title: Extended hydrodynamic approach to quantum-classical nonequilibrium evolution. I. Theory.
abstract: A mixed quantum-classical formulation is developed for a quantum subsystem in strong interaction with an N-particle environment, to be treated as classical in the framework of a hydrodynamic representation. Starting from the quantum Liouville equation for the N-particle distribution and the corresponding reduced single-particle distribution, exact quantum hydrodynamic equations are obtained for the momentum moments of the single-particle distribution coupled to a discretized quantum subsystem. The quantum-classical limit is subsequently taken and the resulting hierarchy of equations is further approximated by various closure schemes. These include, in particular, (i) a Grad-Hermite-type closure, (ii) a Gaussian closure at the level of a quantum-classical local Maxwellian distribution, and (iii) a dynamical density functional theory approximation by which the hydrodynamic pressure term is replaced by a free energy functional derivative. The latter limit yields a mixed quantum-classical formulation which has previously been introduced by I. Burghardt and B. Bagchi, Chem. Phys. 134, 343 (2006).
authors.affiliation: Département de Chimie, Ecole Normale Supérieure, 24 rue Lhomond, F-75231 Paris cedex 05, France.
authors.forename: David
authors.initials: D
authors.lastname: Bousquet
authors.forename: Keith H
authors.initials: KH
authors.lastname: Hughes
authors.forename: David A
authors.initials: DA
authors.lastname: Micha
authors.forename: Irene
authors.initials: I
authors.lastname: Burghardt
mesh_terms: D007700:Kinetics; D008956:Models, Chemical; D011789:Quantum Theory