Relations Between Markov Processes Via Local Time and Coordinate Transformations

Details Relations Between Markov Processes Via Local Time and Coordinate Transformations Relations Between Markov Processes Via Local Time and Coordinate Transformations

1996-08-26

arxiv.org/abs/cond-mat/9608120v2

Physics

Condensed Matter

Final version to appear in Phys. Rev. Letters. Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.h

Scientific paper

10.1103/PhysRevLett.78.565

The Duru-Kleinert (DK) method of solving unknown path integrals of quantum mechanical systems by relating them to known ones does not apply to Markov processes since the DK-transform of a Fokker-Planck equation is in general not a Fokker-Planck equation. In this note, 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.

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