Phase associated with the single-particle density of many-electron systems

Abstract

In excited states of atoms and molecules, as well as in time-dependent situations, the one-electron density no longer suffices to completely characterize the electronic state; in addition, one now requires information about the electronic phase or the current density. We show that, for a stationary electronic state, the continuity equation of quantum fluid dynamics represents a differential equation for the electronic phase, which must be solved subject to certain periodicity conditions. These periodicity conditions arise from the nodal topology of the wave function and give rise to quantized vortices of current. The consequences of writing an electronic "wave function" for a many-electron system directly in terms of the single-particle density and phase have been investigated. We have shown that such a procedure leads to the appearance of an "internal magnetic vector potential." We also establish the connection between the electronic phase and the geometrical ("Berry") phase accompanying the adiabatic transport of a quantal system around a closed loop in parameter space. This leads to a generalization of the current density concept and allows us to discuss the geometrical phase in terms of the circulation of this current in parameter space.