Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1803.09964 · Journal of Functional Analysis

On a system of equations for the normal fluid-condensate interaction in a Bose gas

E. Cortés, Miguel Escobedo

Published Sep 25, 2019• 0 citations
arXivHTMLPDF
DOI
10.1016/j.jfa.2019.108315

Related papers

CONDENSATE OSCILLATIONS, KINETIC EQUATIONS AND TWO-FLUID HYDRODYNAMICS IN A BOSE GAS

Allan Griffin

•Dec 1, 2000•0 citations

Two-fluid hydrodynamics for a trapped weakly interacting Bose gas

E. Zaremba, Adam Griffin, Tetsuro Nikuni

We derive coupled equations of motion for the condensate (superfluid) and noncondensate (normal fluid) degrees of freedom in a trapped Bose gas at finite temperatures. Our results are based on the Hartree-Fock-Popov approximation for the time-dependent condensate wave function, and thermodynamic local equilibrium for the noncondensate atoms. In the special case of a uniform weakly interacting gas, our hydrodynamic equations are shown to be consistent with the two-fluid equations of Landau. The collective modes in a parabolically trapped Bose gas include the analog of the out-of-phase second-sound mode in superfluid ${}^{4}\mathrm{He}$.

arXiv:cond-mat/9705134•Physical Review A•Jun 1, 1998•117 citations

On the linearized system of equations for the condensate–normal fluid interaction at very low temperature

Miguel Escobedo

Abstract The linearization around one of its equilibrium of a system that describes the correlations between the superfluid component and the normal fluid part of a condensed Bose gas in the approximation of very low temperature and small condensate density is studied. A simple and transparent argument gives a necessary and sufficient condition for the existence of global solutions satisfying the conservation of the total number of particles and energy. The global solutions describe the evolution in time of the density of the thermal cloud and, unlike in previous work, that of the condensate's density. Their convergence to a suitable stationary state is also shown and rates of convergence for the normal fluid and superfluid components are obtained.

arXiv:2112.13788•Studies in Applied Mathematics•Nov 23, 2022•5 citations

On the Bose-Einstein condensation of an ideal gas

Lawrence J. Landau, Ivan F. Wilde

Communications in Mathematical Physics•Feb 1, 1979•75 citations

Critical properties of weakly interacting Bose gases as modified by a harmonic confinement

I. Reyes-Ayala, Freddy Jackson Poveda-Cuevas, Jorge Amin Seman +1 more

Abstract The critical properties of the phase transition from a normal gas to a Bose–Einstein condensate (superfluid) of a harmonically confined Bose gas are addressed with the knowledge of an equation of state of the underlying homogeneous Bose fluid. It is shown that while the presence of the confinement trap arrests the usual divergences of the isothermal compressibility and heat capacities, the critical behavior manifests itself now in the divergence of derivatives of the mentioned susceptibilities. This result is illustrated with a mean-field like model of an equation of state for the homogeneous particle density as a function of the chemical potential and temperature of the gas. The model assumes the form of an ideal Bose gas in the normal fluid while in the superfluid state a function is proposed such that, both, asymptotically reaches the Thomas–Fermi solution of a weakly interacting Bose gas at large densities and low temperatures and, at the transition, matches the critical properties of the ideal Bose gas. With this model we obtain the global thermodynamics of the harmonically confined gas, from which we analyze its critical properties. We discuss how these properties can be experimentally tested.

arXiv:1607.02389•Journal of Statistical Mechanics Theory and Experiment•Jul 1, 2017•5 citations

ON THE THERMODYNAMICS OF THE BOSE GAS

Yu.B. Rumer

Zhur. Eksptl'. i Teoret. Fiz.•Sep 1, 1950•0 citations
We derive coupled equations of motion for the condensate (superfluid) and noncondensate (normal fluid) degrees of freedom in a trapped Bose gas at finite temperatures. Our results are based on the Hartree-Fock-Popov approximation for the time-dependent condensate wave function, and thermodynamic local equilibrium for the noncondensate atoms. In the special case of a uniform weakly interacting gas, our hydrodynamic equations are shown to be consistent with the two-fluid equations of Landau. The collective modes in a parabolically trapped Bose gas include the analog of the out-of-phase second-sound mode in superfluid 4He{}^{4}\mathrm{He}4He.
Abstract The linearization around one of its equilibrium of a system that describes the correlations between the superfluid component and the normal fluid part of a condensed Bose gas in the approximation of very low temperature and small condensate density is studied. A simple and transparent argument gives a necessary and sufficient condition for the existence of global solutions satisfying the conservation of the total number of particles and energy. The global solutions describe the evolution in time of the density of the thermal cloud and, unlike in previous work, that of the condensate's density. Their convergence to a suitable stationary state is also shown and rates of convergence for the normal fluid and superfluid components are obtained.
Abstract The critical properties of the phase transition from a normal gas to a Bose–Einstein condensate (superfluid) of a harmonically confined Bose gas are addressed with the knowledge of an equation of state of the underlying homogeneous Bose fluid. It is shown that while the presence of the confinement trap arrests the usual divergences of the isothermal compressibility and heat capacities, the critical behavior manifests itself now in the divergence of derivatives of the mentioned susceptibilities. This result is illustrated with a mean-field like model of an equation of state for the homogeneous particle density as a function of the chemical potential and temperature of the gas. The model assumes the form of an ideal Bose gas in the normal fluid while in the superfluid state a function is proposed such that, both, asymptotically reaches the Thomas–Fermi solution of a weakly interacting Bose gas at large densities and low temperatures and, at the transition, matches the critical properties of the ideal Bose gas. With this model we obtain the global thermodynamics of the harmonically confined gas, from which we analyze its critical properties. We discuss how these properties can be experimentally tested.