Classical-quantum correspondence in the noise-based dissipative systems

TL;DR

This paper explores how classical noise models can be extended to simulate quantum dissipative systems beyond traditional limitations by introducing auxiliary systems, enabling the study of both Markovian and non-Markovian dynamics.

Contribution

It introduces a method to map classical noise to quantum environments using auxiliary systems, allowing simulation of dissipative processes beyond infinite temperature.

Findings

The model reproduces both Markovian and non-Markovian dynamics.

Different system quantities are governed by different model parameters.

The approach can simulate negative temperatures and asymmetric quenches.

Abstract

We investigate the correspondence between classical noise and quantum environments. Although it has been known that the classical noise can be mapped to the quantum environments only for pure dephasing and infinite-temperature dissipation processes, we describe that this limitation can be circumvented by introducing auxiliary systems and conservation. Taking a two-level system as an example, we construct the so-called central spin model with its couplings fluctuating as the classical noise, and then acquire its statistical-average dynamics which captures the dissipations beyond the infinite temperature. By adjusting the number of the auxiliary systems and their initial states, the noise-based model reproduces both Markovian and non-Markovian evolutions. It is also found that different quantities of the two-level system are governed by different model parameters, indicating that the constructed model is an efficient simulator for specific observables, rather than an equivalent form of a realistic open system. In addition, the model is also applicable to investigate topical mechanisms of the open systems, e.g. negative temperatures and asymmetric equidistant quenches.