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Stability of local quantum dissipative systems

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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.

For theoretical and experimental reasons, it is important to estimate the sensitivity of the system agains small perturbations, coming from numerical errors or physical noise. We prove that local observables and correlation functions are stable under local and quasi- local perturbations if the Liouvillian is frustration free, translational invariant (uniformly), has a unique fix point (with no restriction on its rank) and has a mixing time which scales logarithmically with the system size. These conditions can be relaxed to the non-translational invariant case, at the cost of requiring Local Topological Quantum Order.

As a main example we prove that classical Glauber dynamics is stable under local perturbations, including perturbations in the transition rates which do not preserve detailed balance. To our knowledge, this result is new even classically.

This talk is part of the CQIF Seminar series.

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