“Slow energy transfer in Schrödinger type equations”
Mercoledì 3 Dicembre 2025, ore 15:00 - Aula 2AB45 - Beatrice Langella (SISSA, Trieste)
Abstract
In the last decades, a great effort has been made into understanding the long time dynamics of Schrödinger type equations on compact manifolds, and in particular the phenomenon of energy cascades, according to which energy transfers from lower to higher frequency scales. In this talk I will present a new class of systems, that we call globally integrable quantum systems, for which one can prove global-in-time upper bounds on the growth of Sobolev norms for all solutions, also in presence of unbounded perturbations. As a consequence, we deduce that energy cascade phenomena can happen only on very long time scales. The proof is based on normal form techniques and on a quantum adaptation of the geometric part of Nekhoroshev Theorem.
