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Stability analysis of a Bose–Einstein condensate trapped in a generic potential

  • Elías CastellanosEmail author
  • Celia Escamilla-Rivera
  • Mayra J. Reyes-Ibarra
Regular Article

Abstract

We investigate the dynamical behavior of the Gross–Pitaevskii equation for a Bose–Einstein condensate trapped in a spherical power law potential restricted to the repulsive case, from the dynamical system formalism point of view. A five-dimensional dynamical system is found (due the symmetry of the Gross–Pitaevskii equation interacting with a potential), where the Thomas–Fermi approximation constrains the parameter space of solutions. We show that for values of the power law exponent equal or smaller than 2 the system seems to be stable. However, when the corresponding exponent is bigger than 2, the instability of the system grows when the power law exponent grows, indicating that large values of the aforementioned parameter can be related to a loss in the number of particles from the condensed state. This fact can be used also to show that the stability conditions of the condensate are highly sensitive to the exponent associated with the external potential.

Graphical abstract

Keywords

Cold Matter and Quantum Gas 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Elías Castellanos
    • 1
    Email author
  • Celia Escamilla-Rivera
    • 1
  • Mayra J. Reyes-Ibarra
    • 2
  1. 1.Mesoamerican Centre for Theoretical Physics, Universidad Autónoma de Chiapas, Ciudad UniversitariaTuxtla GutiérrezMexico
  2. 2.Departamento de Física, Centro de Investigación y Estudios Avanzados del IPN. A. P. 14–740Ciudad de MéxicoMexico

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