Year: 2007
Type: article
Abstract: We present a constructive derivation of a time-dependent deformation functional theory---a collective variable approach to the nonequilibrium quantum many-body problem. It is shown that the motion of infinitesimal fluid elements (i.e., a set of Lagrangian trajectories) in an interacting quantum system is governed by a closed hydrodynamics equation with the stress force being a universal functional of Green's deformation tensor ${g}_{ij}$. Since the Lagrangian trajectories uniquely determine the current density, this approach can be also viewed as a representation of the time-dependent current-density functional theory. To derive the above theory, we separate a ``convective'' and a ``relative'' motions of particles by reformulating the many-body problem in a comoving Lagrangian frame. Then, we prove that a properly defined many-body wave function (and thus any observable) in the comoving frame is a universal functional of the deformation tensor. Both the hydrodynamic and the Kohn-Sham formulations of the theory are presented. In the Kohn-Sham formulation, we derive a few exact representations of the exchange-correlation potentials, and discuss their implication for construction of nonadiabatic approximations. We also discuss a relation of the present approach to a recent continuum mechanics of the incompressible quantum Hall liquids.
Source: Physical Review B
Author: I. V. Tokatly
Institution: Friedrich-Alexander-Universität Erlangen-Nürnberg
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4241184504