Towards a random matrix theory of non-Markovian open quantum systems

The evolution of open quantum systems depends on how they interact with their environment, which is, unfortunately, notoriously hard to model. One commonly used approximation is to consider memoryless environments (the so-called Markovian approximation), greatly simplifying the analysis. Assuming the system to be complex, and thus employing random matrix techniques, we show that universal properties emerge in random Markovian dynamics. However, such an approach fails in several situations, such as transport setups and noisy intermediate-scale quantum computers. Therefore, we determine universal signatures of non-Markovian dissipative systems by applying random matrix methods to study their spectral and steady-state properties. We focus on quadratic systems where an exact solution can be found and identify how the departure from Markovianity modifies the universal properties of the ergodic regimes identified in the Markovian case. In particular, we establish how the system-bath coupling and the thermodynamic features of the environment affect spectral and steady-state properties.