The spectral gap for Quantum Markov Semigroups

Poletti Damiano, Università di Genova

Gaussian Quantum Markov semigroups are a special class of semigroups that are both relevant in physical applications and interesting from a mathematical standpoint since they provide an infinte dimensional example where many explicit calculations can be performed. In this talk I will present one of the instances where this happens which is the the study of the spectral gap. Gaussian QMSs are in general defined as semigroups on the symmetric Fock Space in different equivalent ways, one of which is that they preserve the set of gaussian states, i.e. those states in which position and momentum operators are distributed as classical gaussian random variables. Here we work on those gaussian QMSs where there exists a unique faithful invariant state which is also gaussian, we will see that these requirements are not at all restrictive but are the natural setting in which to study the spectral gap. Explicitly we are interested in understanding the speed of convergence of any initial state to the invariant one and link it with the parameter of the semigroup itself. The aim of this talk is to present the results we obtained in this direction, providing the exact characterization of the spectral gap.

Area: CS12 - Quantum probability and related fields (Vitonofrio Crismale and Veronica Umanità)

Keywords: Quantum Markov Semigroups, gaussian semigroups, spectral gap

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