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/0301327 · Physical Review A

Generalized coherent state representation of Bose-Einstein condensates

Vladimir Chernyak, Seok Jin Choi, Shaul Mukamel

Published May 22, 2003• 25 citations
arXivHTMLPDF

Abstract

We show that the quantum many-body state of Bose-Einstein condensates consistent with the time-dependent Hartree-Fock-Bogoliubov (TDHFB) equations is a generalized coherent state. At zero temperature, the noncondensate density and the anomalous noncondensate correlation are not independent, allowing us to eliminate one of the three variables in the TDHFB.

DOI
10.1103/physreva.67.053604

Related papers

The time-dependent Hartree–Fock–Bogoliubov equations for Bosons

Volker Bach, Sébastien Breteaux, Thomas Chen +2 more

Abstract We introduce the map of dynamics of quantum Bose gases into dynamics of quasifree states, which we call the “nonlinear quasifree approximation”. We use this map to derive the time-dependent Hartree–Fock–Bogoliubov (HFB) equations describing the dynamics of quantum fluctuations around a Bose–Einstein condensate. We prove global well-posedness of the HFB equations for pair potentials satisfying suitable regularity conditions, and we establish important conservation laws. We show that the space of solutions of the HFB equations has a symplectic structure reminiscent of a Hamiltonian system. This is then used to relate the HFB equations to the HFB eigenvalue equations discussed in the physics literature. We also construct Gibbs equilibrium states at positive temperature associated with the HFB equations, and we establish criteria for the appearance of Bose–Einstein condensation.

arXiv:1602.05171•Journal of Evolution Equations•May 17, 2022•28 citations

On the Hartree-Fock-Bogoliubov equations

Volker Bach, Sébastien Breteaux, Thomas Chen +2 more

We review some results of our paper arXiv:1602.05171v2 on the "nonlinear quasifree approximation" to the many-body Schrödinger dynamics of Bose gases. In that paper, we derive, with the help of this approximation, the time-dependent Hartree-Fock-Bogoliubov (HFB) equations, providing an approximate description of the dynamics of quantum fluctuations around a Bose-Einstein condensate and study properties of these equations.

arXiv:1805.04689•May 12, 2018•0 citations

Gapless mean-field theory of Bose-Einstein condensates

David A. W. Hutchinson, Keith R. Burnett, R. J. Dodd +6 more

We present a topical review of the development of finite-temperature field theories of Bose-Einstein condensation in weakly interacting atomic gases. We highlight the difficulties in obtaining a consistent finite-temperature theory that has a gapless excitation spectrum in accordance with Goldstone's theorem and which is free from both ultraviolet and infrared divergences. We present results from the two consistent theories developed so far. These are the Hartree-Fock-Bogoliubov theory within the Popov approximation and a many-body T -matrix approach which we have termed gapless-Hartree-Fock-Bogoliubov (GHFB). Comparison with the available experimental results is made and the remaining difficulties are highlighted.

Journal of Physics B Atomic Molecular and Optical Physics•Sep 14, 2000•87 citations

Collective excitations of a dilute Bose gas at finite temperature: time dependent Hartree–Fock–Bogoliubov theory

Abdelâali Boudjemâa, Nadia Guebli

Abstract Using the time-dependent Hartree–Fock–Bogoliubov approach, where the condensate is coupled with the thermal cloud and the anomalous density, we study the equilibrium and the dynamical properties of three-dimensional quantum-degenerate Bose gas at finite temperature. Effects of the anomalous correlations on the condensed fraction and the critical temperature are discussed. In uniform Bose gas, useful expressions for the Bogoliubov excitations spectrum, the first and second sound, the condensate depletion and the superfluid fraction are derived. Our results are tested by comparing the findings computed by quantum Monte Carlo simulations. We present also a systematic investigation of the collective modes of a Bose condensate confined in an external trap. Our predictions are in qualitative agreement with previous experimental and theoretical results. We show in particular that our theory is capable of explaining the so-called anomalous behavior of the m = 0 mode.

arXiv:1710.04003•Journal of Physics A Mathematical and Theoretical•Sep 4, 2017•8 citations

Self-consistent Hartree-Fock-Bogoliubov approach for bosons: self-eliminating divergence and pure pair condensate

M. S. Bulakhov, A. S. Peletminskii

We investigate the thermodynamic properties of an interacting Bose gas with a condensate within the energy-functional formulation of the Hartree-Fock-Bogoliubov (HFB) approach. For a contact interaction, we derive a self-consistent solution to the HFB equations that intrinsically eliminates divergence. This solution characterizes the equilibrium state featuring a condensate of correlated pairs of particles. We analyze the temperature dependence of key thermodynamic quantities such as condensate density, chemical potential, entropy, pressure, specific heat capacity at constant volume, and isothermal compressibility and compare them with predictions from the Popov approximation (PA). We predict that the transition temperature shifts to higher values due interactions, with the HFB approach yielding a larger shift than the PA. Analysis of the compressibility indicates that a pure pair condensate is unstable, and the stable equilibrium corresponds to only a mixture of single-particle and pair condensates.

