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:cond-mat/9810150 · Physical Review A

Quantum kinetic theory for a condensed bosonic gas

R. Walser, Jonathan H. Williams, J. Cooper, Murray Holland

Published May 1, 1999• 97 citations
arXivHTMLPDF

Abstract

We present a kinetic theory for Bose-Einstein condensation of a weakly interacting atomic gas in a trap. Starting from first principles, we establish a Markovian kinetic description for the evolution towards equilibrium. In particular, we obtain a set of self-consistent master equations for mean fields, normal densities, and anomalous fluctuations. These kinetic equations generalize the Gross-Pitaevskii mean-field equations, and merge them consistently with a quantum-Boltzmann-equation approach.

DOI
10.1103/physreva.59.3878

Related papers

Quantum kinetic theory: A quantum kinetic master equation for condensation of a weakly interacting Bose gas without a trapping potential

Crispin W. Gardiner, P. Zoller

A quantum kinetic master equation (QKME) for bosonic atoms is formulated. It is a quantum stochastic equation for the kinetics of a dilute quantum Bose gas, and describes the behavior and formation of Bose condensation. The key assumption in deriving the QKME is a Markov approximation for the atomic collision terms. In the present paper the basic structure of the theory is developed, and approximations are stated and justified to delineate the region of validity of the theory. Limiting cases of the QKME include the quantum Boltzmann master equation and the Uehling-Uhlenbeck equation, as well as an equation analogous to the Gross-Pitaevskii equation.

arXiv:quant-ph/9611043•Physical Review A•Apr 1, 1997•163 citations

Reversible and irreversible evolution of a condensed bosonic gas

R. Walser, J. Cooper, Murray Holland

We have formulated a kinetic theory for a condensed atomic gas in a trap, i.e., a generalized Gross-Pitaevskii equation, as well as a quantum-Boltzmann equation for the normal and anomalous fluctuations [R. Walser et al., Phys. Rev. A 59, 3878 (1999)]. In this paper, the theory is applied to the case of an isotropic configuration and we present numerical and analytical results for the reversible real-time propagation, as well as irreversible evolution towards equilibrium.

arXiv:cond-mat/0004257•Physical Review A•Dec 12, 2000•39 citations

Low temperature theory for Bose-Einstein condensates

Murray Holland

Summary form only given. The dilute gas experiments on the Bose-Einstein condensation of magnetically confined alkali vapors have already generated widespread interest across a broad spectrum of traditional fields of physics. They have provided an exciting stage on which to build bridges linking the theory of complex and collective phenomena in superconducting and superfluid systems with the single particle microscopic physics described in quantum optics and laser physics. The approach I discuss is based on a derivation of the quantum kinetic theory from first principles. Based on a microscopic picture of the weakly interacting bosonic gas, a generalized kinetic theory for a Markovian many-body density operator is derived. The density operator is functionally dependent on a few key variables, which must be carefully chosen. These quantities serve as master variables and determine the system's evolution on a coarse-grained time scale. The weak interactions allow a perturbative expansion of the evolution, from which kinetic equations that describe the dynamics of the expectation value of any single-time observable are obtained. The final structure of the theory has many analogies with the quantum theory of the laser, such as amplitude and phase noise for the macroscopic field, squeezing dynamics, and a nonlinear master equation describing the underlying evolution.

•May 7, 2000•0 citations

Bose-Einstein-condensation dynamics with a quantum-kinetic approach

Omar Morandi, Paul-Antoine Hervieux, Giovanni Manfredi

The evolution equation of a weakly interacting boson system is derived. The model includes the interaction between the atoms in the condensate and the surrounding gas of noncondensed particles. The Bogoliubov transformation is introduced in a full quantum context and the scattering kernel between dressed particles and the condensate phase is obtained. The final system is expressed by the Boltzmann evolution equation for noncondensed particles coupled to the Gross-Pitaevskii equation for the condensate. We consider an out-of-equilibrium situation that induces a fast production of condensed particles. We apply our model to study the condensation dynamics of positronium atoms by evaporation.

