Institute for Quantum Information (IQI) Weekly Seminar

Open quantum systems weakly coupled to the environment are modelled by completely positive, trace preserving semigroups of linear maps. The generators of such evolutions are called Liouvillians, and similarly to the Hamiltonian in the case of coherent evolution, they encode the physical properties of the system. In the setting of quantum many-body systems on a lattice it is natural to consider local or exponentially decaying interactions. We will focus on the case of maps with a unique fixed point, and consider the scaling of the mixing time with respect to the system size. In particular, if such scaling is sub-linear, a number of good properties of the evolution can be obtained: local observables are stable against perturbations, the fixed point has a finite correlation length, and in the case of frustration-free systems, satisfies an area law.