Approach to equilibrium in quantum spin systems

I will present the recent results in the ongoing research program on approach to equilibrium. Having reviewed the basics of quantum spin systems, I will discuss the following topics:

1. Equilibrium steady states (ESS), constants of motion, and approach to thermal equilibrium.

2. Dynamical conservation laws via the Lieb-Robinson bound

3. Application of our theory to the mixed-field Ising chain, link to the ongoing research program on nonintegrable systems by Shiraishi et al.

4. Variational characterization of ESS, approach to constrained equilibrium

This initiative is part of the "PhD Lectures" activity of the project "Departments of Excellence 2023-2027" of the Department of Mathematics of Politecnico di Milano. This activity consists of seminars open to PhD students, followed by meetings with the speaker to discuss and go into detail on the topics presented at the talk.