Physical Review A•Aug 27, 2013•12 citations

Equivalence of kinetic theories of Bose-Einstein condensation

J. Wachter, R. Walser, J. Cooper +1 more

We discuss the equivalence of two nonequilibrium kinetic theories that describe the evolution of a dilute, Bose-Einstein condensed atomic gas in a harmonic trap. The second-order kinetic equations of Walser et al. [Phys. Rev. A 63, 013607 (2001)] reduce to the Gross-Pitaevskii equation and the quantum Boltzmann equation in the low- and high-temperature limits, respectively. These kinetic equations thus describe the system in equilibrium (finite temperature) as well as in nonequilibrium (real time). We have found this theory to be equivalent to the nonequilibrium Green's function approach originally proposed by Kadanoff and Baym and more recently applied to inhomogeneous trapped systems by Imamovi\ifmmode \acute{c}\else \'{c}\fi{}-Tomasovi\ifmmode \acute{c}\else \'{c}\fi{} and Griffin [in Progress in Nonequilibrium Green's Functions, edited by M. Bonitz (World Scientific, Singapore, 2000), p. 404].

arXiv:cond-mat/0105181•Physical Review A•Oct 12, 2001•33 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
We present a kinetic theory for Bose-Einstein condensation of a weakly interacting atomic gas in a trap. Starting from first principles, we establish a Markovian kinetic description for the evolution towards equilibrium. In particular, we obtain a set of self-consistent master equations for mean fields, normal densities, and anomalous fluctuations. These kinetic equations generalize the Gross-Pitaevskii mean-field equations, and merge them consistently with a quantum-Boltzmann-equation approach.
A quantum kinetic master equation (QKME) for bosonic atoms is formulated. It is a quantum stochastic equation for the kinetics of a dilute quantum Bose gas, and describes the behavior and formation of Bose condensation. The key assumption in deriving the QKME is a Markov approximation for the atomic collision terms. In the present paper the basic structure of the theory is developed, and approximations are stated and justified to delineate the region of validity of the theory. Limiting cases of the QKME include the quantum Boltzmann master equation and the Uehling-Uhlenbeck equation, as well as an equation analogous to the Gross-Pitaevskii equation.
Summary form only given. The dilute gas experiments on the Bose-Einstein condensation of magnetically confined alkali vapors have already generated widespread interest across a broad spectrum of traditional fields of physics. They have provided an exciting stage on which to build bridges linking the theory of complex and collective phenomena in superconducting and superfluid systems with the single particle microscopic physics described in quantum optics and laser physics. The approach I discuss is based on a derivation of the quantum kinetic theory from first principles. Based on a microscopic picture of the weakly interacting bosonic gas, a generalized kinetic theory for a Markovian many-body density operator is derived. The density operator is functionally dependent on a few key variables, which must be carefully chosen. These quantities serve as master variables and determine the system's evolution on a coarse-grained time scale. The weak interactions allow a perturbative expansion of the evolution, from which kinetic equations that describe the dynamics of the expectation value of any single-time observable are obtained. The final structure of the theory has many analogies with the quantum theory of the laser, such as amplitude and phase noise for the macroscopic field, squeezing dynamics, and a nonlinear master equation describing the underlying evolution.
The evolution equation of a weakly interacting boson system is derived. The model includes the interaction between the atoms in the condensate and the surrounding gas of noncondensed particles. The Bogoliubov transformation is introduced in a full quantum context and the scattering kernel between dressed particles and the condensate phase is obtained. The final system is expressed by the Boltzmann evolution equation for noncondensed particles coupled to the Gross-Pitaevskii equation for the condensate. We consider an out-of-equilibrium situation that induces a fast production of condensed particles. We apply our model to study the condensation dynamics of positronium atoms by evaporation.
We discuss the equivalence of two nonequilibrium kinetic theories that describe the evolution of a dilute, Bose-Einstein condensed atomic gas in a harmonic trap. The second-order kinetic equations of Walser et al. [Phys. Rev. A 63, 013607 (2001)] reduce to the Gross-Pitaevskii equation and the quantum Boltzmann equation in the low- and high-temperature limits, respectively. These kinetic equations thus describe the system in equilibrium (finite temperature) as well as in nonequilibrium (real time). We have found this theory to be equivalent to the nonequilibrium Green's function approach originally proposed by Kadanoff and Baym and more recently applied to inhomogeneous trapped systems by Imamovi\ifmmode \acute{c}\else \'{c}\fi{}-Tomasovi\ifmmode \acute{c}\else \'{c}\fi{} and Griffin [in Progress in Nonequilibrium Green's Functions, edited by M. Bonitz (World Scientific, Singapore, 2000), p. 404].
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.