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:0902.4119 · New Journal of Physics

Multiple condensed phases in attractively interacting Bose systems

M. Männel, Klaus Morawetz, P. Lipavský

Published Mar 9, 2010• 6 citations
arXivHTMLPDF

Abstract

We investigate a Bose gas with finite-range interaction using a scheme to eliminate unphysical processes in the T-matrix approximation. In this way the corrected T-matrix becomes suitable to calculate properties below the critical temperature. For attractive interaction, an Evans-Rashid transition occurs between a quasi-ideal Bose gas and a BCS-like phase with a gaped dispersion. The gap decreases with increasing density and vanishes at a critical density where the single-particle dispersion becomes linear for small momenta indicating Bose-Einstein condensation. The investigation of the pressure shows however, that the mentioned quantum phase transitions might be inaccessible due to a preceding first order transition.

DOI
10.1088/1367-2630/12/3/033013

Related papers

Coexistence of phase transitions and hysteresis near the onset of Bose-Einstein condensation

M. Männel, Klaus Morawetz, P. Lipavský

Multiple phases occurring in a Bose gas with finite-range interaction are investigated. In the vicinity of the onset of Bose-Einstein condensation (BEC), the chemical potential and the pressure show a van der Waals--like behavior indicating a first-order phase transition although there is no long-range attraction. Furthermore, the equation of state becomes multivalued near the BEC transition. For a Hartree-Fock or Popov (Hartree-Fock-Bogoliubov) approximation, such a multivalued region can be avoided by the Maxwell construction. For sufficiently weak interaction, the multivalued region can also be removed using a many-body $T$-matrix approximation. However, for strong interactions there remains a multivalued region even for the $T$-matrix approximation and after the Maxwell construction, which is interpreted as a density hysteresis. This unified treatment of normal and condensed phases becomes possible due to the recently found scheme to eliminate self-interaction in the $T$-matrix approximation, which allows one to calculate properties below and above the critical temperature.

arXiv:1305.5192•Physical Review A•May 22, 2013•5 citations

Bose-Einstein condensation in an interacting Bose liquid

Moshe Schwartz

An exact expression for the single-particle reduced density matrix of a translationally invariant system of bosons is obtained, as an average of a functional of the density and current operators. An approximation scheme, based on small fluctuations in density and current, is used in its lowest order, to approximate the single-particle reduced density matrix and the condensate density by a functional of the structure factor, which is a measurable quantity. This is done for the ground state and for finite temperatures. The resulting expressions for the condensate density are discussed. For the ideal gas the result is correct below the condensation temperature. For the case of an interacting liquid, Bose-Einstein condensation exists, in the ground states for two- and three-dimensional systems, and for finite temperatures it does exist only in three dimensions. The present experimental knowledge of the structure factor enables only a crude estimate of the condensed fraction which is found to be 0.1-0.2.

Physical Review A•Nov 1, 1974•11 citations

Finite-Temperature Bose-Einstein Condensation in Interacting Boson System

D. Anchishkin, Igor N Mishustin, Oleksandr S. Stashko +2 more

Thermodynamical properties of an interacting boson system at finite temperatures and zero chemical potential are studied within the framework of the Skyrme-like mean-field toy model. It is assumed that the mean field contains both attractive and repulsive terms. Self-consistency relations between the mean field and thermodynamic functions are derived. It is shown that, for sufficiently strong attractive interactions, this system develops a first-order phase transition via the formation of a Bose condensate. An interesting prediction of the model is that the condensed phase is characterized by a constant total density of particles. It is shown that the energy density exhibits a jump at the critical temperature.

Ukrainian Journal of Physics•Dec 9, 2019•5 citations

Transition Temperature in One-Dimensional Bose–Einstein Condensation

Shoichi Sakamoto, Hideki Matsumoto

The phase transition of the one-dimensional Bose gas, interacting weakly with a repulsive potential and trapped in an external parabolic potential, is studied in a mean field approximation. The Bose–Einstein condensed (BEC) state is identified by the non-vanishing thermal average of a bose field. Free energies between the BEC state and normal state are compared. A crossing of the free energies occurring at low temperature suggests the first order phase transition in an interacting one-dimensional bose system. From fitting of numerical results, the relation among the transition temperature T c , the total number of bosons N and the interaction V is also provided as a simple power law, T c ∝( N 2 V ) 2/3 .

