Non-Markovian Equilibration Controlled by Symmetry Breaking

We study the effects of symmetry breaking on non-Markovian dynamics in various system-bath arrangements. It is shown that by breaking certain symmetries features signaling non-Markovian time evolution disappear within a finite time t_{g}. We demonstrate numerically that the scaling of t_{g} with the symmetry breaking strength is different for various types of symmetry. We provide a mathematical explanation for these differences related to the spectrum of the total system-bath Hamiltonian and provide arguments that the scaling properties of t_{g} should be universal.