Classical-quantum correspondence in noise-based dissipative systems

We investigate the correspondence between classical noise and quantum environments. Although it is known that classical noise can be mapped to quantum environments for pure dephasing and infinite-temperature dissipation processes, we show how finite-temperature dissipation can be also described using classical noise 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 with the classical noise and then acquire its statistical-average dynamics which captures the dissipation beyond infinite temperature. By adjusting the number of auxiliary systems and their initial states, the noise-based model reproduces both Markovian and non-Markovian evolution. We also find that different quantities of the two-level system are governed by different model parameters, indicating that the constructed model is an effective 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 open systems, e.g., negative temperatures and asymmetric equidistant quenches.