Study of the superfluid transition in two-dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mprescripts /><mml:mrow /><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mrow /><mml:mrow /></mml:mmultiscripts></mml:mrow></mml:math>films

Bishop, David J.; Reppy, J. D.

doi:10.1103/physrevb.22.5171

Cited by 296 publications

(162 citation statements)

References 37 publications

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“…4 He films is measured to be ≃ 5.5 [37]. Thus T m /T KT ≈ 0.26; renormalization of the shear modulus should reduce this result at most by a factor of 2 [12].…”

Section: Dislocation-mediated Meltingmentioning

confidence: 93%

Dislocation-mediated melting in superfluid vortex lattices

Gifford

Baym

2008

Phys. Rev. A

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We describe thermal melting of the two-dimensional vortex lattice in a rotating superfluid by generalizing the Halperin and Nelson theory of dislocation-mediated melting. and derive a melting temperature proportional to the renormalized shear modulus of the vortex lattice. The rigid-body rotation of the superfluid attenuates the effects of lattice compression on the energy of dislocations and hence the melting temperature, while not affecting the shearing. Finally, we discuss dislocations and thermal melting in inhomogeneous rapidly rotating Bose-Einstein condensates; we delineate a phase diagram in the temperature -rotation rate plane, and infer that the thermal melting temperature should lie below the Bose-Einstein transition temperature.

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“…4 He films is measured to be ≃ 5.5 [37]. Thus T m /T KT ≈ 0.26; renormalization of the shear modulus should reduce this result at most by a factor of 2 [12].…”

Section: Dislocation-mediated Meltingmentioning

confidence: 93%

Dislocation-mediated melting in superfluid vortex lattices

Gifford

Baym

2008

Phys. Rev. A

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“…Particularly in the context of superfluidity, the universal jump in the superfluid density was measured in thin films of liquid 4 He [13]. More recently, in the pioneering interference experiment with a weakly interacting Bose gas [14], the emergence of quasi-long-range order and the proliferation of vortices were shown.…”

mentioning

confidence: 99%

“…Several key signatures of BKT physics have been experimentally observed in a variety of systems such as exciton-polariton condensates [10], layered magnets [11,12], liquid 4 He films [13], and trapped Bose gases [14][15][16][17][18][19][20]. Particularly in the context of superfluidity, the universal jump in the superfluid density was measured in thin films of liquid 4 He [13].…”

mentioning

confidence: 99%

“…Although this prevents Bose-Einstein condensation in 2D, a transition to a superfluid phase with quasi-long-range order can still occur, as pointed out by Berezinskii, Kosterlitz, and Thouless (BKT) [6][7][8]. A key prediction of this theory is the scale-invariant behavior of the first-order correlation function g 1 (r), which, in the low-temperature phase, decays algebraically according to g 1 (r) ∝ r −η for large separations r. Importantly, the BKT theory for homogeneous systems predicts a universal value of η c = 1/4 at the critical temperature, accompanied by a universal jump of the superfluid density [9].Several key signatures of BKT physics have been experimentally observed in a variety of systems such as exciton-polariton condensates [10], layered magnets [11,12], liquid 4 He films [13], and trapped Bose gases [14][15][16][17][18][19][20]. Particularly in the context of superfluidity, the universal jump in the superfluid density was measured in thin films of liquid 4 He [13].…”

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confidence: 99%

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Observation of the Berezinskii-Kosterlitz-Thouless Phase Transition in an Ultracold Fermi Gas

