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Group meeting April 15th, 2019

The group seminar on April 15th, 2019, will be given by G. Astrakharchik (Barcelona, Spain):

Thermodynamics of a Bose gas and dynamics of droplets in one dimension.

We show that the chemical potential of a one-dimensional (1D) interacting Bose gas 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.

The structure and dynamics of one-dimensional binary Bose gases forming quantum droplets is studied by solving the corresponding amended Gross-Pitaevskii equation. Two physically different regimes are identified, corresponding to small droplets of an approximately Gaussian shape and large `puddles' with a broad flat-top plateau. Small droplets collide quasi-elastically, featuring the soliton-like behavior. On the other hand, large colliding droplets may merge or suffer fragmentation, depending on their relative velocity. The frequency of a breathing excited state of droplets, as predicted by the dynamical variational approximation based on the Gaussian ansatz, is found to be in good agreement with numerical results. The stability diagram for a single droplet with respect to shape excitations with a given wave number is drawn, being consistent with preservation of the Weber number for large droplets.

[1] 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)

[2] G. E. Astrakharchik and B. A. Malomed,
Dynamics of one-dimensional quantum droplets,
Phys. Rev. A 98, 013631 (2018)

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