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

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.

17 pages, 7 figures, RevTex4; few typos corrected, a figure modified

References in corpus (4)

• Staying positive: going beyond Lindblad with perturbative master equations
• Stochastic Time-Dependent Current-Density-Functional Theory
• Effective single-particle order-N scheme for the dynamics of open non-interacting many-body systems
• The decay of excited He from Stochastic Density-Functional Theory: a quantum measurement theory interpretation