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/9908133 · Physical Review A

Finite-temperature collapse of a Bose gas with attractive interactions

Erich J. Mueller, Gordon Baym

Published Oct 16, 2000• 50 citations
arXivHTMLPDF

Abstract

We study the mechanical stability of the weakly interacting Bose gas with attractive interactions, and construct a unified picture of the collapse valid from the low-temperature condensed regime to the high temperature classical regime. As we show, the noncondensed particles play a crucial role in determining the region of stability, including providing a mechanism for collapse in the noncondensed cloud. Furthermore, we demonstrate that the mechanical instability prevents BCS-type ``pairing'' in the attractive Bose gas. We extend our results to describe domain formation in spinor condensates.

DOI
10.1103/physreva.62.053605

Related papers

Finite Temperature Collapse of a Bose Gas with Attractive Interactions (extended version)

Erich J. Mueller, Gordon Baym

We study the mechanical stability of the weakly interacting Bose gas with attractive interactions, and construct a unified picture of the collapse valid from the low temperature condensed regime to the high temperature classical regime. As we show, the non-condensed particles play a crucial role in determining the region of stability, even providing a mechanism for collapse in the non-condensed cloud. Furthermore, we demonstrate that the mechanical instability prevents BCS-type ``pairing'' in the attractive Bose gas. We extend our results to describe domain formation in spinor condensates.

arXiv:cond-mat/0005323•May 19, 2000•0 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

Pairing instability and mechanical collapse of a Bose gas with an attractive interaction

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

We study the pairing instability and mechanical collapse of a dilute homogeneous Bose gas with an attractive interaction. The pairing phase is found to be a saddle point and is unstable against pairing fluctuations. This pairing saddle point exists above a critical temperature. Below this critical temperature, the system is totally unstable in the pairing channel. Thus the system could collapse in the pairing channel in addition to mechanical collapse. The critical temperatures of pairing instability and mechanical collapse are higher than the Bose-Einstein condensation (BEC) temperature of an ideal Bose gas with the same density. When fluctuations are taken into account, we find that the critical temperature of mechanical collapse is even higher. The difference between the collapse temperature and the BEC temperature is proportional to $(n|{a}_{s}{|}^{3}{)}^{2/9},$ where n is the density and ${a}_{s}$ is the scattering length.

arXiv:cond-mat/0110004•Physical Review A•Jul 19, 2002•21 citations

Bose-Einstein condensation and density collapse in a weakly coupled boson-fermion mixture

Kyoko Shirasaki, Eiji Nakano, Hiroyuki Yabu

We investigate the mechanical instability toward density collapse and the transition temperature of Bose-Einstein condensation (BEC) in the weakly coupled boson-fermion many-body mixture of single-component boson and fermion gases, in the case of the repulsive boson-boson and attractive boson-fermion interactions; no fermion-fermion interaction is assumed to be originated from the Pauli exclusion because of the diluteness of the mixture. The mechanical instability occurs in the bosonic gas where the induced boson-boson attraction mediated by the fermion polarization overcomes the boson-boson repulsive interaction at low temperatures. We calculate the onset temperature of the mechanical instability and the BEC transition temperature for the interaction strength and the boson-fermion number ratio. We also discuss the relation between the mechanical instability and the BEC transition using a diagrammatic method.

arXiv:1412.4491•Physical Review A•Dec 19, 2014•4 citations

Diffusive instability of a vortex in a rotating Bose gas

Ashton S. Bradley, Crispin W. Gardiner

The dissipative dynamics of a vortex in a finite temperature trapped Bose-Einstein condensate are shown to be governed by a {\em diffusive instability}. In the weakly interacting regime we find a cross-over from instability to metastability of the vortex, determined only by the relative rotation rate of the vortex and thermal cloud. Even in the thermodynamically stable regime there is a finite lifetime arising from diffusive instability. We find the mean exit time for the vortex from the condensate, and show that near the critical frequency for thermodynamic stability the lifetime has a universal form which is independent of the condensate size and the vortex precession frequency. In the thermodynamically stable regime the steady-state two-time position correlation predicts `thermal bunching', giving an increased probability of positional coincidence for short times.

arXiv:cond-mat/0509592•Sep 23, 2005•1 citation

Thermodynamic stability, compressibility matrices, and effects of mediated interactions in a strongly interacting Bose-Fermi mixture

Koki Manabe, Yoji Ohashi

We theoretically investigate the thermodynamic stability of a normal-state Bose-Fermi mixture, with a tunable Bose-Fermi pairing interaction $\ensuremath{-}{U}_{\mathrm{BF}}<0$ associated with a heteronuclear Feshbach resonance, as well as a weak repulsive Bose-Bose interaction ${U}_{\mathrm{BB}}\ensuremath{\ge}0$. Including strong heteropairing fluctuations associated with the former interaction within the self-consistent $T$-matrix approximation, as well as the latter within the mean-field level, we calculate the compressibility matrix, to assess the stability of this system against density fluctuations. In the weak- and the intermediate-coupling regimes with respect to $\ensuremath{-}{U}_{\mathrm{BF}}$, we show that an effective attractive interaction between bosons mediated by density fluctuations in the Fermi component makes the system unstable below a certain temperature ${T}_{\mathrm{clp}}$ (leading to density collapse). When ${U}_{\mathrm{BB}}=0, {T}_{\mathrm{clp}}$ is always higher than the Bose-Einstein condensation (BEC) temperature ${T}_{\mathrm{c}}$. When ${U}_{\mathrm{BB}}>0$, the density collapse is suppressed, and the BEC transition becomes possible. It is also suppressed by the formation of tightly bound Bose-Fermi molecules when the heteropairing interaction $\ensuremath{-}{U}_{\mathrm{BF}}$ is strong; however, since the system may be viewed as a molecular Fermi gas in this case, the BEC transition does not also occur. Since quantum gases involving Bose atoms are known to be sensitive to interparticle correlations, our results would be useful for the study of many-body properties of a Bose-Fermi mixture in a stable manner, without facing the unwanted density collapse.

