A microscopic theory of the lambda transition

Toyoda, Tadashi

doi:10.1016/0003-4916(82)90277-9

Cited by 43 publications

(38 citation statements)

References 19 publications

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“…The transition temperature, T c , is determined from Fig. 1, it is decreased by increasing the potential strength, as can be deduced from Table, this result is in consistence with results obtained in [5], Hartree-Fock theory calculation [12], and with renormalization group calculation [13]. As the potential strength increases, the equilibrium interparticle spacing increases and the probability of overlapping between the thermal waves decreases.…”

Section: Resultssupporting

confidence: 77%

Bose-Einstein Condensation of Hard Sphere Homogeneous Gas in Static Fluctuation Approximation

Al-Sugheir

Gasymeh²,

Shatnawi³

et al. 2009

Acta Phys. Pol. A

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The condensation fraction, transition temperature, and energy per particle for a hard sphere interacting homogeneous Bose gas using the static fluctuation approximation have been determined. The transition temperature at liquid helium density has been found to be lower than that for the noninteracting gas. Both superfluidity and the Bose-Einstein condensation have been found to occur at the same transition temperature. Our results are consistent with results obtained by other methods.

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Section: Resultssupporting

confidence: 77%

Bose-Einstein Condensation of Hard Sphere Homogeneous Gas in Static Fluctuation Approximation

Al-Sugheir

Gasymeh²,

Shatnawi³

et al. 2009

Acta Phys. Pol. A

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“…The effect of a weak repulsive two-body interaction on the transition temperature of a dilute gas Bose gas at fixed density has been controversial for a long time [1][2][3][4][5][6]. It has recently been established theoretically [7] that T c increases linearly with the strength of the interaction parametrized in terms of the scattering length a.…”

Section: Introductionmentioning

confidence: 99%

The transition temperature of the dilute interacting Bose gas for N internal states

2000

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We calculate explicitly the variation δT c of the Bose-Einstein condensation temperature T c induced by weak repulsive two-body interactions to leading order in the interaction strength. As shown earlier by general arguments, δT c /T c is linear in the dimensionless product an 1/3 to leading order, where n is the density and a the scattering length. This result is non-perturbative, and a direct perturbative calculation of the amplitude is impossible due to infrared divergences familiar from the study of the superfluid helium lambda transition. Therefore we introduce here another standard expansion scheme, generalizing the initial model which depends on one complex field to one depending on N real fields, and calculating the temperature shift at leading order for large N . The result is explicit and finite. The reliability of the result depends on the relevance of the large N expansion to the situation N = 2, which can in principle be checked by systematic higher order calculations.The large N result agrees remarkably well with recent numerical simulations.

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“…However, the value and even the sign of the coefficient c is controversial [8]. Some authors claimed that repulsive interactions reduce the critical temperature [9][10][11][12], while others indicated an increase of the critical temperature [13][14][15][16][17][18][19][20][21]. In a recent publication [22], the authors obtained a negative constant c ≈ −2.33 by using the model of spatial permutations.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamical Properties of a Trapped Interacting Bose Gas

2012

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The thermodynamical properties of interacting Bose atoms in a harmonic potential are studied within the mean-field approximation. For weak interactions, the quantum statistics is equivalent to an ideal gas in an effective mean-field potential. The eigenvalue of the Gross-Pitaevskii equation is identified as the chemical potential of the ideal gas. The condensation temperature and density profile of atoms are calculated. It is found that the critical temperature Tc decreases as the interactions increase. Below the critical point, the condensation fraction exhibits a universal relation of N0/N = 1 − (T /Tc) γ , with the index γ ≈ 2.3 independent of the interaction strength, the chemical potential, as well as the frequency of the confining potential.

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A microscopic theory of the lambda transition

Cited by 43 publications

References 19 publications

Bose-Einstein Condensation of Hard Sphere Homogeneous Gas in Static Fluctuation Approximation

Bose-Einstein Condensation of Hard Sphere Homogeneous Gas in Static Fluctuation Approximation

The transition temperature of the dilute interacting Bose gas for N internal states

Thermodynamical Properties of a Trapped Interacting Bose Gas

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