Singularity Formation and Collapse in the Attractive Gross-Pitaevskii Equation

Details Singularity Formation and Collapse in the Attractive Gross-Pitaevskii Equation Singularity Formation and Collapse in the Attractive Gross-Pitaevskii Equation

2001-01-11

arxiv.org/abs/cond-mat/0101160v2

Physics

Condensed Matter

4 pages, 1 figure, v2. In this version of the paper we have improved the language and readability in a number of places. We al

Scientific paper

A generic mechanism of collapse in the Gross-Pitaevskii equation with attractive interparticle interactions is gained by reformulating this equation as Newton's equation of motion for a system of particles with a constraint. 'Quantum pressure' effects give rise to formation of a potential barrier around the emerging singularity, which prevents a fraction of the particles from falling into the singularity. For reasonable initial widths of the condensate, the fraction of collapsing particles, which are thereby removed from the condensate, is found to be a 'universal' number $\simeq 0.7$.

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