We investigate the phase transition of interacting Bose gases in general power-law traps in the thermodynamic limit. Using energy-shell renormalization and the $\ensuremath{\epsilon}$ expansion, we evaluate the partition function for the uncondensed gas phase within a renormalization-group framework. This approach allows a unified description of homogeneous as well as inhomogeneous and anisotropic systems. Results for the critical temperature are compared to mean-field theory as well as to a local-density approximation based on renormalization-group theory for the homogeneous Bose gas. This comparison indicates the consistency of our approach. We also make suggestions for an optimized trap design in experiments that measure the transition temperature.We investigate the phase transition of interacting Bose gases in general power-law traps in the thermodynamic limit. Using energy-shell renormalization and the $\ensuremath{\epsilon}$ expansion, we evaluate the partition function for the uncondensed gas phase within a renormalization-group framework. This approach allows a unified description of homogeneous as well as inhomogeneous and anisotropic systems. Results for the critical temperature are compared to mean-field theory as well as to a local-density approximation based on renormalization-group theory for the homogeneous Bose gas. This comparison indicates the consistency of our approach. We also make suggestions for an optimized trap design in experiments that measure the transition temperature.

Physical Review AJun 23, 200416 citations

Phase transitions in ideal Bose gases

B. Ya. Balagurov, Валентин Григорьевич Вакс

Jan 1, 19750 citations

Remarks on phase transition in a perfect Bose gas

B. Ya. Balagurov, Валентин Григорьевич Вакс

Journal of Experimental and Theoretical PhysicsJan 1, 19750 citations

Hydrodynamic Modes in a Trapped Bose Gas above the Bose-Einstein Transition

Adam Griffin, Wen-Chin Wu, S. Stringari

We discuss the collective modes of a trapped Bose gas in the hydrodynamic regime where atomic collisions ensure local thermal equilibrium for the distribution function. Starting from the conservation laws, in the linearized limit we derive a closed equation for the velocity fluctuations in a trapped Bose gas above the Bose-Einstein transition temperature. Explicit solutions for a parabolic trap are given. We find that the surface modes above the transition have the same dispersion relation as the one recently obtained by Stringari for the oscillations of the condensate at $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ within the Thomas-Fermi approximation. Results are also given for the monopole ``breathing'' mode as well as for the $m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ excitations which result from the coupling of the monopole and quadrupole modes in an anisotropic parabolic well.We discuss the collective modes of a trapped Bose gas in the hydrodynamic regime where atomic collisions ensure local thermal equilibrium for the distribution function. Starting from the conservation laws, in the linearized limit we derive a closed equation for the velocity fluctuations in a trapped Bose gas above the Bose-Einstein transition temperature. Explicit solutions for a parabolic trap are given. We find that the surface modes above the transition have the same dispersion relation as the one recently obtained by Stringari for the oscillations of the condensate at $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ within the Thomas-Fermi approximation. Results are also given for the monopole ``breathing'' mode as well as for the $m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ excitations which result from the coupling of the monopole and quadrupole modes in an anisotropic parabolic well.

arXiv:cond-mat/9610187Physical Review LettersMar 10, 199791 citations

Phase diagram and correlation functions of the anisotropic imperfect Bose gas in $d$ dimensionsPhase diagram and correlation functions of the anisotropic imperfect Bose gas in $d$ dimensions

Paweł Jakubczyk, Jacek Wojtkiewicz

We study an anisotropic variant of the $d$ -dimensional imperfect Bose gas, where the asymptotic behaviour of the dispersion $ε_{\bf k}$ at vanishing momentum $\bf{k}$ may differ from the standard quadratic form. The analysis reveals the key role of the shift exponent $ψ$ governing the asymptotic behaviour of the critical temperature $T_c(μ)$ as a function of the chemical potential $μ$ at $T_c\to 0$ . We argue that the universality classes of Bose-Einstein condensation admitted by the model may be classified according to the allowed values of $ψ$ so that spatial dimensionality has only an indirect impact on the transition properties. We analyse the correlation function of the model and discuss its asymptotics depending on the direction. Both for the perfect and imperfect anisotropic Bose gases, the correlation function $χ({\bf x})$ at $T>T_c$ turns out to show either exponential decay or exponentially damped oscillatory behaviour depending on the orientation of ${\bf x}$ with respect to the dispersion anisotropies.We study an anisotropic variant of the $d$-dimensional imperfect Bose gas, where the asymptotic behaviour of the dispersion $ε_{\bf k}$ at vanishing momentum $\bf{k}$ may differ from the standard quadratic form. The analysis reveals the key role of the shift exponent $ψ$ governing the asymptotic behaviour of the critical temperature $T_c(μ)$ as a function of the chemical potential $μ$ at $T_c\to 0$. We argue that the universality classes of Bose-Einstein condensation admitted by the model may be classified according to the allowed values of $ψ$ so that spatial dimensionality has only an indirect impact on the transition properties. We analyse the correlation function of the model and discuss its asymptotics depending on the direction. Both for the perfect and imperfect anisotropic Bose gases, the correlation function $χ({\bf x})$ at $T>T_c$ turns out to show either exponential decay or exponentially damped oscillatory behaviour depending on the orientation of ${\bf x}$ with respect to the dispersion anisotropies.

arXiv:1609.08639Sep 27, 20160 citations

First Order Phase Transition in a Model of a Bose Gas with Attraction

D. M. Chernikova

Journal of Experimental and Theoretical PhysicsJan 1, 19691 citation

T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0

within the Thomas-Fermi approximation. Results are also given for the monopole ``breathing'' mode as well as for the

m\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0

excitations which result from the coupling of the monopole and quadrupole modes in an anisotropic parabolic well.

Phase diagram and correlation functions of the anisotropic imperfect Bose gas in

d

dimensions

We study an anisotropic variant of the

d

-dimensional imperfect Bose gas, where the asymptotic behaviour of the dispersion

ε_{\bf k}

at vanishing momentum

\bf{k}

may differ from the standard quadratic form. The analysis reveals the key role of the shift exponent

ψ

governing the asymptotic behaviour of the critical temperature

T_c(μ)

as a function of the chemical potential

μ

T_c\to 0

. We argue that the universality classes of Bose-Einstein condensation admitted by the model may be classified according to the allowed values of

ψ

so that spatial dimensionality has only an indirect impact on the transition properties. We analyse the correlation function of the model and discuss its asymptotics depending on the direction. Both for the perfect and imperfect anisotropic Bose gases, the correlation function

χ({\bf x})

T>T_c

turns out to show either exponential decay or exponentially damped oscillatory behaviour depending on the orientation of

{\bf x}

with respect to the dispersion anisotropies.