Talks

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.

Global symmetries and gauge symmetries have played a crucial role in physics.  The idea of duality demonstrates that gauge symmetries can be emergent and might not be fundamental.  During the past decades it became clear that the circle of ideas about emergent gauge symmetries and duality is central in different branches of physics including Condensed Matter Physics, Quantum Field Theory, and Quantum Gravity.   We will review these developments, which highlight the unity of physics.