Publication Date
2005
Journal or Book Title
SIAM Journal of Applied Dynamical Systems
Abstract
We consider the Gross--Pitaevskii (GP) equation in the presence of periodic and quasi-periodic superlattices to study cigar-shaped Bose--Einstein condensates (BECs) in such potentials. We examine spatially extended wavefunctions in the form of modulated amplitude waves (MAWs). With a coherent structure ansatz, we derive amplitude equations describing the evolution of spatially modulated states of the BEC. We then apply second-order multiple scale perturbation theory to study harmonic resonances with respect to a single lattice substructure as well as ultrasubharmonic resonances that result from interactions of both substructures of the superlattice. In each case, we determine the resulting system's equilibria, which represent spatially periodic solutions, and subsequently examine the stability of the corresponding wavefunctions by direct simulations of the GP equation, identifying them as typically stable solutions of the model. We then study subharmonic resonances using Hamiltonian perturbation theory, tracing robust spatio-temporally periodic patterns.
Pages
783-807
Volume
4
Issue
4
Recommended Citation
Porter, Mason A. and Kevrekidis, PG, "Bose-Einstein Condensates in Superlattices" (2005). SIAM Journal of Applied Dynamical Systems. 1141.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/1141
Comments
This is the pre-published version harvested from arXiv. The published version is located at http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SJADAY000004000004000783000001&idtype=cvips&gifs=yes