40:48
published on May 21, 2026
Jumps, cusps and fractals in the solution of dispersive equations
By Beatrice Pelloni
Stability analysis of a quantum dissipative system
Appears in collection : Mathematical aspects of the physics with non-self-adjoint operators / Les aspects mathématiques de la physique avec les opérateurs non-auto-adjoints
In this talk I will present the stability properties of plane wave solutions for a system describing quantum particles interacting with a complex environment. From a mathematical point of view, this amounts to studying a system of PDEs coupled in a non-local (in time and space) way, which complicates the analysis considerably compared to the usual nonlinear Schr¨odinger equations. The strategy adopted is based on the identification of suitable Hamiltonian structures and Lyapunov functionals. Work in collaboration with T. Goudon.
