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

Journal of Physics A Mathematical and Theoretical

A kinetic equation for ultra-low temperature Bose–Einstein condensates

L. E. Reichl, Minh-Binh Tran

Published Dec 11, 2018• 12 citations
Publisher

Abstract

Abstract Bose–Einstein condensates (BECs) are starting to play a role in quantum information processing, and there is a need to better understand the dynamical processes at play in the condensates. In this paper, we review recent work on a kinetic model for ultra-low temperature dilute Bose–Einstein condensates that gives correct behavior for first and second sound speeds at very low temperature, and gives explicit expressions and values for decay processes. The predictions of the theory are in agreement with experiment. The method explicitly computes the hydrodynamic modes of the condensate using a method that has also been used to describe decay processes in noble gas mixtures, and thereby opens the way for future analysis of decay processes in BEC mixtures.

DOI
10.1088/1751-8121/aaf7b3

Related papers

Decay of hydrodynamic modes in dilute Bose-Einstein condensates

Erich D. Gust, L. E. Reichl

Expressions for the speed and lifetimes of the sound modes in a dilute Bose-Einstein condensate are obtained using Bogoliubov mean field theory. The condensate has two pairs of sound modes which undergo an avoided crossing as the equilibrium temperature is varied. The two pairs of sound modes decay at very different rates, except in the neighborhood of the avoided crossing, where the identity of the longest-lived mode switches. The predicted speed and lifetime of the longest-lived sound mode are consistent with recent experimental observations on sound in an $^{87}\mathrm{Rb}$ Bose-Einstein condensate.

Physical Review A•Oct 15, 2014•5 citations

Transport theory for a dilute Bose-Einstein condensate

L. E. Reichl, Erich D. Gust

We obtain microscopic expressions for the six hydrodynamic modes of a dilute Bose-Einstein condensate: two transverse (shear) modes and four longitudinal modes corresponding to the first sound (elastic waves) and second sound (temperature waves). Our microscopic expressions include both the speed of the two types of sound and the rate of relaxation of the sound waves. We obtain numerical values for the shear viscosity of a dilute BEC composed of bosons which interact via a contact potential. Our values for the shear viscosity are obtained using the eigenvalues and eigenvectors of the three types of collision operators that govern the relaxation of the condensate.

Physical Review A•Nov 6, 2013•15 citations

Bose-Condensed Gases at Finite Temperatures

Allan Griffin, Tetsuro Nikuni, E. Zaremba

The discovery of Bose Einstein condensation (BEC) in trapped ultracold atomic gases in 1995 has led to an explosion of theoretical and experimental research on the properties of Bose-condensed dilute gases. The first treatment of BEC at finite temperatures, this book presents a thorough account of the theory of two-component dynamics and nonequilibrium behaviour in superfluid Bose gases. It uses a simplified microscopic model to give a clear, explicit account of collective modes in both the collisionless and collision-dominated regions. Major topics such as kinetic equations, local equilibrium and two-fluid hydrodynamics are introduced at an elementary level. Explicit predictions are worked out and linked to experiments. Providing a platform for future experimental and theoretical studies on the finite temperature dynamics of trapped Bose gases, this book is ideal for researchers and graduate students in ultracold atom physics, atomic, molecular and optical physics and condensed matter physics.

Cambridge University Press eBooks•Feb 19, 2009•351 citations

A kinetic model for very low temperature dilute Bose gases

L. E. Reichl, Minh-Binh Tran

We review recent work on a kinetic model for very low temperature dilute Bose gases. The brief derivation, expressions for hydrodynamics modes, and the comparison with a experiment on a BEC of $^{87}{\rm Rb}$ atoms are presented.

arXiv:1709.09982•Sep 26, 2017•10 citations

Nonequilibrium kinetic theory for trapped binary condensates

Matthew Edmonds, Kean Loon Lee, Nick P. Proukakis

We derive a nonequilibrium finite-temperature kinetic theory for a binary mixture of two interacting atomic Bose-Einstein condensates and use it to explore the degree of hydrodynamicity attainable in realistic experimental geometries. Based on the standard separation-of-time-scales argument of kinetic theory, the dynamics of the condensates of the multicomponent system are shown to be described by dissipative Gross-Pitaevskii equations self-consistently coupled to corresponding quantum Boltzmann equations for the noncondensate atoms: On top of the usual mean-field contributions, our scheme identifies a total of eight distinct collisional processes, whose dynamical interplay is expected to be responsible for the system's equilibration. In order to provide their first characterization, we perform a detailed numerical analysis of the role of trap frequency and geometry on collisional rates for experimentally accessible mixtures of $^{87}\mathrm{Rb}\ensuremath{-}^{41}\mathrm{K}$ and $^{87}\mathrm{Rb}\ensuremath{-}^{85}\mathrm{Rb}$, discussing the extent to which the system may approach the hydrodynamic regime with regard to some of those processes as a guide for future experimental investigations of ultracold Bose gas mixtures.

