Abstract.

In this talk I will overview variational problems arising from the study ofquantum matter interacting with a macroscopic force field. These interactions are verycommon in both solid state and condensed matter physics, as well as in higher energysettings. In particular, I will focus on the link between the effective and microscopicdescription of such variational problems, using techniques of quasi-classical analysisdeveloped in recent years in collaboration with M. Correggi and M. Olivieri.