Stochastic time-dependent current-density functional theory: a functional theory of open quantum systems

TL;DR

This paper extends time-dependent current-density-functional theory to stochastic open quantum systems, enabling microscopic analysis of energy transport, dissipation, and decoherence phenomena with practical numerical methods.

Contribution

It introduces stochastic TDCDFT for open quantum systems, linking it to density matrix formalism and providing a numerical approach for solving the equations of motion.

Findings

Applied to a 1D bosonic gas in a harmonic trap with an external bath.

Demonstrated the theory's capability to describe dissipative quantum dynamics.

Provided a numerically feasible method for solving stochastic TDCDFT equations.

Abstract

The dynamics of a many-body system coupled to an external environment represents a fundamentally important problem. To this class of open quantum systems pertains the study of energy transport and dissipation, dephasing, quantum measurement and quantum information theory, phase transitions driven by dissipative effects, etc. Here, we discuss in detail an extension of time-dependent current-density-functional theory (TDCDFT), we named stochastic TDCDFT [Phys. Rev. Lett. {\bf 98}, 226403 (2007)], that allows the description of such problems from a microscopic point of view. We discuss the assumptions of the theory, its relation to a density matrix formalism, and the limitations of the latter in the present context. In addition, we describe a numerically convenient way to solve the corresponding equations of motion, and apply this theory to the dynamics of a 1D gas of excited bosons confined in a harmonic potential and in contact with an external bath.