Collective excitations and superfluid properties of a two-dimensional interacting Bose gas in an external potential

Abstract

We develop an approach for a description of collective excitations in a two-dimensional gas of interacting Bose particles in an external potential. We present a method of finding an approximate analytical solution for the spectra of collective excitations of a Bose gas in a linear potential and in a potential of the form u(r)=m-u₀cosh²x/l, where m is the chemical potential. Numerical study shows that the analytical solution corresponds to collective modes localized at the edge or at the low-density region. We investigate the influence of the external potential on a critical velocity of a superfluid flow. It is shown that the effect of strong suppression of the critical velocity takes place in a nonuniform Bose system. We discuss a possibility of Bose-Einstein condensation (BEC) in the systems under investigations at nonzero temperatures and find that in case of a finite number of the particles BEC can emerge.