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Updated: Aug 15, 2026

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
Published on: March 30, 2017
Bose-Einstein condensates in the presence of a magnetic trap and optical lattice
Todd Kapitula1, P G Kevrekidis
1Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131, USA. kapitula@math.unm.edu
Abstract:
In this paper we consider solutions of a nonlinear Schrodinger equation with a parabolic and a periodic potential motivated from the dynamics of Bose-Einstein condensates. Our starting point is the corresponding linear problem which we analyze through regular perturbation and homogenization techniques. We then use Lyapunov-Schmidt theory to establish the persistence and bifurcation of the linear states in the presence of attractive and repulsive nonlinear inter-particle interactions. Stability of such solutions is also examined and a count is given of the potential real, complex and imaginary eigenvalues with negative Krein signature that such solutions may possess. The results are corroborated with numerical computations.
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