Berlin 2008 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 29: Poster II
DY 29.16: Poster
Donnerstag, 28. Februar 2008, 16:00–18:00, Poster C
Path Integrals Without Integrals — •Antun Balaž1, Aleksandar Bogojević1, Ivana Vidanović1, and Axel Pelster2 — 1Scientific Computing Laboratory, Institute of Physics Belgrade, Pregrevica 118, 11080 Belgrade, Serbia — 2Fachbereich Physik, Universität Duisburg-Essen, Lotharstraße 1, 47048 Duisburg, Germany
Studying the relationship between path integral discretizations of different coarseness, a hierarchy of discretized effective actions was recently derived, which yields an improved (β/N)p convergence of discretized transition amplitudes to the continuum limit up to p=12 [1,2]. In this contribution we present a simpler procedure for obtaining these results through the derivation and solution of a set of recursive relations, and determine the effective actions even up to order p=25. Higher values of p make it possible to have higher precision results even for small values of N. Ultimately, for short propagation times β<1 it is possible to set N=1 and obtain closed analytic expressions for path integrals of a generic quantum-mechanical theory. We verify the obtained formula by comparison with perturbative expansion, loop expansion, and exact Monte Carlo simulations for the case of an anharmonic oscillator with quartic coupling. Finally, we discuss the numerical and analytical use of the obtained effective actions for long propagation times β>1.
[1] A. Bogojevic, A. Balaz, and A. Belic, Phys. Rev. Lett. 94, 180403 (2005)
[2] A. Bogojevic, A. Balaz, and A. Belic, Phys. Lett. A 344, 84 (2005)