When does a quantum many-body system mix rapidly?

A quantum memory can be described by the evolution of an open quantum many-body system in a thermal bath with which it weakly interacts, which can be modelled by a quantum Markov semigroup. The time that it takes for an initial state on the system to reach the equilibrium with the bath is called mixing time. The mixing time of these Markovian dissipative evolutions of open quantum many-body systems represents in particular the time that would take for some quantum information stored in a quantum memory to be destroyed, and it 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, I’ll 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 2022, Ángela Capel received one of the awards in the eighth edition of the Vicent Caselles Awards, annually granted by the Royal Spanish Mathematical Society and the BBVA Foundation. According to the jury, she was recognized “for the quality of the results obtained in her research, published in internationally renowned journals, as well as for their pioneering nature and the undeniable impact they will have”.