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/0107613 · Physical Review A

Phases in weakly interacting finite Bose systems

David J. Dean, T. Papenbrock

Published Mar 14, 2002• 7 citations
arXivHTMLPDF

Abstract

We study precursors of thermal phase transitions in finite systems of interacting Bose gases. For weakly repulsive interactions there is a phase transition to the one-vortex state. The distribution of zeros of the partition function indicates that this transition is first order, and the precursors of the phase transition are already displayed in systems of a few dozen bosons. Systems of this size do not exhibit new phases as more vortices are added to the system.

DOI
10.1103/physreva.65.043603

Related papers

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

Phase transitions in ideal and weakly interacting Bose gases with a finite number of particles confined in a box

Jian-hui Wang, Yong-li Ma

We generalize the scheme to characterize phase transitions of finite systems in a complex temperature plane and approach the classifications of phase transitions in ideal and weakly interacting Bose gases of a finite number of particles, confined in a cubic box of volume L3 with different boundary conditions. For this finite ideal Bose system, by extending the classification parameters to all regions, we predict that the phase transition for periodic boundary conditions is of second order, while the transition in Dirichlet boundary conditions is of first order. For a weakly interacting Bose gas with periodic boundary conditions, we discuss the effects of finite particle numbers and inter-particle interactions on the nature of the phase transitions. We show that this homogenous weakly interacting Bose gas undergoes a second-order phase transition, which is in accordance with universality arguments for infinite systems. We also discuss the dependence of transition temperature on interaction strengths and particle numbers.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 4, 2009•9 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

Quantum Phases of Vortices in Rotating Bose-Einstein Condensates

Nigel R. Cooper, Nicola K. Wilkin, J. M. F. Gunn

We investigate the ground states of weakly interacting bosons in a rotating trap as a function of the number of bosons, N, and the average number of vortices, N(V). We identify the filling fraction nu identical with N/N(V) as the parameter controlling the nature of these states. We present results indicating that, as a function of nu, there is a zero temperature phase transition between a triangular vortex lattice phase, and strongly correlated vortex liquid phases. The vortex liquid phases appear to be the Read-Rezayi parafermion states.

arXiv:cond-mat/0107005•Physical Review Letters•Aug 30, 2001•454 citations

Quantum Phase Transition in a Low-Dimensional Weakly Interacting Bose Gas

Luca Fontanesi

This thesis is devoted to the study of the effect of disorder on low-dimensional weakly interacting Bose gases. In particular, the disorder triggers a quantum phase transition in one dimension at zero temperature that is investigated here through the study of the long-range behaviour of the one-body density matrix. An algebraic spatial decay of the coherence marks the quasicondensate, whereas, in the case of strong disorder, an exponential decay is recovered and it characterizes the insulating Bose-glass phase. This analysis is performed using an extended Bogoliubov theory to treat low dimensional Bose gases within a density-phase approach. A systematic numerical study allowed to draw the phase diagram of 1D weakly interacting bosons. The phase boundary obeys two different power laws between interaction and disorder strength depending on the regime of the gas where the transition occurs. These relations can be explained by means of scaling arguments valid in the white noise limit and in the Thomas-Fermi regime of the Bose gas. The phase transition to a quasicondensed phase comes along with the onset of superfluidity: the inspection of the superfluid fraction of the gas is consistent with these predictions for the boundary. The finite temperature case and the scenario in two dimensions are briefly discussed. The quantum phase transition is caused by low-energy phase fluctuations that destroy the quasi-long-range order characterizing the uniform system. Within the approach presented here, the phase fluctuations are identified as the low-lying Bogoliubov modes. Their properties have been investigated in detail to understand which changes trigger the phase transition and we found that the transition to the insulating phase is accompanied by a diverging density of states and a localization length, measured through the inverse participation ratio, that diverges as a power-law with power – 1 for vanishing energy. The fragmentation of the gas is also studied: this notion is very often associated with the onset of the insulating phase. The characterization of the density fragmentation is performed by analyzing the probability distribution of the density. A density profile is defined as fragmented when the probability distribution at vanishing density is finite or divergent and this happens for a gas in the Bose-glass phase. On the contrary, the superfluid phase is characterized by a zero limiting probability of having vanishing densities. This definition is derived analytically, and confirmed by a numerical study. This fragmentation criterion is particularly suited for detecting the phase transition in experiments: when a harmonic trap is included, the transition to the insulating phase can be extracted from the statistics of the local density distribution.

•Jan 1, 2011•1 citation

Vortices and vortex lattices at finite temperatures

Allan Griffin, Tetsuro Nikuni, E. Zaremba

The goal of creating and observing quantized vortices in trapped Bose gases arose almost immediately following the first achievements of Bose–Einstein condensation. The motivation for doing so was the obvious analogy with vortices in liquid helium and in type-II superconductors, and the fact that the quantization of circulation is directly associated with superfluid flow. It was recognized that the observation of quantized vortices could be taken as indisputable evidence for the existence of superfluidity in these systems. The review by Fetter and Svidzinsky (2001) contains a summary of the early experiments and the theoretical background for understanding the vortex state in a weakly interacting Bose gas based on the GP equation. This material will not be repeated here apart from those aspects that have a direct bearing on the focus of the present chapter, namely the properties of vortices at finite temperature. Although there have been some theoretical contributions to this subject, much remains to be done. The discussion in this chapter provides a framework for addressing the finite-temperature properties of vortex formation and vortex lattices in the context of the ZNG theory. The results in this chapter have not been published before, apart from those in subsection 9.8.1, which are based on Williams et al. (2002). There are several issues that relate to finite temperatures. First, there is the nucleation and formation of vortices from an initial highly nonequilibrium state. Second, there is the interaction of vortices with thermal excitations, which is responsible for the dissipative dynamics of a nonequilibrium vortex state. Third, there is the question of the final equilibrium state, with respect to the condensate and noncondensate densities in the vicinity of a vortex and to the geometrical arrangement of vortices in space.

