Effect of weak interactions on the ultrarelativistic Bose-Einstein condensation temperature

Bedingham, Daniel; Evans, T. S.

doi:10.1103/physrevd.64.105018

Cited by 6 publications

(10 citation statements)

References 28 publications

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“…Finally, we shall follow the original PMS prescription [18] and optimize φ 2 (δ) u and r (δ) c separately. This procedure was also adopted in the ultra relativistic case where it has produced good results [36]. In order to select the appropriate roots we recur again to the AO convergence studies where the existence and behavior of optima families was fully investigated to order-δ 47 [21].…”

Section: Numerical Results For the Temperature Shiftmentioning

confidence: 99%

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Higher-order evaluation of the critical temperature for interacting homogeneous dilute Bose gases

et al. 2002

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We use the nonperturbative linear δ expansion method to evaluate analytically the coefficients c1 and c ′′ 2 which appear in the expansion for the transition temperature for a dilute, homogeneous, three dimensional Bose gas given by Tc = T0{1+c1an 1/3 +[c ′ 2 ln(an 1/3 )+c ′′ 2 ]a 2 n 2/3 +O(a 3 n)}, where T0 is the result for an ideal gas, a is the s-wave scattering length and n is the number density. In a previous work the same method has been used to evaluate c1 to order-δ 2 with the result c1 = 3.06. Here, we push the calculation to the next two orders obtaining c1 = 2.45 at order-δ 3 and c1 = 1.48 at order-δ 4 . Analysing the topology of the graphs involved we discuss how our results relate to other nonperturbative analytical methods such as the self-consistent resummation and the 1/N approximations. At the same orders we obtain c ′′ 2 = 101.4, c ′′ 2 = 98.2 and c ′′ 2 = 82.9. Our analytical results seem to support the recent Monte Carlo estimates c1 = 1.32 ± 0.02 and c ′′ 2 = 75.7 ± 0.4.

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Section: Numerical Results For the Temperature Shiftmentioning

confidence: 99%

“…A successful extension to the ultra-relativistic case was performed by Bedingham and Evans in Ref. [36].…”

Section: A the Linear δ Expansionmentioning

confidence: 99%

Higher-order evaluation of the critical temperature for interacting homogeneous dilute Bose gases

et al. 2002

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“…For the interested reader Refs. [17,18,19,20,21,22,23,25,26,27,28,29,30,31,32,33] provide an extensive (but far from complete) list of successful applications of the method to different problems.…”

Section: Lde and The Interpolated Effective Scalar Theory For Becmentioning

confidence: 99%

“…where the J i coefficients are given by 19) and z = k/η * . Analytically, the two ways we have presented for obtaining the perturbative evaluation of φ…”

Section: (K)mentioning

confidence: 99%

Asymptotically improved convergence of optimized perturbation theory in the Bose-Einstein condensation problem

2003

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We investigate the convergence properties of optimized perturbation theory, or linear δ expansion (LDE), within the context of finite temperature phase transitions. Our results prove the reliability of these methods, recently employed in the determination of the critical temperature Tc for a system of weakly interacting homogeneous dilute Bose gas. We carry out the explicit LDE optimized calculations and also the infrared analysis of the relevant quantities involved in the determination of Tc in the large-N limit, when the relevant effective static action describing the system is extended to O(N ) symmetry. Then, using an efficient resummation method, we show how the LDE can exactly reproduce the known large-N result for Tc already at the first non-trivial order. Next, we consider the finite N = 2 case where, using similar resummation techniques, we improve the analytical results for the nonperturbative terms involved in the expression for the critical temperature allowing comparison with recent Monte Carlo estimates of them. To illustrate the method we have considered a simple geometric series showing how the procedure as a whole works consistently in a general case.

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“…See, for instance, [12,13] and references therein. The LDE has also been used successfully in many other situations, including studies of scalar theories [14].…”

Section: Linear Delta Expansionmentioning

confidence: 99%

Quantum field dynamics of the slow rollover in the linear delta expansion

Bedingham

Jones

2003

Phys. Rev. D

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We show how the linear delta expansion, as applied to the slow-roll transition in quantum mechanics, can be recast in the closed time-path formalism. This results in simpler, explicit expressions than were obtained in the Schrödinger formulation and allows for a straightforward generalization to higher dimensions. Motivated by the success of the method in the quantummechanical problem, where it has been shown to give more accurate results for longer than existing alternatives, we apply the linear delta expansion to four-dimensional field theory.At small times all methods agree. At later times, the first-order linear delta expansion is consistently higher that Hartree-Fock, but does not show any sign of a turnover. A turnover emerges in second-order of the method, but the value of Φ 2 (t) at the turnover is larger that that given by the Hartree-Fock approximation. Based on this calculation, and our experience in the corresponding quantum-mechanical problem, we believe that the Hartree-Fock approximation does indeed underestimate the value of Φ 2 (t) at the turnover. In subsequent applications of the method we hope to implement the calculation in the context of an expanding universe, following the line of earlier calculations by Boyanovsky et al., who used the Hartree-Fock and large-N methods. It seems clear, however, that the method will become unreliable as the system enters the reheating stage. IntroductionA period of inflation in the early universe could have the desirable consequence that a general initial condition will evolve towards the homogeneity, isotropy and flatness which we observe. Basic models require the slow evolution of a scalar field from an initial unstable vacuum state to a final stable state. Without knowing how to perform this inherently non-perturbative calculation exactly, approximation attempts must first prove themselves in the simpler situation of the quantummechanical slow roll. Though this simpler problem cannot be solved analytically, the degrees of freedom are sufficiently few that an exact numerical solution can be found. This allows us to test non-perturbative methods before proceeding to a calculation for the four-dimensional scalar field.The quantum-mechanical slow roll was first treated by Guth and Pi [1], who considered the evolution of a Gaussian wave-packet initially centred at the top of a potential hill V = − 1 2 mωq 2 . Following this, the Dirac time-dependent variational method was used for a potential V = λ(q 2 − a 2 ) 2 /24, first by Cooper et al. [2], who used a Gaussian wave function ansatz, and *

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Effect of weak interactions on the ultrarelativistic Bose-Einstein condensation temperature

Cited by 6 publications

References 28 publications

Higher-order evaluation of the critical temperature for interacting homogeneous dilute Bose gases

Higher-order evaluation of the critical temperature for interacting homogeneous dilute Bose gases

Asymptotically improved convergence of optimized perturbation theory in the Bose-Einstein condensation problem

Quantum field dynamics of the slow rollover in the linear delta expansion

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