Applications of the density-functional formalism to inhomogeneous multiparticle systems /

Berthold‐Georg Englert, Heinz K. H. Siedentop, Martin-Isbjörn Trappe

Marvin McClendon

A three-dimensional stochastic process which has the particle density as its probability density is constructed from Nelson's stochastic mechanics, yielding a particle trajectory picture for density-functional theory. This diffusion process enables simulating the detailed behavior of multiparticle quantum systems with substantial computational economy. A stochastic-mechanical form of the Heisenberg uncertainty principle holds in the new context. Moreover, a kinetic energy functional is defined and shown to be connected with other kinetic energy expressions, and in the case of a time-independent ground state a formal dynamics for the process is proposed. A related real-space version is developed of Bohm's quantum potential formalism.

Yu. M. Poluéktov

A self-consistent field (SCF) model is constructed for spatially inhomogeneous Bose systems with broken symmetry. A system of self-consistent equations is obtained for the wave functions of the quasiparticles and the wave function of the condensate particles and another system of equations for the normal and anomalous single-particle density matrices. The many-particle wave function is found. The thermodynamics of multiparticle Bose systems is constructed on the basis of a microscopic treatment in the SCF approximation. It is stressed that Bose condensation in the ideal gas model is substantially different from Bose condensation in a system of interacting Bose particles because a pair condensate is necessarily present as well as the single-particle condensate, even for an arbitrarily weak interaction. The role of single-particle and collective excitations in Bose systems is discussed.

И.П. Базаров, Pavel Nikolaev

Philip R. Wallace

Adam Griffin

The density functional theory originally developed by Hohenberg, Kohn, and Sham provides a rigorous conceptual framework for dealing with inhomogeneous interacting Fermi systems. We extend this approach to deal with inhomogeneous interacting Bose-condensed systems, limiting this presentation to setting up the formalism to deal with ground-state (T = 0) properties. The key new feature is that one must deal with energy functionals of both the local density n(r) and the local complex macroscopic wave function Φ(r) associated with the Bose broken-symmetry (the local condensate density is [Formula: see text]. Implementing the Kohn–Sham scheme, we reduce the problem to a gas of weakly interacting Bosons moving in self-consistent diagonal and off-diagonal one-body potentials. Our formalism should provide the basis for studies of the surface properties of liquid 4He as well as the properties of Bose-condensed atomic gases trapped in external potentials.