Improved optimization of perturbation theory: Applications to the oscillator energy levels and Bose-Einstein condensate critical temperature

2004/01/31 by Jean-Loı̈c Kneur, J. -L. Kneur, A. Neveu +2 · 2 citations
Physics and Astronomy · #Anharmonicity #Bose–Einstein condensate #Cold Atom Physics and Bose-Einstein Condensates #Lattice (music) #Mathematical physics #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Physics #Physics of Superconductivity and Magnetism #Quantum electrodynamics #Quantum mechanics #Quantum, superfluid, helium dynamics #cond-mat.soft #hep-th

paper · pdf · doi:10.1103/physreva.69.053624

published as Phys. Rev. A69, 053624 (2004) · 9 pages, no figures. v2: minor wording changes in title/abstract, to appear in Phys.Rev. A

openalex publication_date 2004/05/24 · arxiv created 2004/09/21 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Improving perturbation theory via a variational optimization has generally produced in higher orders an embarrassingly large set of solutions, most of them unphysical (complex). We introduce an extension of the optimized perturbation method which leads to a drastic reduction of the number of acceptable solutions. The properties of this method are studied and it is then applied to the calculation of relevant quantities in different \ensuremathφ⁴ models, such as the anharmonic oscillator energy levels and the critical Bose-Einstein condensation temperature shift \ensuremathΔT_c recently investigated by various authors. Our present estimates of \ensuremathΔT_c, incorporating the most recently available six and seven loop perturbative information, are in excellent agreement with all the available lattice numerical simulations. This represents a very substantial improvement over previous treatments.

Citations

• Critical exponents from seven-loop strong-couplingφ4theory in three dimensions
• Higher-order evaluation of the critical temperature for interacting homogeneous dilute Bose gases
• BEC Transition Temperature of a Dilute Homogeneous Imperfect Bose Gas
• T_c for dilute Bose gases: Beyond leading order in 1/N
• Effective classical partition functions
• Asymptotically improved convergence of optimized perturbation theory in the Bose-Einstein condensation problem
• Convergence of the optimized δ expansion for the connected vacuum amplitude: Anharmonic oscillator
• Convergence of the optimized δ expansion for the connected vacuum amplitude: Zero dimensions
• Bose-Einstein condensation temperature of a homogeneous weakly interacting Bose gas in variational perturbation theory through six loops

Cited by

• Massive renormalization scheme and perturbation theory at finite temperature
• Asymptotically free theory with scale invariant thermodynamics