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Eigenvalues for the extremely underdamped Brownian motion in an inclined periodic potential

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Zeitschrift für Physik B Condensed Matter

Abstract

The eigenvalues for the Brownian motion in a periodic potential with an additive constant force are investigated in the low friction limit. First the Fokker-Planck equation for the distribution function in velocity and position space is transformed to energy and position coordinates. By a proper averaging process over the position coordinate a differential equation for the distribution function depending on the energy only is obtained. Next the eigenvalues and eigenfunctions are calculated from this equation by a Runge-Kutta method. Finally the problem is formulated in terms of an integral equation from which the lowest non-zero eigenvalue is obtained analytically in the bistability region in the zero temperature limit.

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Authors and Affiliations

  1. Abteilung für Theoretische Physik der Universität Ulm, Oberer Eselsberg, D-7900, Ulm, Germany

    P. Jung & H. Risken

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  1. P. Jung
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  2. H. Risken
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Jung, P., Risken, H. Eigenvalues for the extremely underdamped Brownian motion in an inclined periodic potential. Z. Physik B - Condensed Matter 54, 357–370 (1984). https://doi.org/10.1007/BF01485833

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  • DOI: https://doi.org/10.1007/BF01485833

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