Exact treatment of the memory kernel under time-dependent system-environment coupling via a train of delta distributions

TL;DR

This paper presents an exact analytical method for solving nonstationary memory kernel equations in open quantum systems using a train of delta functions, demonstrated on specific models.

Contribution

It introduces a nonperturbative solution technique for nonstationary memory kernels using Dirac-delta switchings, advancing the analysis of open quantum system dynamics.

Findings

Solution asymptotes to known exact solutions in the continuum limit.

Method enables visualization of environmental memory effects.

Applicable to models like the damped Jaynes-Cummings and harmonic oscillator.

Abstract

Memory effects in a quantum system coupled to an environment are one of the central features in the theory of open quantum systems. The dynamics of such quantum systems are typically governed by an equation of motion with a time-convolution integral of the memory kernel. However, solving such integro-differential equations is challenging, especially when the memory kernel is nonstationary (not time-translation invariant). In this paper, we analytically and nonperturbatively solve such integro-differential equations with a nonstationary memory kernel by employing a train of Dirac-delta switchings. We then apply this method to the damped Jaynes-Cummings model and the damped harmonic oscillator model to demonstrate that (i) our solution asymptotes to the well-known exact solution in the continuum limit, and that (ii) our method also enables us to visualize the memory effect in the environment.