Fractional Feynman-Kac equation for non-brownian functionals

We derive backward and forward fractional Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing anomalous diffusion. Fractional substantial derivatives introduced by Friedrich and co-workers [Phys. Rev. Lett. 96, 230601 (2006)10.1103/PhysRevLett.96.230601] pr...

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Bibliographic Details
Published in:Physical review letters 2009-11, Vol.103 (19), p.190201-190201, Article 190201
Main Authors: Turgeman, Lior, Carmi, Shai, Barkai, Eli
Format: Article
Language:English
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Summary:We derive backward and forward fractional Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing anomalous diffusion. Fractional substantial derivatives introduced by Friedrich and co-workers [Phys. Rev. Lett. 96, 230601 (2006)10.1103/PhysRevLett.96.230601] provide the correct fractional framework for the problem. For applications, we calculate the distribution of occupation times in half space and show how the statistics of anomalous functionals is related to weak ergodicity breaking.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.103.190201