Bose condensation in dilute gas of hard spheres with attraction

Abstract

Critical temperature is calculated for Bose-Einstein condensation of hard spheres with attraction using the path-integral Monte Carlo (PIMC) method and finite-size scaling. It is demonstrated that the scattering length is not the only parameter which the critical temperature depends on. It is also shown that Bose condensation may be observed in the case of negative scattering length.

Large-N properties of a non-ideal Bose gas

“…The application of this method to two-dimensional Bose systems [18] revealed very interesting phenomenon, namely, the appearance of thermallystimulated roton minimum in the spectrum of collective excitations. Recently, we have demonstrated [19] that the application of this technique to the problem of critical temperature calculation for a Bose gas with point-like repulsive interaction leads to the result which coincides semi-quantitatively well with that of the Monte Carlo simulations [20,21] in a whole range of the interaction parameter. The latter observation inspires confidence in the use of the large-N -based expansion for studying of the finite-temperature thermodynamic properties of Bose gas not only in the dilute limit.…”

$1/N$-expansion for the critical temperature of the Bose gas

“…On the level of our 1/Napproximation this effective mass of a moving particle is nothing but the hydrodynamic mass of a single impurity atom immersed in the "phonon" field ϕ(x). This situation with the function f (1) (an 1/3 ) when it grows at small an 1/3 and rapidly falls down to negative values in the strong-coupling limit is consistent with experiments [33] and with the results of simulations [26,27] and has a simple physical interpretation. For our model the enhancement of the interaction can be naively treated as an increase of the particle size.…”

“…We have argued that for a FIG. 3: The comparison of our leading-order 1/N calculations (circles) of the critical temperature with the results of pathintegral [26] (squares) and quantum [27] (triangles) Monte Carlo simulations.…”

1/N-expansion for the critical temperature of the Bose gas

“…The goal of the present study is to explore the leadingorder large-N correction to the Bose-Einstein condensation temperature in the wide region of the interparticle interaction strength and compare the obtained results with recent Monte Carlo calculations [26,27].…”