Avoiding Infrared Catastrophes in Trapped Bose-Einstein Condensates
P.G. Kevrekidis (1), G. Theocharis (2), D.J. Frantzeskakis (2), and A., Trombettoni (3) ((1) Department of Mathematics, Statistics, University of, Massachusetts, USA; (2) Department of Physics, University of Athens, Greece;, (3) Istituto Nazionale per la Fisica della Materia
TL;DR
This paper investigates long wavelength instabilities in Bose-Einstein condensates and proposes trapping strategies to suppress these instabilities, supported by analytical estimates and numerical comparisons.
Contribution
It provides explicit estimates and mechanisms for engineering trapping conditions to prevent infrared catastrophes in BECs, enhancing stability control.
Findings
Tight trapping potentials suppress instabilities in BECs.
Analytical estimates match numerical simulations.
Identifies regimes where instabilities can be avoided.
Abstract
This paper is concerned with the long wavelength instabilities (infrared catastrophes) occurring in Bose-Einstein condensates (BECs). We examine the modulational instability in ``cigar-shaped'' (1D) attractive BECs and the transverse instability of dark solitons in ``pancake'' (2D) repulsive BECs. We suggest mechanisms, and give explicit estimates, on how to ``engineer'' the trapping conditions of the condensate to avoid such instabilities: the main result being that a tight enough trapping potential suppresses the instabilities present in the homogeneous limit. We compare the obtained estimates with numerical results and we highlight the relevant regimes of dynamical behavior.
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