The Nonlinear Schroedinger Equation with a random potential: Results and Puzzles
Mathematical Physics
2013-08-30 v1 Disordered Systems and Neural Networks
Quantum Gases
math.MP
Abstract
The Nonlinear Schroedinger Equation (NLSE) with a random potential is motivated by experiments in optics and in atom optics and is a paradigm for the competition between the randomness and nonlinearity. The analysis of the NLSE with a random (Anderson like) potential has been done at various levels of control: numerical, analytical and rigorous. Yet, this model equation presents us with a highly inconclusive and often contradictory picture. We will describe the main recent results obtained in this field and propose a list of specific problems to focus on, that we hope will enable to resolve these outstanding questions.
Cite
@article{arxiv.1108.2956,
title = {The Nonlinear Schroedinger Equation with a random potential: Results and Puzzles},
author = {Shmuel Fishman and Yevgeny Krivolapov and Avy Soffer},
journal= {arXiv preprint arXiv:1108.2956},
year = {2013}
}
Comments
21 pages, 4 figures