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DY: Dynamik und Statistische Physik

DY 13: Allgemeine Statistische Physik II

DY 13.5: Talk

Tuesday, March 18, 1997, 18:30–18:45, R4

Relations Between Markov Processes Via Local Time and Coordinate Transformations — •A. Pelster and H. Kleinert — Institut f"ur Theoretische Physik, Freie Universit"at Berlin, Arnimallee 14, D-14195 Berlin

The Duru-Kleinert method [1,2] of solving unknown path integrals of quantum mechanical systems by relating them to known ones does not apply to Markov processes since a Fokker-Planck equation is in general not transformed to a Fokker-Planck equation. In the letter [3] we present a significant modification of the method, based again on a combination of path-dependent time and coordinate transformations, to obtain such relations after all. As an application we express unknown Green functions for a one-parameter family of Markov processes in terms of the known one for the Schenzle-Brandt process.

[1] H. Kleinert, Path Integrals in Quantum Mechanics, Statistics and Polymer Physics, Second Edition, World Scientific (1995)

[2] A. Pelster, Zur Theorie und Anwendung nichtintegrabler Raum-Zeit-Transformationen in der klassischen Mechanik und in der Quantenmechanik, Dissertation, Universit"at Stuttgart, Shaker-Verlag Aachen (1996)

[3] A. Pelster, H. Kleinert, Phys. Rev. Lett., in press