Some problems in large deviations for quantum systems.
We discuss several issues in quantum large deviations. The first
problem we discuss is a generalization of Laplace-Vardhan lemma to
quantum spin systems or in the language of statistical mechanics a
proof of a variational principle for systems with short range and mean
field interactions. (Joint work with W. De Roeck, C. Maes and
K. Netockny). The second problem we address is a proof a large
deviation principle for macroscopic observables in quantum systems.
We apply to the quantum case an approach to large deviations which
goes back to Lanford and Ruelle and use direct sub additivity
arguments. (Joint work with Y. Ogata). Finally we will discuss some
open problems.