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:1407.3568 · New Journal of Physics

Superfluid behavior of a Bose–Einstein condensate in a random potential

Martin Könenberg, T Moser, Robert Seiringer, Jakob Yngvason

Published Jan 15, 2015• 13 citations
arXivHTMLPDF

Abstract

We investigate the relation between Bose–Einstein condensation (BEC) and superfluidity in the ground state of a one-dimensional model of interacting bosons in a strong random potential. We prove rigorously that in a certain parameter regime the superfluid fraction can be arbitrarily small while complete BEC prevails. In another regime there is both complete BEC and complete superfluidity, despite the strong disorder.

DOI
10.1088/1367-2630/17/1/013022

Related papers

Superuidity and BEC in a Model of Interacting Bosons in a Random Potential

Martin Könenberg, Thomas Moser, Robert Seiringer +1 more

We report on a mathematically rigorous analysis of the superfluid properties of a Bose- Einstein condensate in the many-body ground state of a one-dimensional model of interacting bosons in a random potential.

arXiv:1512.07176•Journal of Physics Conference Series•Feb 1, 2016•1 citation

Disordered Bose–Einstein condensates with interaction in one dimension

Robert Seiringer, Jakob Yngvason, Valentin Anatol'evich Zagrebnov

We study the effects of random scatterers on the ground state of the one-dimensional Lieb–Liniger model of interacting bosons on the unit interval in the Gross–Pitaevskii regime. We prove that Bose–Einstein condensation survives even a strong random potential with a high density of scatterers. The character of the wavefunction of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers and strong interactions the wavefunction extends over the whole interval. A high density of scatterers and weak interactions, on the other hand, lead to localization of the wavefunction in a fragmented subset of the interval.

arXiv:1207.7054•Journal of Statistical Mechanics Theory and Experiment•Nov 9, 2012•19 citations

BCS-BEC Crossover in a Random External Potential

Giuliano Orso

We investigate the ground state properties of a disordered superfluid Fermi gas across the BCS-BEC (Bose-Einstein condensate) crossover. We show that, for weak disorder, both the depletion of the condensate fraction of pairs and the normal fluid density exhibit a nonmonotonic behavior as a function of the interaction parameter 1/k{F}a, reaching their minimum value near unitarity. We find that, moving away from the weak-coupling BCS regime, Anderson's theorem ceases to apply and the superfluid order parameter is more and more affected by the random potential.

arXiv:0709.2621•Physical Review Letters•Dec 17, 2007•38 citations

Bose-Einstein condensation and superfluidity of a dilute Bose gas in a random potential

Michikazu Kobayashi, Makoto Tsubota

There is a growing interest in the relation between Bose-Einstein condensation (BEC) and the superfluidity. A Bose system confined in random media such as porous glass is suitable for studying this relation because BEC and superfluidity can be suppressed and controlled in such a disordered environment. However, it is not clear how this relation is affected by disorder and there are few theoretical studies that can be quantitatively tested by experiment. In this work we develop a dilute Bose gas model with a random potential that takes into account the pore-size dependence of porous glass. Then we compare our model with the measured low-temperature specific heat, condensate density, and superfluid density of ${}^{4}\mathrm{He}$ in Vycor glass. This comparison uses no free parameters. We predict phenomena at low temperatures: First, the random potential causes a T-linear specific heat instead of the ${T}^{3}$ dependence that is usually caused by phonons. Second, the BEC can remain even when the superfluidity disappears at low densities. Third, the system makes a reentrant transition at low densities; that is, the superfluid phase changes to the normal phase again as the temperature is reduced. This reentrant transition is more likely to be observed when the strength of the random potential is increased.

arXiv:cond-mat/0202364•Physical review. B, Condensed matter•Nov 18, 2002•66 citations

Bose-Einstein-condensed gases in arbitrarily strong random potentials

Vyacheslav I. Yukalov, Elizaveta P. Yukalova, Konstantin V. Krutitsky +1 more

Bose-Einstein-condensed gases in external spatially random potentials are considered in the frame of a stochastic self-consistent mean-field approach. This method permits the treatment of the system properties for the whole range of the interaction strength, from zero to infinity, as well as for arbitrarily strong disorder. Besides a condensate and superfluid density, a glassy number density due to a spatially inhomogeneous component of the condensate occurs. For very weak interactions and sufficiently strong disorder, the superfluid fraction can become smaller than the condensate fraction, while at relatively strong interactions, the superfluid fraction is larger than the condensate fraction for any strength of disorder. The condensate and superfluid fractions, and the glassy fraction always coexist, being together either nonzero or zero. In the presence of disorder, the condensate fraction becomes a nonmonotonic function of the interaction strength, displaying an antidepletion effect caused by the competition between the stabilizing role of the atomic interaction and the destabilizing role of the disorder. With increasing disorder, the condensate and superfluid fractions jump to zero at a critical value of the disorder parameter by a first-order phase transition.