arXiv:2103.16843•Physical Review A•Jun 23, 2021•10 citations
We study the mechanical stability of the weakly interacting Bose gas with attractive interactions, and construct a unified picture of the collapse valid from the low-temperature condensed regime to the high temperature classical regime. As we show, the noncondensed particles play a crucial role in determining the region of stability, including providing a mechanism for collapse in the noncondensed cloud. Furthermore, we demonstrate that the mechanical instability prevents BCS-type ``pairing'' in the attractive Bose gas. We extend our results to describe domain formation in spinor condensates.
We study the mechanical stability of the weakly interacting Bose gas with attractive interactions, and construct a unified picture of the collapse valid from the low temperature condensed regime to the high temperature classical regime. As we show, the non-condensed particles play a crucial role in determining the region of stability, even providing a mechanism for collapse in the non-condensed cloud. Furthermore, we demonstrate that the mechanical instability prevents BCS-type ``pairing'' in the attractive Bose gas. We extend our results to describe domain formation in spinor condensates.
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].
We study the pairing instability and mechanical collapse of a dilute homogeneous Bose gas with an attractive interaction. The pairing phase is found to be a saddle point and is unstable against pairing fluctuations. This pairing saddle point exists above a critical temperature. Below this critical temperature, the system is totally unstable in the pairing channel. Thus the system could collapse in the pairing channel in addition to mechanical collapse. The critical temperatures of pairing instability and mechanical collapse are higher than the Bose-Einstein condensation (BEC) temperature of an ideal Bose gas with the same density. When fluctuations are taken into account, we find that the critical temperature of mechanical collapse is even higher. The difference between the collapse temperature and the BEC temperature is proportional to (n∣as∣3)2/9,(n|{a}_{s}{|}^{3}{)}^{2/9},(n∣as​∣3)2/9, where n is the density and as{a}_{s}as​ is the scattering length.
We investigate the mechanical instability toward density collapse and the transition temperature of Bose-Einstein condensation (BEC) in the weakly coupled boson-fermion many-body mixture of single-component boson and fermion gases, in the case of the repulsive boson-boson and attractive boson-fermion interactions; no fermion-fermion interaction is assumed to be originated from the Pauli exclusion because of the diluteness of the mixture. The mechanical instability occurs in the bosonic gas where the induced boson-boson attraction mediated by the fermion polarization overcomes the boson-boson repulsive interaction at low temperatures. We calculate the onset temperature of the mechanical instability and the BEC transition temperature for the interaction strength and the boson-fermion number ratio. We also discuss the relation between the mechanical instability and the BEC transition using a diagrammatic method.
The dissipative dynamics of a vortex in a finite temperature trapped Bose-Einstein condensate are shown to be governed by a {\em diffusive instability}. In the weakly interacting regime we find a cross-over from instability to metastability of the vortex, determined only by the relative rotation rate of the vortex and thermal cloud. Even in the thermodynamically stable regime there is a finite lifetime arising from diffusive instability. We find the mean exit time for the vortex from the condensate, and show that near the critical frequency for thermodynamic stability the lifetime has a universal form which is independent of the condensate size and the vortex precession frequency. In the thermodynamically stable regime the steady-state two-time position correlation predicts `thermal bunching', giving an increased probability of positional coincidence for short times.
We theoretically investigate the thermodynamic stability of a normal-state Bose-Fermi mixture, with a tunable Bose-Fermi pairing interaction $\ensuremath{-}{U}_{\mathrm{BF}}<0$ associated with a heteronuclear Feshbach resonance, as well as a weak repulsive Bose-Bose interaction ${U}_{\mathrm{BB}}\ensuremath{\ge}0$. Including strong heteropairing fluctuations associated with the former interaction within the self-consistent TTT-matrix approximation, as well as the latter within the mean-field level, we calculate the compressibility matrix, to assess the stability of this system against density fluctuations. In the weak- and the intermediate-coupling regimes with respect to $\ensuremath{-}{U}_{\mathrm{BF}}$, we show that an effective attractive interaction between bosons mediated by density fluctuations in the Fermi component makes the system unstable below a certain temperature Tclp{T}_{\mathrm{clp}}Tclp​ (leading to density collapse). When UBB=0,Tclp{U}_{\mathrm{BB}}=0, {T}_{\mathrm{clp}}UBB​=0,Tclp​ is always higher than the Bose-Einstein condensation (BEC) temperature Tc{T}_{\mathrm{c}}Tc​. When UBB>0{U}_{\mathrm{BB}}>0UBB​>0, the density collapse is suppressed, and the BEC transition becomes possible. It is also suppressed by the formation of tightly bound Bose-Fermi molecules when the heteropairing interaction $\ensuremath{-}{U}_{\mathrm{BF}}$ is strong; however, since the system may be viewed as a molecular Fermi gas in this case, the BEC transition does not also occur. Since quantum gases involving Bose atoms are known to be sensitive to interparticle correlations, our results would be useful for the study of many-body properties of a Bose-Fermi mixture in a stable manner, without facing the unwanted density collapse.