Critical Temperature Shift in Weakly Interacting Bose Gas

Kashurnikov, V. A.; Prokof’ev, Nikolay; Svistunov, Boris

doi:10.1103/physrevlett.87.120402

Cited by 243 publications

(349 citation statements)

References 15 publications

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“…Compared with the most recent numerical results of Refs. [23,24], c ≃ 1.3, our value is still acceptable; the complexity of the mathematical problem does not permit one to make a definitive prediction of the prefactor of the linear term from an analytic analysis.…”

Section: Discussionmentioning

confidence: 87%

“…This provides a possible explanation for the discrepancy of the different Monte Carlo results [20,23,24] and [19]; whereas Refs. [20,23,24] calculated the linear corrections directly in the limit n 1/3 a → 0, Ref. [19] performed several calculations in the density regime 10 −6 < na 3 < ∼ 0.1 finding a shift of the critical density much smaller than expected from the linear formula of Refs.…”

Section: T /Tmentioning

confidence: 96%

“…An alternative is to use lattice calculations to solve the threedimensional classical field theory. Results of such calculations have been presented recently [23,24].…”

Section: Explicit Calculationsmentioning

confidence: 99%

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Bose-Einstein transition in a dilute interacting gas

et al. 2001

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We study the effects of repulsive interactions on the critical density for the Bose-Einstein transition in a homogeneous dilute gas of bosons. First, we point out that the simple mean field approximation produces no change in the critical density, or critical temperature, and discuss the inadequacies of various contradictory results in the literature. Then, both within the frameworks of Ursell operators and of Green's functions, we derive self-consistent equations that include correlations in the system and predict the change of the critical density. We argue that the dominant contribution to this change can be obtained within classical field theory and show that the lowest order correction introduced by interactions is linear in the scattering length, a, with a positive coefficient. Finally, we calculate this coefficient within various approximations, and compare with various recent numerical estimates.

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Section: Discussionmentioning

confidence: 87%

Section: T /Tmentioning

confidence: 96%

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Bose-Einstein transition in a dilute interacting gas

et al. 2001

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“…Using our result a M /a = 0.59 obtained from solving the flow equations in vacuum, the coefficient determining the shift in T c compared with the free Bose gas yields k = 1.39 (see also [22]). In Arnold & Moore [52] and Kashurnikov et al [53], the result for an interacting BEC is determined as k = 1.31 (dashed curve on BEC side of figure 6b) see also [54,55] for a functional RG study. This is in reasonable agreement with our result.…”

Section: Resultsmentioning

confidence: 96%

Functional renormalization for the Bardeen–Cooper–Schrieffer to Bose–Einstein condensation crossover

Scherer

Floerchinger

Gies

2011

Phil. Trans. R. Soc. A.

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We review the functional renormalization group (RG) approach to the Bardeen-CooperSchrieffer to Bose-Einstein condensation (BCS-BEC) crossover for an ultracold gas of fermionic atoms. Formulated in terms of a scale-dependent effective action, the functional RG interpolates continuously between the atomic or molecular microphysics and the macroscopic physics on large length scales. We concentrate on the discussion of the phase diagram as a function of the scattering length and the temperature, which is a paradigm example for the non-perturbative power of the functional RG. A systematic derivative expansion provides for both a description of the many-body physics and its expected universal features as well as an accurate account of the few-body physics and the associated BEC and BCS limits.

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“…One of the basic questions is about the nature and size of the shift of the BEC transition temperature due to the interactions. Although attempts at the problem have a long history [1,2], only the recent advent of experimental realizations of BEC in dilute gases have prompted considerable work to finally solve the problem both qualitatively and quantitatively [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. Here we treat the case of a homogenous gas as opposed to, e.g., the case of a harmonic trap [21].…”

mentioning

confidence: 99%

Bose-Einstein condensation temperature of a homogeneous weakly interacting Bose gas in variational perturbation theory through six loops

Kastening

2003

Phys. Rev. A

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We compute the shift of the transition temperature for a homogenous weakly interacting Bose gas in leading order in the scattering length a for given particle density n. Using variational perturbation theory through six loops in a classical three-dimensional scalar field theory, we obtain ∆Tc/Tc = 1.25 ± 0.13 an 1/3 , in agreement with recent Monte-Carlo results.PACS numbers: 03.75. Hh, 05.30.Jp, 12.38.Cy A dilute homogenous Bose gas with particle density n, where the scattering length a is small compared to the interparticle spacing ∼ n −1/3 is a fine example of how, under the right conditions, collective effects can generate strongly coupled modes from microscopic degrees of freedom exhibiting non-zero, but arbitrarily weak interactions. These conditions are met when the temperature is close to the transition temperature for Bose-Einstein condensation (BEC). Naive perturbation theory (PT) then breaks down for physical quantities sensitive to the collective long-wavelength modes. One of the basic questions is about the nature and size of the shift of the BEC transition temperature due to the interactions. Although attempts at the problem have a long history [1,2], only the recent advent of experimental realizations of BEC in dilute gases have prompted considerable work to finally solve the problem both qualitatively and quantitatively [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20]. Here we treat the case of a homogenous gas as opposed to, e.g., the case of a harmonic trap [21].The appropriate formal framework for the treatment of the many-particle Schrödinger equation describing a gas of identical spin-0 bosons is non-relativistic (3 + 1)-dimensional field theory. Being interested only in equilibrium quantities, we switch to imaginary time τ = it and consider the Euclidean action S 3+1

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Critical Temperature Shift in Weakly Interacting Bose Gas

Cited by 243 publications

References 15 publications

Bose-Einstein transition in a dilute interacting gas

Bose-Einstein transition in a dilute interacting gas

Functional renormalization for the Bardeen–Cooper–Schrieffer to Bose–Einstein condensation crossover

Bose-Einstein condensation temperature of a homogeneous weakly interacting Bose gas in variational perturbation theory through six loops

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