N. Chernov, C. Dettmann
The existence of Burnett coefficients in the periodic Lorentz gas
(24K, LATeX)
ABSTRACT. The linear super-Burnett coefficient gives
corrections to the diffusion equation in the form of higher
derivatives of the density. Like the diffusion coefficient, it
can be expressed in terms of integrals of correlation functions,
but involving four different times. The power law decay of
correlations in real gases (with many moving particles) and the
random Lorentz gas (with one moving particle and fixed scatterers)
are expected to cause the super-Burnett coefficient to diverge in
most cases. Here we show that the expression for the super-Burnett
coefficient of the periodic Lorentz gas converges as a result of
exponential decay of correlations and a nontrivial cancellation of
divergent contributions.