Schrodinger fluid dynamics of many-electron systems in a time-dependent density-functional framework

Abstract

For an N electron system, a connection is explored between density-functional theory and quantum fluid dynamics, through a dynamical extension of the former. First, we prove the Hohenberg-Kohn theorem for a time-dependent harmonic perturbation under conditions which guarantee the existence of the corresponding steady (or quasiperiodic) states of the system. The corresponding one-particle time-dependent Schrodinger equation is then variationally derived starting from a fluid-dynamical Lagrangian density. The subsequent fluid-dynamical interpretation preserves the "particle" description of the system in the sense that the N-electron fluid has N components each of which is an independent-particle Schrodinger fluid characterized by a density function ρ _j and an irrotational velocity field u_j, j = 1,…,N. However, the mean velocity u of the fluid is not irrotational, in general. The force densities and the stress tensor occurring in the Navier-Stokes equation are physically interpreted. The present work is another step towards the interpretation of physicochemical phenomena in three dimensional space.