Journal of the Physical Society of Japan

Singularity Formation and Self-Similar Solution in the Magnetically Trapped Bose-Einstein Condensate

Takeya Tsurumi, Miki Wadati

Published Apr 15, 1998• 11 citations

Abstract

We investigate the singularity of the magnetically trapped Bose-Einstein condensate with attractive interatomic interactions. By using a model equation, three-dimensional attractive nonlinear Schrödinger equation with anisotropic harmonic potential terms, we show the scaling laws for the system near the singularity. We also discuss the self-similar behavior of the wavefunction in detail.

DOI: 10.1143/jpsj.67.1197

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Journal of the Physical Society of Japan

Singularity Formation and Self-Similar Solution in the Magnetically Trapped Bose-Einstein Condensate

Takeya Tsurumi, Miki Wadati

Published Apr 15, 1998• 11 citations

Publisher

Abstract

DOI: 10.1143/jpsj.67.1197

Related papers

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Physical Review AApr 1, 1996133 citations

We consider dynamics of Bose-Einstein condensates with long-range attractive interaction proportional to

1/{r}^{b}

and arbitrary angular dependence. It is shown exactly that collapse of a Bose-Einstein condensate without contact interactions is possible only for $b\ensuremath{\geqslant}2$. The case

b=2

is critical and requires the number of particles to exceed a critical value to allow collapse. The critical collapse in that case is a strong one, trapping into the collapsing region a finite number of particles. The case

b>2

is supercritical with an expected weak collapse which traps a rapidly decreasing number of particles during approach to collapse. For

b<2

a singularity at

r=0

is not strong enough to allow collapse but an attractive

1/{r}^{b}

interaction admits stable self-trapping (a stable three-dimensional soliton solution) even in the absence of an external trapping potential.

^{87}\mathrm{Rb}

atoms was recently formed [M. H. Anderson et al., Science 269, 198 (1995)]. These results were obtained by solving the time-independent nonlinear Schr\"odinger equation with anisotropic harmonic trapping potential. We also find vortex solutions for the trap and the critical rotation frequency required for their formation.