High-Order Variational Perturbation Theory for the Free Energy

Details High-Order Variational Perturbation Theory for the Free Energy High-Order Variational Perturbation Theory for the Free Energy

2002-03-04

arxiv.org/abs/quant-ph/0203014v3

Phys. Rev. E 66, 036129 (2002)

Physics

Quantum Physics

11 pages, 6 figures; Phys. Rev. E (in press)

Scientific paper

10.1103/PhysRevE.66.036129

In this paper we introduce a generalization to the algebraic Bender-Wu recursion relation for the eigenvalues and the eigenfunctions of the anharmonic oscillator. We extend this well known formalism to the time-dependent quantum statistical Schroedinger equation, thus obtaining the imaginary-time evolution amplitude by solving a recursive set of ordinary differential equations. This approach enables us to evaluate global and local quantum statistical quantities of the anharmonic oscillator to much higher orders than by evaluating Feynman diagrams. We probe our perturbative results by deriving a perturbative expression for the free energy which is then subject to variational perturbation theory as developed by Kleinert, yielding convergent results for the free energy for all values of the coupling strength.

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