Abstract
Point scatterers are placed on the real line such that the distances between scatterers are independent identically distributed random variables (stationary renewal process). For a fixed configuration of scatterers a particle performs the following random walk: The particle starts at the pointx with velocityυ, ¦υ¦=1. In between scatterers the particle moves freely. At a scatterer the particle is either transmitted or reflected, both with probability 1/2. For given initial conditions of the particle the velocity autocorrelation function is a random variable on the scatterer configurations. If this variable is averaged over the distribution of scatterers, it decays not faster thant −3/2.
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Work supported in part by Petroleum Research Fund Grant 8429-AC6.
Work supported in part by a Heisenberg fellowship of the Deutsche Forschungs-gemeinschaft.
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Beijeren, H.v., Spohn, H. Transport properties of the one-dimensional stochastic Lorentz model: I. Velocity autocorrelation function. J Stat Phys 31, 231–254 (1983). https://doi.org/10.1007/BF01011581
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DOI: https://doi.org/10.1007/BF01011581