title: Fractional Feynman-Kac equation for non-brownian functionals.
abstract: 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.
authors.affiliation: Department of Physics, Bar Ilan University, Ramat-Gan 52900 Israel.
authors.forename: Lior
authors.initials: L
authors.lastname: Turgeman
authors.forename: Shai
authors.initials: S
authors.lastname: Carmi
authors.forename: Eli
authors.initials: E
authors.lastname: Barkai