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Systematic Density Expansion of the Lyapunov Exponents for a Two-Dimensional Random Lorentz Gas

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Abstract

We study the Lyapunov exponents of a two-dimensional, random Lorentz gas at low density. The positive Lyapunov exponent may be obtained either by a direct analysis of the dynamics, or by the use of kinetic theory methods. To leading orders in the density of scatterers it is of the form A 0ñln ñ+B 0ñ, where A 0 and B 0 are known constants and ñ is the number density of scatterers expressed in dimensionless units. In this paper, we find that through order (ñ2), the positive Lyapunov exponent is of the form A 0ñln ñ+B 0ñ+A 1ñ2ln ñ +B 1ñ2. Explicit numerical values of the new constants A 1 and B 1 are obtained by means of a systematic analysis. This takes into account, up to O(ñ2), the effects of all possible trajectories in two versions of the model; in one version overlapping scatterer configurations are allowed and in the other they are not.

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Authors and Affiliations

  1. Institute for Theoretical Physics, University of Utrecht, Utrecht, TD, Postbus 80.195, 3508, The Netherlands

    H. V. Kruis, Debabrata Panja & Henk van Beijeren

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  1. H. V. Kruis
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  2. Debabrata Panja
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  3. Henk van Beijeren
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Kruis, H.V., Panja, D. & van Beijeren, H. Systematic Density Expansion of the Lyapunov Exponents for a Two-Dimensional Random Lorentz Gas. J Stat Phys 124, 823–842 (2006). https://doi.org/10.1007/s10955-005-9001-y

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  • DOI: https://doi.org/10.1007/s10955-005-9001-y

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