Thermalisation in non-Markovian environments

Thermodynamics tells us that a system weakly coupled to an infinite environment will reach thermal equilibrium. In the language of open quantum systems this means we expect a thermal steady state to arise. Under the Born-Markov approximations a the bath is assumed to relax instantaneously, and equations of motion can be derived to ensure thermal equilibrium is reached. However, in many realistic systems of interest these approximations no longer hold. Here we use a variety of exact numerical methods such as time evolving matrix product operators (TEMPO) and the hierarchy of pure states (HOPS) to investigate how non-Markovian environments can perturb the thermal equilibrium state of strongly interacting many-body quantum systems.