arXiv:0705.3768•Physical Review A•Nov 27, 2007•51 citations

Bose-Einstein-condensed systems in random potentials

Vyacheslav I. Yukalov, R. Graham

The properties of systems with Bose-Einstein condensate in external time-independent random potentials are investigated in the frame of a self-consistent stochastic mean-field approximation. General considerations are presented, which are valid for finite temperatures, arbitrary strengths of the interaction potential, and for arbitrarily strong disorder potentials. The special case of a spatially uncorrelated random field is then treated in more detail. It is shown that the system consists of three components, condensed particles, uncondensed particles, and a glassy density fraction, but that the pure Bose glass phase with only a glassy density does not appear. The theory predicts a first-order phase transition for increasing disorder parameter, where the condensate fraction and the superfluid fraction simultaneously jump to zero. The influence of disorder on the ground-state energy, the stability conditions, the compressibility, the structure factor, and the sound velocity are analyzed. The uniform ideal condensed gas is shown to be always stochastically unstable, in the sense that an infinitesimally weak disorder destroys the Bose-Einstein condensate, returning the system to the normal state; but the uniform Bose-condensed system with finite repulsive interactions becomes stochastically stable and exists in a finite interval of the disorder parameter.

arXiv:cond-mat/0611357•Physical Review A•Feb 22, 2007•88 citations
We investigate the relation between Bose–Einstein condensation (BEC) and superfluidity in the ground state of a one-dimensional model of interacting bosons in a strong random potential. We prove rigorously that in a certain parameter regime the superfluid fraction can be arbitrarily small while complete BEC prevails. In another regime there is both complete BEC and complete superfluidity, despite the strong disorder.
We study the effects of random scatterers on the ground state of the one-dimensional Lieb–Liniger model of interacting bosons on the unit interval in the Gross–Pitaevskii regime. We prove that Bose–Einstein condensation survives even a strong random potential with a high density of scatterers. The character of the wavefunction of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers and strong interactions the wavefunction extends over the whole interval. A high density of scatterers and weak interactions, on the other hand, lead to localization of the wavefunction in a fragmented subset of the interval.
We investigate the ground state properties of a disordered superfluid Fermi gas across the BCS-BEC (Bose-Einstein condensate) crossover. We show that, for weak disorder, both the depletion of the condensate fraction of pairs and the normal fluid density exhibit a nonmonotonic behavior as a function of the interaction parameter 1/k{F}a, reaching their minimum value near unitarity. We find that, moving away from the weak-coupling BCS regime, Anderson's theorem ceases to apply and the superfluid order parameter is more and more affected by the random potential.
There is a growing interest in the relation between Bose-Einstein condensation (BEC) and the superfluidity. A Bose system confined in random media such as porous glass is suitable for studying this relation because BEC and superfluidity can be suppressed and controlled in such a disordered environment. However, it is not clear how this relation is affected by disorder and there are few theoretical studies that can be quantitatively tested by experiment. In this work we develop a dilute Bose gas model with a random potential that takes into account the pore-size dependence of porous glass. Then we compare our model with the measured low-temperature specific heat, condensate density, and superfluid density of 4He{}^{4}\mathrm{He}4He in Vycor glass. This comparison uses no free parameters. We predict phenomena at low temperatures: First, the random potential causes a T-linear specific heat instead of the T3{T}^{3}T3 dependence that is usually caused by phonons. Second, the BEC can remain even when the superfluidity disappears at low densities. Third, the system makes a reentrant transition at low densities; that is, the superfluid phase changes to the normal phase again as the temperature is reduced. This reentrant transition is more likely to be observed when the strength of the random potential is increased.
Bose-Einstein-condensed gases in external spatially random potentials are considered in the frame of a stochastic self-consistent mean-field approach. This method permits the treatment of the system properties for the whole range of the interaction strength, from zero to infinity, as well as for arbitrarily strong disorder. Besides a condensate and superfluid density, a glassy number density due to a spatially inhomogeneous component of the condensate occurs. For very weak interactions and sufficiently strong disorder, the superfluid fraction can become smaller than the condensate fraction, while at relatively strong interactions, the superfluid fraction is larger than the condensate fraction for any strength of disorder. The condensate and superfluid fractions, and the glassy fraction always coexist, being together either nonzero or zero. In the presence of disorder, the condensate fraction becomes a nonmonotonic function of the interaction strength, displaying an antidepletion effect caused by the competition between the stabilizing role of the atomic interaction and the destabilizing role of the disorder. With increasing disorder, the condensate and superfluid fractions jump to zero at a critical value of the disorder parameter by a first-order phase transition.
The properties of systems with Bose-Einstein condensate in external time-independent random potentials are investigated in the frame of a self-consistent stochastic mean-field approximation. General considerations are presented, which are valid for finite temperatures, arbitrary strengths of the interaction potential, and for arbitrarily strong disorder potentials. The special case of a spatially uncorrelated random field is then treated in more detail. It is shown that the system consists of three components, condensed particles, uncondensed particles, and a glassy density fraction, but that the pure Bose glass phase with only a glassy density does not appear. The theory predicts a first-order phase transition for increasing disorder parameter, where the condensate fraction and the superfluid fraction simultaneously jump to zero. The influence of disorder on the ground-state energy, the stability conditions, the compressibility, the structure factor, and the sound velocity are analyzed. The uniform ideal condensed gas is shown to be always stochastically unstable, in the sense that an infinitesimally weak disorder destroys the Bose-Einstein condensate, returning the system to the normal state; but the uniform Bose-condensed system with finite repulsive interactions becomes stochastically stable and exists in a finite interval of the disorder parameter.