Aula Seminari, Dipartimento di Matematica
Quantum Markov Semigroups constitute a mathematically tractable yet physically relevant class of evolutions for open quantum systems. Under the assumption that the semigroup is ergodic, an interesting question is how to obtain estimates on the time it takes to reach the unique steady state, i.e., the mixing time of the process.
In this talk, I will present some recent results in the context of quantum spin systems on lattices, in which case one wants to control the growth of the mixing time as a function of the volume of the system considered. Specifically, I will consider the case in which the semigroup describes a thermalization process at a positive temperature and present some results about 1D and 2D models.