Dynamics and spectrum in the semiclassical limit for non-self-adjoint operators

Abstract: One of the early achievements of microlocal and semiclassical analysis was the asymptotic description, in a large frequency / small parameter case, of eigenvalues and (in the integrable case) eigenfunctions of self-adjoint operators. This is related to a refined description of the dynamics through the well-known Egorov theorem: quantum evolution is well-approximated by classical evolution. The non-self-adjoint case presents serious additional difficulties. Making sense of the appropriate "classical" objects, and proving the correspondence, necessitates a great deal of supplementary geometric and analytic work. In this talk, I will present the challenges associated with non-self-adjoint semiclassical analysis, and describe recent results as well as perspectives.

MathematicsPhysics

Audience: researchers in the topic

Probability, Statistical Mechanics and Quantum Fields