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Transition from resonances to bound states in nonlinear systems: application to Bose–Einstein condensates

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Nimrod Moiseyev1,5, L D Carr2,6, Boris A Malomed3 and Y B Band4

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LETTER TO THE EDITOR

It is shown using the Gross–Pitaevskii equation that resonance states of Bose–Einstein condensates with attractive interactions can be stabilized into true bound states. A semiclassical variational approximation and an independent quantum variational numerical method are used to calculate the energies (chemical potentials) and linewidths of resonances of the time-independent Gross–Pitaevskii equation; both methods produce similar results. Borders between the regimes of resonances, bound states and, in two and three dimensions, collapse are identified.


PACS

03.75.Hh Static properties of condensates; thermodynamical, statistical and structural properties

02.30.Xx Calculus of variations

Subjects

Quantum gases, liquids and solids

Mathematical physics

Dates

Issue 9 (14 May 2004)

Received 22 March 2004

Published 23 April 2004



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