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Path-integral formulation for Levy flights: Evaluation of the propagator for free, linear, and harmonic potentials in the over- and underdamped limits

Janakiraman, Deepika and Sebastian, KL (2012) Path-integral formulation for Levy flights: Evaluation of the propagator for free, linear, and harmonic potentials in the over- and underdamped limits. In: PHYSICAL REVIEW E, 86 (6, Par).

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Official URL: http://dx.doi.org/10.1103/PhysRevE.86.061105

Abstract

Levy flights can be described using a Fokker-Planck equation, which involves a fractional derivative operator in the position coordinate. Such an operator has its natural expression in the Fourier domain. Starting with this, we show that the solution of the equation can be written as a Hamiltonian path integral. Though this has been realized in the literature, the method has not found applications as the path integral appears difficult to evaluate. We show that a method in which one integrates over the position coordinates first, after which integration is performed over the momentum coordinates, can be used to evaluate several path integrals that are of interest. Using this, we evaluate the propagators for (a) free particle, (b) particle subjected to a linear potential, and (c) harmonic potential. In all the three cases, we have obtained results for both overdamped and underdamped cases. DOI: 10.1103/PhysRevE.86.061105

Item Type: Journal Article
Additional Information: Copyright for this article belongs to AMER PHYSICAL SOC, USA
Department/Centre: Division of Chemical Sciences > Inorganic & Physical Chemistry
Depositing User: Francis Jayakanth
Date Deposited: 02 Jan 2013 11:23
Last Modified: 02 Jan 2013 11:23
URI: http://eprints.iisc.ac.in/id/eprint/45573

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