Geodesic
Lévy Transport in Slab Geometry of Inhomogeneous Media
A. Iomin1 ; T. Sandev2, 3
1 Department of Physics, Technion, Haifa 32000, Israel
2 Max Planck Institute for the Physics of Complex Systems Nöthnitzer Strasse 38, 01187 Dresden, Germany
3 Radiation Safety Directorate, Partizanski odredi 143, P.O. Box 22, 1020 Skopje, Macedonia
Mathematical modelling of natural phenomena, Tome 11 (2016) no. 3, pp. 51-62.

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We present a physical example, where a fractional (both in space and time) Schrödinger equation appears only as a formal effective description of diffusive wave transport in complex inhomogeneous media. This description is a result of the parabolic equation approximation that corresponds to the paraxial small angle approximation of the fractional Helmholtz equation. The obtained effective quantum dynamics is fractional in both space and time. As an example, Lévy flights in an infinite potential well are considered numerically. An analytical expression for the effective wave function of the quantum dynamics is obtained as well.
DOI : 10.1051/mmnp/201611304

A. Iomin 1 ; T. Sandev 2, 3

1 Department of Physics, Technion, Haifa 32000, Israel
2 Max Planck Institute for the Physics of Complex Systems Nöthnitzer Strasse 38, 01187 Dresden, Germany
3 Radiation Safety Directorate, Partizanski odredi 143, P.O. Box 22, 1020 Skopje, Macedonia 
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A. Iomin; T. Sandev. Lévy Transport in Slab Geometry of Inhomogeneous Media. Mathematical modelling of natural phenomena, Tome 11 (2016) no. 3, pp. 51-62. doi : 10.1051/mmnp/201611304. https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/201611304/

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