# Internal structure of a quantum soliton and classical excitations due to trap opening

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## Abstract

We analytically solve two problems that may be useful in the context of the recent observation of matter wave bright solitons in a one-dimensional attractive atomic Bose gas. The first problem is strictly beyond mean field: from the Bethe ansatz solution we extract the *internal* correlation function of the particle positions in the quantum soliton, that is for a *fixed* center of mass position. The second problem is solved in the limit of a large number of particles, where the mean field theory is asymptotically correct: it deals with the number of excitations created by the opening of the trap, starting from a pure soliton in a weakly curved harmonic potential.

## PACS

03.75.Lm Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations 03.75.Hh Static properties of condensates; thermodynamical, statistical, and structural properties 03.75.Kk Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow## Preview

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## References

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© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2008