Anderson localisation and sub-diffusion for the nonlinear Schrodinger equtation: results and puzzles
Seminar Room 1, Newton Institute
AbstractIt is well known that transport is suppressed in disordered media in one dimension, which is known as Anderson localization. However, it is not known, even numerically, if adding nonlinearity destroys dynamical localization in the limit of long times. We have conducted an analytical and rigorous research that sheds some light on this subject. Using perturbation theory in the nonlinearity strength we have demonstrated that an initial wavepacket does not spread for short time scales and for long time scales it spreads at most logarithmically. These results provide better ground for understanding of the underlying processes of the competition between the randomness and the nonlinearity.
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