Journal of the Physical Society of Japan•Aug 1, 2002•1 citation

First-order Bose-Einstein condensation with three-body interacting bosons

Hui Hu, Zeng-Qiang Yu, Jia Wang +1 more

Bose-Einstein condensation, observed in either strongly interacting liquid helium or weakly interacting atomic Bose gases, is widely known to be a second-order phase transition. Here we predict a first-order Bose-Einstein condensation in a cloud of harmonically trapped bosons interacting with both attractive two-body interaction and repulsive three-body interaction, characterized respectively by an $s$-wave scattering length $a<0$ and a three-body scattering hypervolume $D>0$. It happens when the harmonic trapping potential is weak, so with increasing temperature the system changes from a low-temperature liquidlike quantum droplet to a normal gas and therefore experiences a first-order liquid-to-gas transition. At large trapping potential, however, the quantum droplet can first turn into a superfluid gas, rendering the condensation transition occurring later from a superfluid gas to a normal gas smooth. We determine a rich phase diagram and show the existence of a tricritical point, where the three phases, i.e., quantum droplet, superfluid gas, and normal gas, meet. We argue that an ensemble of spin-polarized tritium atoms could be a promising candidate to observe the predicted first-order Bose-Einstein condensation, across which the condensate fraction or central condensate density jumps to zero and the surface-mode frequencies diverge.

arXiv:2103.16044•Physical Review A•Oct 4, 2021•11 citations

Pairing Instability of Bose Gas with Attractive Interaction

Gun Sang Jeon, Lan Yin, Sung Wu Rhee +1 more

We study the Evans-Imry pairing phase of dilute homogeneous bose gas with attractive interaction. We find that it is generally unstable against fluctuations in pairing. Therefore in addition to the well-known mechanical collapse, the system can also collapse due to the pairing instability. Under certain conditions the critical temperature of pairing instability can be higher than that of mechanical collapse. 1 The system of bose gas with attractive interaction has received a lot of attention recently due to the success in cooling 7 Li [1] and 85 Rb [2] systems. In these trapped systems, Bose Einstein condensation can be realized at zero temperature if the number of atoms in the condensate is below a critical value [3] due to finite size effect. In 7 Li system, the condensate experiences repetitive growth and collapse as the system is cooled down [1]. In 85 Rb system, the interaction can be tuned from being repulsive to being attractive by Feshbach resonance technique. During this process, the system loses particles until the critical number is reached [2].