arXiv:1507.05078•Physical Review A•Dec 3, 2015•6 citations

Second Sound in Ultracold Atomic Gases

Лев П. Питаевский, S. Stringari

We provide an overview of the recent theoretical and experimental advances in the study of second sound in ultracold atomic gases. Starting from the Landau two fluid hydrodynamic equations we develop the theory of first and second sound in various configurations characterized by different geometries and quantum statistics. These include the weakly interacting 3D Bose gas, the strongly interacting Fermi gas at unitarity in the presence of highly elongated traps and the dilute 2D Bose gas, characterized by the Berezinskii-Kosterlitz-Thouless transition. An explicit comparison with the propagation of second sound in liquid Helium is carried out to elucidate the main analogies and differences. We also make an explicit comparison with the available experimental data and point out the crucial role played by the superfluid density in determining the temperature dependence of the second sound speed.

arXiv:1510.01306•Cambridge University Press eBooks•Oct 4, 2018•15 citations
Abstract Bose–Einstein condensates (BECs) are starting to play a role in quantum information processing, and there is a need to better understand the dynamical processes at play in the condensates. In this paper, we review recent work on a kinetic model for ultra-low temperature dilute Bose–Einstein condensates that gives correct behavior for first and second sound speeds at very low temperature, and gives explicit expressions and values for decay processes. The predictions of the theory are in agreement with experiment. The method explicitly computes the hydrodynamic modes of the condensate using a method that has also been used to describe decay processes in noble gas mixtures, and thereby opens the way for future analysis of decay processes in BEC mixtures.
Expressions for the speed and lifetimes of the sound modes in a dilute Bose-Einstein condensate are obtained using Bogoliubov mean field theory. The condensate has two pairs of sound modes which undergo an avoided crossing as the equilibrium temperature is varied. The two pairs of sound modes decay at very different rates, except in the neighborhood of the avoided crossing, where the identity of the longest-lived mode switches. The predicted speed and lifetime of the longest-lived sound mode are consistent with recent experimental observations on sound in an 87Rb^{87}\mathrm{Rb}87Rb Bose-Einstein condensate.
We obtain microscopic expressions for the six hydrodynamic modes of a dilute Bose-Einstein condensate: two transverse (shear) modes and four longitudinal modes corresponding to the first sound (elastic waves) and second sound (temperature waves). Our microscopic expressions include both the speed of the two types of sound and the rate of relaxation of the sound waves. We obtain numerical values for the shear viscosity of a dilute BEC composed of bosons which interact via a contact potential. Our values for the shear viscosity are obtained using the eigenvalues and eigenvectors of the three types of collision operators that govern the relaxation of the condensate.
The discovery of Bose Einstein condensation (BEC) in trapped ultracold atomic gases in 1995 has led to an explosion of theoretical and experimental research on the properties of Bose-condensed dilute gases. The first treatment of BEC at finite temperatures, this book presents a thorough account of the theory of two-component dynamics and nonequilibrium behaviour in superfluid Bose gases. It uses a simplified microscopic model to give a clear, explicit account of collective modes in both the collisionless and collision-dominated regions. Major topics such as kinetic equations, local equilibrium and two-fluid hydrodynamics are introduced at an elementary level. Explicit predictions are worked out and linked to experiments. Providing a platform for future experimental and theoretical studies on the finite temperature dynamics of trapped Bose gases, this book is ideal for researchers and graduate students in ultracold atom physics, atomic, molecular and optical physics and condensed matter physics.
We review recent work on a kinetic model for very low temperature dilute Bose gases. The brief derivation, expressions for hydrodynamics modes, and the comparison with a experiment on a BEC of 87Rb^{87}{\rm Rb}87Rb atoms are presented.
We derive a nonequilibrium finite-temperature kinetic theory for a binary mixture of two interacting atomic Bose-Einstein condensates and use it to explore the degree of hydrodynamicity attainable in realistic experimental geometries. Based on the standard separation-of-time-scales argument of kinetic theory, the dynamics of the condensates of the multicomponent system are shown to be described by dissipative Gross-Pitaevskii equations self-consistently coupled to corresponding quantum Boltzmann equations for the noncondensate atoms: On top of the usual mean-field contributions, our scheme identifies a total of eight distinct collisional processes, whose dynamical interplay is expected to be responsible for the system's equilibration. In order to provide their first characterization, we perform a detailed numerical analysis of the role of trap frequency and geometry on collisional rates for experimentally accessible mixtures of $^{87}\mathrm{Rb}\ensuremath{-}^{41}\mathrm{K}$ and $^{87}\mathrm{Rb}\ensuremath{-}^{85}\mathrm{Rb}$, discussing the extent to which the system may approach the hydrodynamic regime with regard to some of those processes as a guide for future experimental investigations of ultracold Bose gas mixtures.
We provide an overview of the recent theoretical and experimental advances in the study of second sound in ultracold atomic gases. Starting from the Landau two fluid hydrodynamic equations we develop the theory of first and second sound in various configurations characterized by different geometries and quantum statistics. These include the weakly interacting 3D Bose gas, the strongly interacting Fermi gas at unitarity in the presence of highly elongated traps and the dilute 2D Bose gas, characterized by the Berezinskii-Kosterlitz-Thouless transition. An explicit comparison with the propagation of second sound in liquid Helium is carried out to elucidate the main analogies and differences. We also make an explicit comparison with the available experimental data and point out the crucial role played by the superfluid density in determining the temperature dependence of the second sound speed.