Geodesic
Feynman-Kac Equations for Random Walks in Disordered Media
V. P. Shkilev1
1 Chuiko Institute of Surface Chemistry National Academy of Sciences of Ukraine 17, General Naumov Str., 03164 Kiev, Ukraine
Mathematical modelling of natural phenomena, Tome 11 (2016) no. 3, pp. 63-75.

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The problem of finding the distribution of functional of a trajectory of a particle executing a random walk in a disordered medium containing both traps and obstacles is considered. As a model of disordered medium, the Schirmacher model, a combination of random barriers model and multiple-trapping model, is used. Forward and backward Feynman-Kac equations with the boundary conditions at discontinuity points are formulated. As an example, the distribution of the residence time in a half-space is obtained. It is shown that the anomalous subdiffusion due to traps and that due to obstacles give very different distributions.
DOI : 10.1051/mmnp/201611305

V. P. Shkilev 1

1 Chuiko Institute of Surface Chemistry National Academy of Sciences of Ukraine 17, General Naumov Str., 03164 Kiev, Ukraine 
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V. P. Shkilev. Feynman-Kac Equations for Random Walks in Disordered Media. Mathematical modelling of natural phenomena, Tome 11 (2016) no. 3, pp. 63-75. doi : 10.1051/mmnp/201611305. https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/201611305/

[1] N. Agmon J. Chem. Phys. 1984 3644 3647

[2] A. Bar-Haim, J. Klafter J. Chem. Phys. 1998 5187 5193

[3] A. Cairoli, A. Baule. Anomalous processes with general waiting times: functionals and multi-point structures arXiv:1411.7005[cond-mat.stat-mech].

[4] S. Carmi, L. Turgeman, E. Barkai J. Stat. Phys. 2010 1071 1092

[5] G. Foltin, K. Oerding, Z. Racz, R.L. Workman, R.P.K. Zia Phys. Rev. E 1994 R639

[6] A.H. Gandjbakhche, G.H. Weiss Phys. Rev. E 2000 6958 6970

[7] K. Godzik, W. Schirmacher J. de Phys. (Paris) 1981 127 131

[8] D.S. Grebenkov Phys. Rev. E 2007 041139

[9] D.S. Grebenkov Rev. Mod. Phys. 2007 1077 1137

[10] R.L. Jack, P. Sollich. Duality symmetries and effective dynamics in disordered hopping models J. Stat. Mech.: Theory and Experiment (2009), P11011.

[11] M. Kac Trans. Am. Math. Soc. 1949 1 13

[12] V.M. Kenkre, Z. Kalay, P.E. Parris Phys. Rev. E 2009 011114

[13] S.N. Majumdar, A. Comtet Phys. Rev. Lett. 2002 060601

[14] S.N. Majumdar Curr. Sci. 2005 2076

[15] B. Movaghar, M. Grunewald, B. Pohlmann J. Stat. Phys. 1983 315 334

[16] O. Ovaskainen, S.J. Cornell J. Appl. Prob. 2003 557 580

[17] S. Sabhapandit, S.N. Majumdar, A. Comtet Phys. Rev. E 2006 051102

[18] W. Schirmacher Sol. State Comm. 1981 893 897

[19] V.P. Shkilev J. Exp. Theor. Phys. 2012 172 181

[20] V.P. Shkilev J. Exp. Theor. Phys. 2013 703 710

[21] V.P. Shkilev J. Exp. Theor. Phys. 2013 1066 1070

[22] L. Turgeman, S. Carmi, E. Barkai Phys. Rev. Lett. 2009 190201

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