Speaker: Beatrice Langella, Sissa Trieste.
Energy cascades for quantum harmonic oscillators in dimension 2
Energy cascades are a widely observed phenomenon in physical systems, yet providing a rigorous mathematical proof of their occurrence remains in many cases a major challenge. Here we focus on a class of linear Schrödinger equations whose Hamiltonians are bounded, time-periodic perturbations of the two-dimensional harmonic oscillator. We investigate whether Sobolev norms can grow unboundedly for a generic choice of perturbations, and under which conditions such growth occurs.
The proof combines pseudo-differential normal form techniques, Mourre theory, and dynamical systems methods, to identify the class of perturbations that give rise to energy cascades and drive the unbounded transfer of energy across modes.
This is a joint work with A. Maspero and M. T. Rotolo.
Where: Università di Roma Tre (Largo S. Murialdo 1, aula M3)
