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) over right arrow ,t) and the current density (j) over right arrow((r) over right arrow ,t) of a many-particle system that evolves under the action of external scalar and vector potentials V((r) over right arrow ,t) and (A) over right arrow((r) over right arrow ,t) and is initially in the quantum state parallel topsi(0)> can be reproduced in another many-particle system with a different two-particle interaction, subjected to external potentials V-'((r) over right arrow ,t) and (A) over right arrow (')((r) over right arrow ,t) and starting from an initial state \psi(')(0)>, which yields the same density and current as \psi(0)>. Here we show that given the initial state of this other many-particle system, the potentials V-'(r,t) 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.

[发布日期] 2004-11-01

[关键词] SYSTEMS