Publication Date
2005
Journal or Book Title
New Journal of Physics
Abstract
Motivated by the examples of a curved waveguide embedded in a photonic crystal and cold atoms moving in a waveguide created by a spatially inhomogeneous electromagnetic field, we examine the effects of geometry in a 'quantum channel' of parabolic form. Starting with the linear case we derive exact as well as approximate expressions for the eigenvalues and eigenfunctions of the linear problem. We then proceed to the nonlinear setting and its stationary states in a number of limiting cases that allow for analytical treatment. The results of our analysis are used as initial conditions in direct numerical simulations of the nonlinear problem and in this case localized excitations are found to persist. We found also interesting relaxational dynamics. Analogies of the present problem in context related to atomic physics and particularly to Bose–Einstein condensation are discussed.
Pages
52-
Volume
7
Recommended Citation
Gaididei, Yu B.; Christiansen, P L.; and Kevrekidis, PG, "Localization of nonlinear excitations in curved waveguides" (2005). New Journal of Physics. 1100.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1100
Comments
This is the pre-published version harvested from arXiv. The published version is located at http://iopscience.iop.org/1367-2630/7/1/052/