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- Logarithmic Sobolev Inequalities for Quantum Many-Body Systems.

The mixing time of Markovian dissipative evolutions of open quantum many-body systems can be bounded using optimal constants of certain quantum functional inequalities, such as the logarithmic Sobolev constant. For classical spin systems, the positivity of such constants follows from a mixing condition for the Gibbs measure, via quasi-factorization results for the entropy.

Inspired by the classical case, we present a strategy to derive the positivity of the logarithmic Sobolev constant associated to the dynamics of certain quantum systems from some clustering conditions on the Gibbs state of a local, commuting Hamiltonian. In particular we address this problem for the heat-bath dynamics in 1D and the Davies dynamics, showing that the first one is positive under the assumptions of a mixing condition on the Gibbs state and a strong quasi-factorization of the relative entropy, and the second one under some strong clustering of correlations.

Collection/Series:

Event Type:

Seminar

Speaker(s):

Event Date:

Wednesday, October 16, 2019 - 16:00 to 17:30

Location:

Bob Room

Room #:

405

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©2012 Perimeter Institute for Theoretical Physics