Memory Effects In Nonequilibrium Quantum Impurity Models

Abstract

Memory effects play a key role in the dynamics of strongly correlated systems driven out of equilibrium. In the present study, we explore the nature of memory in the nonequilibrium Anderson impurity model. The Nakajima--Zwanzig--Mori formalism is used to derive an exact generalized quantum master equation for the reduced density matrix of the interacting quantum dot, which includes a non-Markovian memory kernel. A real-time path integral formulation is developed, in which all diagrams are stochastically sampled in order to numerically evaluate the memory kernel. We explore the effects of temperature down to the Kondo regime, as well as the role of source--drain bias voltage and band width on the memory. Typically, the memory decays on timescales significantly shorter than the dynamics of the reduced density matrix itself, yet under certain conditions it develops a smaller long tail. In addition we address the conditions required for the existence, uniqueness and stability of a steady-state.

4 pages, 3 figures

References in corpus (7)

• Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach
• Real-time path integral approach to nonequilibrium many-body quantum system
• Diagrammatic Monte Carlo simulation of non-equilibrium systems
• Iterative real-time path integral approach to nonequilibrium quantum transport
• Kinetic Equations for Transport Through Single-Molecule Transistors
• A perturbative nonequilibrium renormalization group method for dissipative quantum mechanics: Real-time RG in frequency space (RTRG-FS)
• Anderson impurity model in nonequilibrium: analytical results versus quantum Monte Carlo data

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