Stochastic Time-Dependent Current-Density-Functional Theory

TL;DR

This paper develops a stochastic time-dependent current-density-functional theory for open quantum systems, proving that identical ensemble-averaged currents imply equivalent vector potentials up to gauge, enabling advanced first-principles simulations.

Contribution

It introduces a new stochastic TD-CDFT framework for open systems, extending the applicability of density-functional theory to non-Hamiltonian dynamics.

Findings

Proves the uniqueness of vector potentials given ensemble-averaged current densities.

Extends TD-DFT to systems interacting with arbitrary external baths.

Enables first-principles calculations of many-particle open quantum systems.

Abstract

A time-dependent current-density-functional theory for many-particle systems in interaction with arbitrary external baths is developed. We prove that, given the initial quantum state $|\Psi_0>$ and the particle-bath interaction operator, two external vector potentials ${\bf A}({\bf r},t)$ and ${\bf A}'({\bf r},t)$ that produce the same ensemble-averaged current density, $\bar{{\bf j}({\bf r},t)}$, must necessarily coincide up to a gauge transformation. This result greatly expands the applicability of time-dependent density-functional theory to open quantum systems, and allows for first-principles calculations of many-particle time evolution beyond Hamiltonian dynamics.