Memory Effects In Nonequilibrium Quantum Impurity Models

TL;DR

This paper investigates memory effects in the nonequilibrium Anderson impurity model, deriving an exact quantum master equation with a non-Markovian kernel and analyzing how temperature, bias, and bandwidth influence memory dynamics.

Contribution

It introduces a real-time path integral approach to evaluate the memory kernel and explores conditions for steady-state stability in nonequilibrium quantum impurity systems.

Findings

Memory typically decays faster than system dynamics

Longer memory tails can develop under certain conditions

Steady-state existence and stability depend on system parameters

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.