Nonequilibrium steady states in multi-bath quantum collision models

TL;DR

This paper compares single-bath and two-bath collision models for open quantum systems, revealing how different setups lead to distinct steady states and highlighting the role of non-Markovian dynamics and correlations in quantum thermodynamics.

Contribution

It introduces a two-bath collision model with nonequilibrium steady states and analyzes the effects of non-Markovian interactions on thermalization processes.

Findings

Both models reach the same thermal steady state under certain conditions.

Two-bath setup exhibits nonequilibrium steady states with finite heat currents.

Non-Markovian interactions generate strong correlations affecting steady states.

Abstract

Collision models provide a simple and versatile setting to capture the dynamics of open quantum systems. The standard approach to thermalisition in this setting involves an environment of independent and identically-prepared thermal qubits, interacting sequentially for a finite duration $\Delta t$ with the system. We compare this to a two-bath scenario in which collisional qubits are prepared in either their ground or excited states and the environment temperature is encoded in system-environment couplings. The system reaches the same thermal steady state for both settings, although even in this limit they describe fundamentally different physical processes, with the two-bath setup yielding a nonequilibrium state with finite heat currents. Non-Markovian dynamics arise when intra-environment interactions in either setting are introduced. Here, the system in the single-bath setup again reaches a steady state at the canonical temperature of the bath, but the nonequilibrium steady state of the two-bath setup tends to a different temperature due to the generation of strong system-environment and intra-environment correlations. The two-bath setting is particularly suited to studying quantum trajectories, which are well-defined also for the non-Markovian case. We showcase this with a trajectory analysis of the heat currents within a two-point measurement scheme. Finally, we consider how our results are impacted when the system-environment interaction leads to strict homogenisation. Our results provide insights into the dynamics and thermodynamics of thermalisation towards nonequilibrium steady states and the role of non-Markovian interactions.