Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2001-11-21
Physics
Condensed Matter
Soft Condensed Matter
6 pages, 2 tables
Scientific paper
By examining the bound-state spectra of transverse fluctuations about one-dimensional, spatially localized dark and bright soliton wavetrains of the Gross-Pitaevskii equation, it is established that the low-temperature ground states of repulsive and attractive quasi-one-dimensional Bose-Einstein condensates are degenerate. In the one-soliton limit, both ground states are shown to possess two distinct transverse fluctuation modes which can couple to the spatial soliton: the first involves zero-energy exchange, costing only the soliton shape dressing via uniform translation of its centre of mass. The second mode contributes in a negative energy for the repulsive case, but positive energy in the attractive case. This unstability of the repulsive spatial soliton against localized transverse fluctuation modes invalidates the Gross-Pitaevskii equation for stationary solitonic processes in repulsive 1D Bose-Einstein-Condensate systems.
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