This research project is to study the long time behavior of solutions of nonlinear Schroedinger equations. The potential may be either random or deterministic and close to a harmonic oscillator. In both cases the analysis is done in all of space and the linear equation is assumed to only have bound states.
These equations are fundamental for quantum mechanics. It is expected that the results obtained here may have applications to the design of memory chips, in fiber optics and for quadrupole radio-frequency traps.
