Dynamics of shallow dark solitons in a trapped gas of impenetrable bosons

Details Dynamics of shallow dark solitons in a trapped gas of impenetrable bosons Dynamics of shallow dark solitons in a trapped gas of impenetrable bosons

2004-04-05

arxiv.org/abs/cond-mat/0404102v1

Physics

Condensed Matter

Soft Condensed Matter

4 pages, Phys. Rev. A (in press)

Scientific paper

10.1103/PhysRevA.70.015601

The dynamics of linear and nonlinear excitations in a Bose gas in the Tonks-Girardeau (TG) regime with longitudinal confinement are studied within a mean field theory of quintic nonlinearity. A reductive perturbation method is used to demonstrate that the dynamics of shallow dark solitons, in the presence of an external potential, can effectively be described by a variable-coefficient Korteweg-de Vries equation. The soliton oscillation frequency is analytically obtained to be equal to the axial trap frequency, in agreement with numerical predictions obtained by Busch {\it et al.} [J. Phys. B {\bf 36}, 2553 (2003)] via the Bose-Fermi mapping. We obtain analytical expressions for the evolution of both soliton and emitted radiation (sound) profiles.

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