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 on 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. Subsequently, we
apply this strategy to address this problem for the heat-bath dynamics.
Ponente: Ángela Capel. ICMAT, Madrid
Fecha y hora: Miércoles, 4 de diciembre de 2019 a las 11 horas.
Lugar: Seminario de Física Estadística. Planta baja del edificio de Física (junto a las pantallas). Facultad de Ciencias. Granada.
