# Séminaire du LPTMS : Grigory Astrakharchik

## Lieb’s soliton-like excitations in harmonic traps

### Grigory Astrakharchik (Universitat Politècnica de Catalunya, Barcelona)

We study the solitonic Lieb II branch of excitations the in 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 $\omega_h/\sqrt{2}$ in the high density mean field regime to $\omega_h$ in the low density Tonks-Girardeau regime with $\omega_h$ the frequency of the harmonic trapping. Particular attention is paid to the effective mass of a soliton with velocity near the speed of sound.

G. E. Astrakharchik and L. P. Pitaevskii Lieb’s soliton-like excitations in harmonic traps EPL, 102, 30004 (2013)

Date/Time : 21/01/2015 - 14:30 - 16:00