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

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• A brief compendium of time-dependent density-functional theory
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• The Driven Liouville von Neumann Equation in Lindblad Form
• Relaxation and dephasing in open quantum systems time-dependent density functional theory: Properties of exact functionals from an exactly-solvable model system
• Probing quantum coherence in ultrafast molecular processes: an ab initio approach to open quantum systems
• Non-Markovian Fermionic Stochastic Schrödinger Equation for Open System Dynamics
• Stochastic Quantum Molecular Dynamics
• Towards a dynamical approach to the calculation of the figure of merit of thermoelectric nanoscale devices
• Time-Dependent Density Functional Theory of Open Quantum Systems in the Linear-Response Regime
• Stochastic quantum molecular dynamics for finite and extended systems
• Exponential Integrators for Stochastic Schrödinger Equation
• Quantum Spinon Oscillations
• Measuring excitation-energy transfer with a real-time time-dependent density functional theory approach
• Foundations of stochastic time-dependent current-density functional theory for open quantum systems: Potential pitfalls and rigorous results
• Application of a time-convolutionless stochastic Schrödinger equation to energy transport and thermal relaxation
• Dissipation and spontaneous emission in quantum electrodynamical density functional theory based on optimized effective potential: A proof of concept study
• Thermoelectric phenomena in disordered open quantum systems
• A State Representation Approach for Atomistic Time-Dependent Transport Calculations in Molecular Junctions
• Interaction as stochastic noise