00-115 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 two-time correlation functions, the discrete time version of the Green-Kubo 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 two-time 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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