•Sep 28, 2001•0 citations
We investigate a Bose gas with finite-range interaction using a scheme to eliminate unphysical processes in the T-matrix approximation. In this way the corrected T-matrix becomes suitable to calculate properties below the critical temperature. For attractive interaction, an Evans-Rashid transition occurs between a quasi-ideal Bose gas and a BCS-like phase with a gaped dispersion. The gap decreases with increasing density and vanishes at a critical density where the single-particle dispersion becomes linear for small momenta indicating Bose-Einstein condensation. The investigation of the pressure shows however, that the mentioned quantum phase transitions might be inaccessible due to a preceding first order transition.
Multiple phases occurring in a Bose gas with finite-range interaction are investigated. In the vicinity of the onset of Bose-Einstein condensation (BEC), the chemical potential and the pressure show a van der Waals--like behavior indicating a first-order phase transition although there is no long-range attraction. Furthermore, the equation of state becomes multivalued near the BEC transition. For a Hartree-Fock or Popov (Hartree-Fock-Bogoliubov) approximation, such a multivalued region can be avoided by the Maxwell construction. For sufficiently weak interaction, the multivalued region can also be removed using a many-body TTT-matrix approximation. However, for strong interactions there remains a multivalued region even for the TTT-matrix approximation and after the Maxwell construction, which is interpreted as a density hysteresis. This unified treatment of normal and condensed phases becomes possible due to the recently found scheme to eliminate self-interaction in the TTT-matrix approximation, which allows one to calculate properties below and above the critical temperature.
An exact expression for the single-particle reduced density matrix of a translationally invariant system of bosons is obtained, as an average of a functional of the density and current operators. An approximation scheme, based on small fluctuations in density and current, is used in its lowest order, to approximate the single-particle reduced density matrix and the condensate density by a functional of the structure factor, which is a measurable quantity. This is done for the ground state and for finite temperatures. The resulting expressions for the condensate density are discussed. For the ideal gas the result is correct below the condensation temperature. For the case of an interacting liquid, Bose-Einstein condensation exists, in the ground states for two- and three-dimensional systems, and for finite temperatures it does exist only in three dimensions. The present experimental knowledge of the structure factor enables only a crude estimate of the condensed fraction which is found to be 0.1-0.2.
Thermodynamical properties of an interacting boson system at finite temperatures and zero chemical potential are studied within the framework of the Skyrme-like mean-field toy model. It is assumed that the mean field contains both attractive and repulsive terms. Self-consistency relations between the mean field and thermodynamic functions are derived. It is shown that, for sufficiently strong attractive interactions, this system develops a first-order phase transition via the formation of a Bose condensate. An interesting prediction of the model is that the condensed phase is characterized by a constant total density of particles. It is shown that the energy density exhibits a jump at the critical temperature.
The phase transition of the one-dimensional Bose gas, interacting weakly with a repulsive potential and trapped in an external parabolic potential, is studied in a mean field approximation. The Bose–Einstein condensed (BEC) state is identified by the non-vanishing thermal average of a bose field. Free energies between the BEC state and normal state are compared. A crossing of the free energies occurring at low temperature suggests the first order phase transition in an interacting one-dimensional bose system. From fitting of numerical results, the relation among the transition temperature T c , the total number of bosons N and the interaction V is also provided as a simple power law, T c ∝( N 2 V ) 2/3 .
Bose-Einstein condensation, observed in either strongly interacting liquid helium or weakly interacting atomic Bose gases, is widely known to be a second-order phase transition. Here we predict a first-order Bose-Einstein condensation in a cloud of harmonically trapped bosons interacting with both attractive two-body interaction and repulsive three-body interaction, characterized respectively by an sss-wave scattering length a<0a<0a<0 and a three-body scattering hypervolume D>0D>0D>0. It happens when the harmonic trapping potential is weak, so with increasing temperature the system changes from a low-temperature liquidlike quantum droplet to a normal gas and therefore experiences a first-order liquid-to-gas transition. At large trapping potential, however, the quantum droplet can first turn into a superfluid gas, rendering the condensation transition occurring later from a superfluid gas to a normal gas smooth. We determine a rich phase diagram and show the existence of a tricritical point, where the three phases, i.e., quantum droplet, superfluid gas, and normal gas, meet. We argue that an ensemble of spin-polarized tritium atoms could be a promising candidate to observe the predicted first-order Bose-Einstein condensation, across which the condensate fraction or central condensate density jumps to zero and the surface-mode frequencies diverge.
We study the Evans-Imry pairing phase of dilute homogeneous bose gas with attractive interaction. We find that it is generally unstable against fluctuations in pairing. Therefore in addition to the well-known mechanical collapse, the system can also collapse due to the pairing instability. Under certain conditions the critical temperature of pairing instability can be higher than that of mechanical collapse. 1 The system of bose gas with attractive interaction has received a lot of attention recently due to the success in cooling 7 Li [1] and 85 Rb [2] systems. In these trapped systems, Bose Einstein condensation can be realized at zero temperature if the number of atoms in the condensate is below a critical value [3] due to finite size effect. In 7 Li system, the condensate experiences repetitive growth and collapse as the system is cooled down [1]. In 85 Rb system, the interaction can be tuned from being repulsive to being attractive by Feshbach resonance technique. During this process, the system loses particles until the critical number is reached [2].