Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Seven Loops

Abstract

The shift of the Bose-Einstein condensation temperature for a homogenous weakly interacting Bose gas in leading order in the scattering length `a' is computed for given particle density `n.' Variational perturbation theory is used to resum the corresponding perturbative series for Delta<phi^2>/Nu in a classical three-dimensional scalar field theory with coupling `u' and where the physical case of N=2 field components is generalized to arbitrary N. Our results for N=1,2,4 are in agreement with recent Monte-Carlo simulations; for N=2, we obtain Delta T_c/T_c = 1.27 +/- 0.11 a n^(1/3). We use seven-loop perturbative coefficients, extending earlier work by one loop order.

8 pages; typos and errors of presentation fixed; beautifications; results unchanged

References in corpus (37)

• Critical Phenomena and Renormalization-Group Theory
• Worm algorithms for classical statistical models
• Condensate fraction and critical temperature of a trapped interacting Bose gas
• The transition temperature of the dilute interacting Bose gas
• Transition temperature of a dilute homogeneous imperfect Bose gas
• Critical Temperature of Bose-Einstein Condensation of Hard Sphere Gases
• Renormalization Group Theory of the Three-Dimensional Dilute Bose Gas
• Seven-Loop Critical Exponents from Strong-Coupling phi^4-Theory in Three Dimensions
• The transition temperature of the dilute interacting Bose gas for $N$ internal degrees of freedom
• Transition Temperature of the homogeneous, weakly interacting Bose gas
• Bose-Einstein transition in a dilute interacting gas
• T_c for dilute Bose gases: beyond leading order in 1/N
• Addendum to paper: Strong-Coupling Behavior of ${\varphi }^4$-Theories and Critical Exponents [Phys. Rev. D 57, 2264 (1998)]
• Transition Temperature of a Uniform Imperfect Bose Gas
• Monte Carlo simulation of O(2) phi^4 field theory in three dimensions
• T_c for homogeneous dilute Bose gases: a second-order result
• Transition Temperature for Weakly Interacting Homogeneous Bose Gases
• Non-analytic dependence of the transition temperature of the homogeneous dilute Bose gas on scattering length
• T_c for trapped dilute Bose gases: a second-order result
• Convergent resummed linear delta expansion in the critical O(N) (ϕ_i^2)^2_{3d} model
• Higher Order Evaluation of the Critical Temperature for Interacting Homogeneous Dilute Bose Gases
• Five-Loop Critical Temperature Shift in Weakly Interacting Homogeneous Bose-Einstein Condensate
• Bose-Einstein condensation of interacting gases
• Recursive Graphical Construction of Feynman Diagrams and Their Multiplicities in phi^4- and in phi^2A-Theory
• Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Six Loops
• Asymptotically Improved Convergence of Optimized Perturbation Theory in the Bose-Einstein Condensation Problem
• Monte Carlo studies of three-dimensional O(1) and O(4) \boldmath{${\varphi }^4$} theory related to BEC phase transition temperatures
• Convergence of the Linear Delta Expansion in the Critical O(N) Field Theory
• Variational Interpolation Algorithm between Weak- and Strong-Coupling Expansions
• Dependence of the BEC transition temperature on interaction strength: a perturbative analysis
• On the Convergence of the Linear Delta Expansion for the Shift in T_c for Bose-Einstein Condensation
• Theory and Satellite Experiment for Critical Exponent alpha of lambda-Transition in Superfluid Helium
• Three-loop critical exponents, amplitude functions, and amplitude ratios from variational perturbation theory
• Recursive Graphical Construction of Feynman Diagrams in phi^4 Theory: Asymmetric Case and Effective Energy
• Dependence of Variational Perturbation Expansions on Strong-Coupling Behavior. Inapplicability of delta-Expansion to Field Theory
• Thermodynamic properties of confined interacting Bose gases - a renormalization group approach
• Finite size scaling and the role of the thermodynamic ensemble in the transition temperature of a dilute Bose gas

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