Universal Properties of Non-Markovian Dissipative Quantum Systems

In this work, we study the spectral, steady-state, and transport properties of a generic non-

Markovian quantum system of free fermions. We consider a setup connected to two reservoirs at

the same temperature and with symmetric chemical potentials. The system’s Hamiltonian and its coupling to each reservoir are described by random matrices from the Gaussian unitary ensemble and the Laguerre unitary ensemble, respectively.

By analyzing the Liouvillian spectrum, we observe that it is similar to the Markovian counterpart and remains unaffected by the characteristics of the environment. We compute the evolution of the decoherence rates and of the non-Markovian measure $f_{nM}$, verifying that they approach a stationary regime.

Further, we examine the Markovian limits and explore the distribution of decoherence rates across different limiting cases. For the remaining parameter space, we focus on particular regions where we are able to make analytical or empirical statements.

Lastly, we investigate conductance fluctuations, presenting novel numerical results for the dependence of conductance variance on parameters $m$, the decoherence channel density, and $g$, the environment coupling. This deviates from the expected universal conductance fluctuation value for random matrices.