Application of a time-convolutionless stochastic Schr\"odinger equation to energy transport and thermal relaxation

TL;DR

This paper evaluates a time-convolutionless stochastic Schrödinger equation for efficiently modeling non-Markovian quantum dynamics, demonstrating its effectiveness in thermal relaxation and energy transport in spin chains with manageable computational costs.

Contribution

It introduces and validates a local-in-time stochastic Schrödinger equation for non-Markovian dynamics, enabling efficient simulation of thermal relaxation and energy transport.

Findings

Accurately describes thermal relaxation processes.

Successfully applied to energy transport in spin chains.

Offers a computationally efficient alternative to traditional methods.

Abstract

Quantum stochastic methods based on effective wave functions form a framework for investigating the generally non-Markovian dynamics of a quantum-mechanical system coupled to a bath. They promise to be computationally superior to the master-equation approach, which is numerically expensive for large dimensions of the Hilbert space. Here, we numerically investigate the suitability of a known stochastic Schr\"odinger equation that is local in time to give a description of thermal relaxation and energy transport. This stochastic Schr\"odinger equation can be solved with a moderate numerical cost, indeed comparable to that of a Markovian system, and reproduces the dynamics of a system evolving according to a general non-Markovian master equation. After verifying that it describes thermal relaxation correctly, we apply it for the first time to the energy transport in a spin chain. We also discuss a portable algorithm for the generation of the coloured noise associated with the numerical solution of the non-Markovian dynamics.