makoto Tsubota, Michikazu Kobayashi, Hiromitsu Takeuchi

Irène Burghardt, Klaus B. Møller, Gérard Parlant +2 more

Abstract The formulation of quantum hydrodynamics for mixed states provides a complement, in a quantum‐statistical context, to its pure‐state “Bohmian mechanics” analogue. We summarize our recent work in this area, focusing on two key aspects. We first describe the formulation of a generalized hydrodynamic force, which includes the effects of thermal fluctuations and “quantum fluctuations” and thus determines the time evolution under the influence of dissipation. Second, we introduce a mixed hydrodynamic–Liouville space representation in terms of partial moments, as applied in the context of coupled electronic states and mixed quantum‐classical dynamics. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Irène Burghardt, L. S. Cederbaum

Quantum-mechanical hydrodynamic equations are considered for mixed quantum states, and the corresponding equations for pure quantum states are derived as a particular case. A generalization of the “quantum potential” of Bohmian mechanics is formulated. In the mixed-state case, an infinite hierarchy of kinetic equations arises that may be truncated by introducing suitable approximations. The influence of dissipation on the kinetic equations is discussed.

Irène Burghardt

The theoretical framework of the mixed quantum-classical description given by Burghardt and Parlant [J. Chem. Phys. 120, 3055 (2004)] is detailed. A representation in terms of partial hydrodynamic moments is developed, the dynamics of which is determined by a hierarchy of equations derived from the quantum Liouville equation. Exact equations of motion are obtained, whose quantum-classical approximants are associated with a fluid-dynamical trajectory representation which couples classical variables to quantum hydrodynamic variables. The latter evolve under a generalized hydrodynamic force which also depends upon the classical phase-space variables. The hydrodynamic moment description is shown to be closely connected to mixed quantum-classical phase-space methods.