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Continued fraction solutions of discrete master equations not obeying detailed balance II

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Zeitschrift für Physik B Condensed Matter

Abstract

In this paper we continue to extend our previous investigation of continued fraction (CF) solutions for the stationary probability of discrete one-variable master equations which generally do not satisfy detailed balance. We derive explicit expressions, directly in terms of the elementary transition rates, for the continued fraction recursion coefficients. Further, we derive several approximate CF-solutions, i.e., we deduce non-systematic and systematic truncation error estimates. The method is applied to two master equations with two-particle jumps for which we derive the exact probability solution and make a comparison with approximate solutions. The investigation is also extended to the case of master equations with multiple birth and death transitions of maximal orderR.

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-7000, Stuttgart 80, Germany

    G. Haag

  2. Department of Chemistry, University of California, San Diego, 92093, La Jolla, California, USA

    P. Hänggi

Authors
  1. G. Haag
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  2. P. Hänggi
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Supported in part by Deutsche Forschungsgemeinschaft and by National Science Foundation Grant CHE78-21460

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Haag, G., Hänggi, P. Continued fraction solutions of discrete master equations not obeying detailed balance II. Z. Physik B - Condensed Matter 39, 269–279 (1980). https://doi.org/10.1007/BF01292672

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  • DOI: https://doi.org/10.1007/BF01292672

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