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

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.

Quantitative semiclassical analysis of ultracold weakly interacting bose gas trapped in optical boxes

“…( 5) can be converted into an integral over the phase space by replacing the discrete E n with a continuous variable ε(r; p) depending on position r and momentum p, which corresponds to the classical energy associated with the single-particle Hamiltonian for the system given in Eq. ( 2) [10,17]. Within this approximation Eq.…”

“…In this work we want to provide an approach which enables one to deal with any kind of power-law potential conditions, including the anisotropic harmonic oscillator potential and the most relevant rigid boxes potential. Our motivation is to extend and clarify the previous works, and also provide a more detailed discussion of the physical contents of the theory [7][8][9][10][11][12][13]. In spite of the interest in this topic and the progress made so far, none of these works provides a complete picture of the problem.…”