et al. 2015

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We experimentally investigate the first-order correlation function of a trapped Fermi gas in the two-dimensional BEC-BCS crossover. We observe a transition to a low-temperature superfluid phase with algebraically decaying correlations. We show that the spatial coherence of the entire trapped system can be characterized by a single temperature-dependent exponent. We find the exponent at the transition to be constant over a wide range of interaction strengths across the crossover. This suggests that the phase transitions in both the bosonic regime and the strongly interacting crossover regime are of Berezinskii-Kosterlitz-Thouless type and lie within the same universality class. On the bosonic side of the crossover, our data are well-described by the quantum Monte Carlo calculations for a Bose gas. In contrast, in the strongly interacting regime, we observe a superfluid phase which is significantly influenced by the fermionic nature of the constituent particles.Long-range coherence is the hallmark of superfluidity and Bose-Einstein condensation [1,2]. The character of spatial coherence in a system and the properties of the corresponding phase transitions are fundamentally influenced by dimensionality. The two-dimensional case is particularly intriguing as for a homogeneous system, true long-range order cannot persist at any finite temperature due to the dominant role of phase fluctuations with large wavelengths [3][4][5]. Although this prevents Bose-Einstein condensation in 2D, a transition to a superfluid phase with quasi-long-range order can still occur, as pointed out by Berezinskii, Kosterlitz, and Thouless (BKT) [6][7][8]. A key prediction of this theory is the scale-invariant behavior of the first-order correlation function g 1 (r), which, in the low-temperature phase, decays algebraically according to g 1 (r) ∝ r −η for large separations r. Importantly, the BKT theory for homogeneous systems predicts a universal value of η c = 1/4 at the critical temperature, accompanied by a universal jump of the superfluid density [9].Several key signatures of BKT physics have been experimentally observed in a variety of systems such as exciton-polariton condensates [10], layered magnets [11,12], liquid 4 He films [13], and trapped Bose gases [14][15][16][17][18][19][20]. Particularly in the context of superfluidity, the universal jump in the superfluid density was measured in thin films of liquid 4 He [13]. More recently, in the pioneering interference experiment with a weakly interacting Bose gas [14], the emergence of quasi-long-range order and the proliferation of vortices were shown.There are still important aspects of superfluidity in two-dimensional systems that remain to be understood, which we aim to elucidate in this work with ultracold atoms. One question is whether the BKT phenomenology can also be extended to systems with nonuniform density. Indeed, if the microscopic symmetries are the same, the general physical picture involving phase fluctuations should be valid also for inhomogeneous systems. However, it ...

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“…Such mappings provide a relationship between seemingly different physical systems and provide an efficient tool for analyzing two dimensional problems in statistical mechanics [29,30].…”

Section: Introductionmentioning

confidence: 99%

Renormalization Group Analysis of Equilibrium and Non-equilibrium Charged Systems

Barkhudarov¹

2014

Springer Theses

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In this thesis we investigate properties of equilibrium and non-equilibrium systems by means of renormalization group (RG) analysis. In the study of the d−dimensional Coulomb gas we have formulated a continuum model from the underlying hyper-cubic lattice and employed the irreducible differential formulation of the Wilson RG. We have identified a Thouless-Kosterletz transition in d = 2 and found no non-trivial fixed points for d > 2. As an example of a non-equilibrium system, we have investigated properties of quasi-neutral plasmas which are governed by stochastic magnetohydrodynamic (MHD) equations. The present method is based upon the Martin-Siggia-Rose field-theory formulation of stochastic dynamics. We develop a diagrammatic representation for the theory and carry out a momentum-shell RG of Wilson-Kadanoff type. An infinite set of diagrams is identified which are marginal in the RG sense. We have shown, in accordance with previous literature, that the same problem arises for the randomly-forced Navier-Stokes equation. The problem of marginal variables can be suppressed by working near equilibrium, where stochastic forcing represents thermal fluctuations.In a similar manner we have considered regimes when MHD equations are subject either to kinetic or magnetic forcing only. In such models the macroscopic limit can be taken such that all marginal terms are irrelevant and the dynamics is governed by linear equations. Furthermore, non-trivial fixed points are identified in such regimes and limiting values of either kinematic viscosity or magnetic diffusivity are derived. A consistent description of MHD dynamics far from equilibrium is still absent. We highlight some of the aspects of the functional integral formulation with regards to the symmetries of the system and propose possible ways in which the system can be studied non-pertubatively. 1

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Study of the superfluid transition in two-dimensionalHe4films

Cited by 296 publications

References 37 publications

Dislocation-mediated melting in superfluid vortex lattices

Dislocation-mediated melting in superfluid vortex lattices

Observation of the Berezinskii-Kosterlitz-Thouless Phase Transition in an Ultracold Fermi Gas

Renormalization Group Analysis of Equilibrium and Non-equilibrium Charged Systems

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