Mapping from current densities to vector potentials in time-dependent current density functional theory

摘要

Under reasonable assumptions the time-dependent particle density n(r,t) and the current density j(r,t) of a many-particle system that evolves under the action of external scalar and vector potentials V(r, t) and A(r,t) and is initially in the quantum state | ψ(0) > can be reproduced in another many-particle system with a different two-particle interaction, subjected to external potentials V′(r,t) and A′(r,t) and starting from an initial state |ψ′(0) >, which yields the same density and current as |ψ(0) >. Here we show that given the initial state of this other many-particle system, the potentials V′(r,i) and A′(r,t), if they exist, are uniquely determined up to gauge transformations that do not alter the initial state. As a special case, we obtain a simpler proof of the Runge-Gross theorem for time-dependent current density functional theory. This theorem provides a formal basis for the application of time-dependent current density functional theory to transport problems.