 00115 C. P. Dettmann
 The Burnett expansion of the periodic Lorentz gas
(25K, latex)
Mar 15, 00

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Abstract. The macroscopic limit of some deterministic scattering processes can be
described by the diffusion equation partial_t rho = D nabla^2 rho,
where the diffusion coefficient D is given by a sum over twotime
correlation functions, the discrete time version of the GreenKubo integral
over the velocity autocorrelation function. The approximation can be
improved by
allowing higher spatial derivatives; in this case the coefficients are
called Burnett coefficients, and are given by sums over
multiple time correlation functions. The periodic Lorentz gas has exponential
decay of twotime correlation functions, implying the existence of the
diffusion coefficient.
Recent work has established a stretched exponential decay of multiple
correlation functions and the existence of the fourth order Burnett coefficient
for the periodic Lorentz gas. Here we give expressions for the higher
coefficients, show that these expressions converge, and give a plausible
argument based on similar models that the expansion composed of the Burnett
coefficients has a finite radius of convergence.
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