|
Applied Math Seminar
Ground State Selection and Energy Equipartition |
|
Nonlinear Schroedinger / Gross-Pitaevskii equations are an important class of dispersive Hamiltonian PDEs. They govern diverse phenomena in quantum physics and optics. In the weakly nonlinear and semi-classical regimes, the nonlinear ground state plays a distinguished role. We prove that for large time, excited states decay; energy is transferred from excited states to the nonlinear ground state and to radiation modes. The mechanism is nonlinear resonant interactions of discrete and radiation (continuous spectral) modes. We also prove a result on asymptotic distribution of the transferred energy. |