arXiv:2506.13413•Jun 16, 2025•0 citations

Finite-temperature density-functional theory of Bose-Einstein condensates

Nathan Argaman, Y. B. Band

The thermodynamic approach to density-functional theory (DFT) is used to derive a versatile theoretical framework for the treatment of finite-temperature (and in the limit, zero-temperature) Bose-Einstein condensates (BECs). The simplest application of this framework, using the overall density of bosons alone, would yield the DFT of Nunes [J. Phys. B 32, 4293 (1999)]. It is argued that a significant improvement in accuracy may be obtained by using additional density fields: the condensate amplitude and the anomalous density. Thus, two advanced schemes are suggested, one corresponding to a generalized two-fluid model of condensate systems, and another scheme, which explicitly accounts for anomalous density contributions and anomalous effective potentials. The latter reduces to the Hartree-Fock-Bogoliubov approach in the limit of weak interactions. For stronger interactions, a local-density approximation is suggested, but its implementation requires accurate data for the thermodynamic properties of uniform interacting BEC systems, including fictitious perturbed states of such systems. Provided that such data become available (e.g., from quantum Monte Carlo computation), DFT can be used to obtain high-accuracy theoretical results for the equilibrium states of BECs of various geometries and external potentials.

arXiv:1011.4907•Physical Review A•Feb 18, 2011•10 citations
We show that the quantum many-body state of Bose-Einstein condensates consistent with the time-dependent Hartree-Fock-Bogoliubov (TDHFB) equations is a generalized coherent state. At zero temperature, the noncondensate density and the anomalous noncondensate correlation are not independent, allowing us to eliminate one of the three variables in the TDHFB.
Abstract We introduce the map of dynamics of quantum Bose gases into dynamics of quasifree states, which we call the “nonlinear quasifree approximation”. We use this map to derive the time-dependent Hartree–Fock–Bogoliubov (HFB) equations describing the dynamics of quantum fluctuations around a Bose–Einstein condensate. We prove global well-posedness of the HFB equations for pair potentials satisfying suitable regularity conditions, and we establish important conservation laws. We show that the space of solutions of the HFB equations has a symplectic structure reminiscent of a Hamiltonian system. This is then used to relate the HFB equations to the HFB eigenvalue equations discussed in the physics literature. We also construct Gibbs equilibrium states at positive temperature associated with the HFB equations, and we establish criteria for the appearance of Bose–Einstein condensation.
We present a topical review of the development of finite-temperature field theories of Bose-Einstein condensation in weakly interacting atomic gases. We highlight the difficulties in obtaining a consistent finite-temperature theory that has a gapless excitation spectrum in accordance with Goldstone's theorem and which is free from both ultraviolet and infrared divergences. We present results from the two consistent theories developed so far. These are the Hartree-Fock-Bogoliubov theory within the Popov approximation and a many-body T -matrix approach which we have termed gapless-Hartree-Fock-Bogoliubov (GHFB). Comparison with the available experimental results is made and the remaining difficulties are highlighted.
Abstract Using the time-dependent Hartree–Fock–Bogoliubov approach, where the condensate is coupled with the thermal cloud and the anomalous density, we study the equilibrium and the dynamical properties of three-dimensional quantum-degenerate Bose gas at finite temperature. Effects of the anomalous correlations on the condensed fraction and the critical temperature are discussed. In uniform Bose gas, useful expressions for the Bogoliubov excitations spectrum, the first and second sound, the condensate depletion and the superfluid fraction are derived. Our results are tested by comparing the findings computed by quantum Monte Carlo simulations. We present also a systematic investigation of the collective modes of a Bose condensate confined in an external trap. Our predictions are in qualitative agreement with previous experimental and theoretical results. We show in particular that our theory is capable of explaining the so-called anomalous behavior of the m = 0 mode.
We investigate the thermodynamic properties of an interacting Bose gas with a condensate within the energy-functional formulation of the Hartree-Fock-Bogoliubov (HFB) approach. For a contact interaction, we derive a self-consistent solution to the HFB equations that intrinsically eliminates divergence. This solution characterizes the equilibrium state featuring a condensate of correlated pairs of particles. We analyze the temperature dependence of key thermodynamic quantities such as condensate density, chemical potential, entropy, pressure, specific heat capacity at constant volume, and isothermal compressibility and compare them with predictions from the Popov approximation (PA). We predict that the transition temperature shifts to higher values due interactions, with the HFB approach yielding a larger shift than the PA. Analysis of the compressibility indicates that a pure pair condensate is unstable, and the stable equilibrium corresponds to only a mixture of single-particle and pair condensates.
The thermodynamic approach to density-functional theory (DFT) is used to derive a versatile theoretical framework for the treatment of finite-temperature (and in the limit, zero-temperature) Bose-Einstein condensates (BECs). The simplest application of this framework, using the overall density of bosons alone, would yield the DFT of Nunes [J. Phys. B 32, 4293 (1999)]. It is argued that a significant improvement in accuracy may be obtained by using additional density fields: the condensate amplitude and the anomalous density. Thus, two advanced schemes are suggested, one corresponding to a generalized two-fluid model of condensate systems, and another scheme, which explicitly accounts for anomalous density contributions and anomalous effective potentials. The latter reduces to the Hartree-Fock-Bogoliubov approach in the limit of weak interactions. For stronger interactions, a local-density approximation is suggested, but its implementation requires accurate data for the thermodynamic properties of uniform interacting BEC systems, including fictitious perturbed states of such systems. Provided that such data become available (e.g., from quantum Monte Carlo computation), DFT can be used to obtain high-accuracy theoretical results for the equilibrium states of BECs of various geometries and external potentials.