Efficient simulation of non-Markovian system-environment interaction

TL;DR

This paper presents a novel combination of TEDOPA and TTM methods to efficiently simulate long-time non-Markovian quantum dynamics, especially at low temperatures and with complex spectral densities.

Contribution

The paper introduces a combined approach of TEDOPA and TTM, enabling access to long-time dynamics of non-Markovian quantum systems previously difficult to simulate.

Findings

Successful benchmark demonstrating method viability

Ability to simulate long-time dynamics in complex spectral environments

Potential for broader applications in quantum system analysis

Abstract

In this work, we combine an established method for open quantum systems -- the time evolving density matrix using orthogonal polynomials algorithm (TEDOPA) -- with the transfer tensors formalism (TTM), a new tool for the analysis, compression and propagation of non-Markovian processes. This enables the investigation of previously inaccessible long-time dynamics, such as those ensuing from low temperature regimes with arbitrary, possibly highly structured, spectral densities. We briefly introduce both methods, followed by a benchmark to prove viability and combination synergies. Subsequently we illustrate the capabilities of this approach at the hand of specific examples and conclude our analysis by highlighting possible further applications of our method.