Quantum Systems: A Mathematical Journey from Few to Many Particles

Hydrodynamic theory of tunneling in quantum mechanics and beyond

Avy Soffer

Rutgers University

I will describe a method, based on the hydrodynamic formalism, to study the problem of soliton and vortex tunneling from wells, and related phenomena. In particular, I show how this approach uncovers a new structure of tunneling processes, for both LINEAR and nonlinear Schroedinger equations. This new process, in which the tunneled wave appears as blips outside the well, has been observed experimentally; the extension to two dimension, which imply the formation of jets from Vortex decay , may also be observed. Other results will also be mentioned.