Volume 102, Number 3, May 2013
|Number of page(s)||5|
|Published online||15 May 2013|
Lieb's soliton-like excitations in harmonic traps
1 Departament de Física i Enginyeria Nuclear, Campus Nord B4- B5, Universitat Politècnica de Catalunya E-08034 Barcelona, Spain, EU
2 INO- CNR BEC Center and Dipartimento di Fisica, Università di Trento - I-38123 Povo, Trento, Italy, EU
3 P.L. Kapitza Institute for Physical Problems, RAS - Kosygina 2, 119334 Moscow, Russia
Received: 31 October 2012
Accepted: 17 April 2013
We study the solitonic Lieb II branch of excitations in the one-dimensional Bose gas in homogeneous and trapped geometry. Using Bethe-ansatz Lieb's equations we calculate the “effective number of atoms” and the “effective mass” of the excitation. The equations of motion of the excitation are defined by the ratio of these quantities. The frequency of oscillations of the excitation in a harmonic trap is calculated. It changes continuously from its “soliton-like” value in the high-density mean-field regime to in the low-density Tonks-Girardeau regime with the frequency of the harmonic trapping. Particular attention is paid to the effective mass of a soliton with velocity near the speed of sound.
PACS: 03.75.Lm – Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations / 05.30.Jp – Boson systems / 03.75.Kk – Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow
© EPLA, 2013
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