Cambridge University Press eBooks•Feb 19, 2009•1 citation
We study precursors of thermal phase transitions in finite systems of interacting Bose gases. For weakly repulsive interactions there is a phase transition to the one-vortex state. The distribution of zeros of the partition function indicates that this transition is first order, and the precursors of the phase transition are already displayed in systems of a few dozen bosons. Systems of this size do not exhibit new phases as more vortices are added to the system.
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 .
We generalize the scheme to characterize phase transitions of finite systems in a complex temperature plane and approach the classifications of phase transitions in ideal and weakly interacting Bose gases of a finite number of particles, confined in a cubic box of volume L3 with different boundary conditions. For this finite ideal Bose system, by extending the classification parameters to all regions, we predict that the phase transition for periodic boundary conditions is of second order, while the transition in Dirichlet boundary conditions is of first order. For a weakly interacting Bose gas with periodic boundary conditions, we discuss the effects of finite particle numbers and inter-particle interactions on the nature of the phase transitions. We show that this homogenous weakly interacting Bose gas undergoes a second-order phase transition, which is in accordance with universality arguments for infinite systems. We also discuss the dependence of transition temperature on interaction strengths and particle numbers.
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.
We investigate the ground states of weakly interacting bosons in a rotating trap as a function of the number of bosons, N, and the average number of vortices, N(V). We identify the filling fraction nu identical with N/N(V) as the parameter controlling the nature of these states. We present results indicating that, as a function of nu, there is a zero temperature phase transition between a triangular vortex lattice phase, and strongly correlated vortex liquid phases. The vortex liquid phases appear to be the Read-Rezayi parafermion states.
This thesis is devoted to the study of the effect of disorder on low-dimensional weakly interacting Bose gases. In particular, the disorder triggers a quantum phase transition in one dimension at zero temperature that is investigated here through the study of the long-range behaviour of the one-body density matrix. An algebraic spatial decay of the coherence marks the quasicondensate, whereas, in the case of strong disorder, an exponential decay is recovered and it characterizes the insulating Bose-glass phase. This analysis is performed using an extended Bogoliubov theory to treat low dimensional Bose gases within a density-phase approach. A systematic numerical study allowed to draw the phase diagram of 1D weakly interacting bosons. The phase boundary obeys two different power laws between interaction and disorder strength depending on the regime of the gas where the transition occurs. These relations can be explained by means of scaling arguments valid in the white noise limit and in the Thomas-Fermi regime of the Bose gas. The phase transition to a quasicondensed phase comes along with the onset of superfluidity: the inspection of the superfluid fraction of the gas is consistent with these predictions for the boundary. The finite temperature case and the scenario in two dimensions are briefly discussed. The quantum phase transition is caused by low-energy phase fluctuations that destroy the quasi-long-range order characterizing the uniform system. Within the approach presented here, the phase fluctuations are identified as the low-lying Bogoliubov modes. Their properties have been investigated in detail to understand which changes trigger the phase transition and we found that the transition to the insulating phase is accompanied by a diverging density of states and a localization length, measured through the inverse participation ratio, that diverges as a power-law with power – 1 for vanishing energy. The fragmentation of the gas is also studied: this notion is very often associated with the onset of the insulating phase. The characterization of the density fragmentation is performed by analyzing the probability distribution of the density. A density profile is defined as fragmented when the probability distribution at vanishing density is finite or divergent and this happens for a gas in the Bose-glass phase. On the contrary, the superfluid phase is characterized by a zero limiting probability of having vanishing densities. This definition is derived analytically, and confirmed by a numerical study. This fragmentation criterion is particularly suited for detecting the phase transition in experiments: when a harmonic trap is included, the transition to the insulating phase can be extracted from the statistics of the local density distribution.
The goal of creating and observing quantized vortices in trapped Bose gases arose almost immediately following the first achievements of Bose–Einstein condensation. The motivation for doing so was the obvious analogy with vortices in liquid helium and in type-II superconductors, and the fact that the quantization of circulation is directly associated with superfluid flow. It was recognized that the observation of quantized vortices could be taken as indisputable evidence for the existence of superfluidity in these systems. The review by Fetter and Svidzinsky (2001) contains a summary of the early experiments and the theoretical background for understanding the vortex state in a weakly interacting Bose gas based on the GP equation. This material will not be repeated here apart from those aspects that have a direct bearing on the focus of the present chapter, namely the properties of vortices at finite temperature. Although there have been some theoretical contributions to this subject, much remains to be done. The discussion in this chapter provides a framework for addressing the finite-temperature properties of vortex formation and vortex lattices in the context of the ZNG theory. The results in this chapter have not been published before, apart from those in subsection 9.8.1, which are based on Williams et al. (2002). There are several issues that relate to finite temperatures. First, there is the nucleation and formation of vortices from an initial highly nonequilibrium state. Second, there is the interaction of vortices with thermal excitations, which is responsible for the dissipative dynamics of a nonequilibrium vortex state. Third, there is the question of the final equilibrium state, with respect to the condensate and noncondensate densities in the vicinity of a vortex and to the geometrical arrangement of vortices in space.