Contribution to the theory of the spectrum of a Bose system with condensate at small momenta

A. R. Knyazev, Yu. A. Nepomnyashchiǐ

S. V. Andreev

Since the pioneering works of Landau and Feynman, the origin of a roton minimum in the excitation spectrum of a quantum Bose liquid has been debated. A consensus has been reached on relation of the roton to eventual solidification, but this viewpoint still remains to be connected to the polaronic concept of an impurity pushing through a dense medium. The diagrammatic theory allows one to approach the problem qualitatively from a dilute limit. We revisit the equation for the elementary excitation spectrum obtained in the ladder approximation and argue that polaronic renormalization of the quasiparticle mass has a contribution due to matter-wave refraction. At low energies attenuation of the quasiparticle wave turns out to be dramatically suppressed by the condensate. Refractive correction to the mass is enhanced by Bose statistics at high momenta and produces autolocalization of an elementary excitation upon increasing the density.

P. D�rre

Andrei V. Turlapov

Interference of a chain of Bose condensates qualitatively depends on the relation between the condensate phases. If the phases are equal, the Talbot effect is observed. Even a small randomness in the relative phases alters the density spectrum: Peaks appears at momenta that are unusual for the Talbot effect. Here this alteration of the spectrum is simulated within a simple model. Also the relation between the temperature and the density spectrum of the interference fringes is described.

P. Szépfalusy

Mohd Faudzi Umar, Nurisya Mohd Shah, Mohamad Nazri Abdul Halif

Bose-Einstein condensates, formed at ultracold temperatures, provide a unique platform for exploring quantum phenomena at a macroscopic scale. In this paper, we explore the effect of noncommutativity in both coordinates and momenta on the energy spectrum of the Gross-Pitaevskii equation for a Bose-Einstein condensate that is harmonically trapped and interacting. This study is conducted within the framework of noncommutative quantum mechanics, focusing on a first-order approximation in the noncommutative parameters, given their very small magnitude. The result shows that the introduction of noncommutative effects leads to the emergence of vortex formation in the condensate. By comparing our theoretical findings with experimental data, we estimate the value of the noncommutative parameter.