Abstract

Continuous time random walk (CTRW) is a model for subdiffusion [1]. Fractional Fokker planck (FFPE) is a well known description for systems modeled according to the CTRW [2]. We investigate statistical properties of the time average  for a particle undergoing CTRW. We use CTRW model in order to generalize Fractional Fokker Planck Equation (FFPE) to  include time average of position . We also consider functionals of the path of CTRW, we find an exact expression for the distribution of functionals for a wide class of random walks In Fourier-Laplace space. In the anomalous diffusion phase of the model we derive a real time fractional Schrödinger equation for the problem ,We solve this equation for the free particle case and for a particle under the influence of binding potential [3]. The results in the long time limit are in accordance with the main results of weak ergodicity breaking [4].

References

[1] E.W. Montroll, G.H. Weiss, J. Math. Phys. 6,167 (1965)

[2] E. Barkai ,R. Metzler, J. Klafter Phys. Rev. E 61,132 (2000)

[3]L. Turgeman, S .Carmi, E. Barkai, Phys. Rev. Lett (in press)

[4] A. Rebenshtok ,E. Barkai, Phys. Rev. Lett 99,210601(2007)