Oliver Ruebenacker | Searcharxiv

arXiv2004

Weakly interacting Bose gas in the vicinity of the critical point

We consider a three-dimensional weakly interacting Bose gas in the fluctuation region (and its vicinity) of the normal-superfluid phase transition point. We establish relations between basic thermodynamic functions: density, $n(T,μ)$, superfluid density $n_s(T,μ)$, and condensate density, $n_{\rm cnd} (T,μ)$. Being universal for all weakly interacting $|ψ|^4$ systems, these relations are obtained from Monte Carlo simulations of the classical $|ψ|^4$ model on a lattice. Comparing with the mean-field results yields a quantitative estimate of the fluctuation region size. Away from the fluctuation region, on the superfluid side, all the data perfectly agree with the predictions of the quasicondensate mean field theory.--This demonstrates that the only effect of the leading above-the-mean-field corrections in the condensate based treatments is to replace the condensate density with the quasicondensate one in all local thermodynamic relations. Surprisingly, we find that a significant fraction of the density profile of a loosely trapped atomic gas might correspond to the fluctuation region.

cond-mat.supr-con↗

arXiv2001

Critical Point of a Weakly Interacting Two-Dimensional Bose Gas

We study the Berezinskii-Kosterlitz-Thouless transition in a weakly interacting 2D quantum Bose gas using the concept of universality and numerical simulations of the classical $|ψ|^4$-model on a lattice. The critical density and chemical potential are given by relations $n_c=(mT/2π\hbar^2) \ln(ξ\hbar^2/ mU)$ and $μ_c=(mTU/π\hbar^2) \ln(ξ_μ \hbar^2/ mU)$, where $T$ is the temperature, $m$ is the mass, and $U$ is the effective interaction. The dimensionless constant $ξ= 380 \pm 3$ is very large and thus any quantitative analysis of the experimental data crucially depends on its value. For $ξ_μ$ our result is $ξ_μ = 13.2 \pm 0.4 $. We also report the study of the quasi-condensate correlations at the critical point.

cond-mat↗