Laboratoire de Physique Théorique
Toulouse - UMR 5152

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.

We show that the chemical potential exhibits a nonmonotonic temperature dependence which is peculiar of superfluids. The effect is a direct consequence of the phononic nature of the excitation spectrum at large wavelengths exhibited by 1D Bose gases. We demonstrate that the quadratic coefficient in the expansion low-temperature expansion of the chemical potential is entirely defined by the zero-temperature density dependence of the sound velocity, while the quartic coefficient experiences opposite-direction effects originating from (a) non-linearity of the excitation spectrum (b) negative excluded-volume corrections.

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

[2] Giulia De Rosi, Grigori E. Astrakharchik, and Sandro Stringari, "Thermodynamic behavior of a one-dimensional Bose gas at low temperature," Phys. Rev. A 96, 013613 (2017)

[3] De Rosi, P. Massignan, M. Lewenstein and G. E. Astrakharchik, "Thermodynamics of a one-dimensional Bose gas with repulsive contact interactions", arXiv:1905.07391 (2019)