**II Coloquio**__ Premio Rubio de Francia __

**Angelo Lucia**

**California Institute of Technology**

**Premio Rubio de Francia 2017**

**" Rapid mixing in dissipative many-body quantum systems"**

**Viernes 5 de octubre de 2018, 11: 30 horas**

**Seminario del Departamento de Matemáticas, aula M-17, 520**

**Facultad de Ciencias, UAM**I will show that in the rapid mixing regime a number of very interesting properties of the system can be obtained. First of all, the evolution is stable, in the appropriate sense, under weak but extensive perturbations. Secondarily, the unique fixed point of the evolution has only short-ranged correlations, and it satisfies an area law for the mutual information. I will also comment on how the spectrum of the generator of the evolution does not contain enough information to determine whether a given system is rapidly mixing, and how one can use a quantum version of the log-Sobolev inequality to show it instead.