Long-time tails in lattice Lorentz gases |
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Authors: | M H Ernst G A van Velzen |
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Institution: | (1) Institute for Theoretical Physics, 3508 TA Utrecht, The Netherlands |
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Abstract: | We consider a Lorentz gas on a square lattice with a fraction c of scattering sites. The collision laws are deterministic (fixed mirror model) or stochastic (with transmission, reflection, and deflection probabilities ,, and respectively). If all mirrors are parallel, the mirror model is exactly solvable. For the general case a self-consistent ring kinetic equation is used to calculate the longtime tails of the velocity correlation function (0) (t) and the tensor correlation Q(0)Q(t) withQ=
x
y
. Both functions showt
–2 tails, as opposed to the continuous Lorentz gas, where the tails are respectivelyt
–2 andt
–3. Inclusion of the self-consistent ring collisions increases the low-density coefficient of the tail in (0)(t) by 30–100% as compared to the simple ring collisions, depending on the model parameters. |
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Keywords: | Lorentz gas cellular automaton fluids diffusion velocity correlation function long-time tail |
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