The existence of Burnett coefficients in the periodic Lorentz gas

The linear super-Burnett coefficient gives corrections to the diffusion equ ation in the form of higher derivatives of the density. Like the diffusion coefficient, it can be expressed in terms of integrals of correlation funct ions, but involving four different times. The power-law decay of correlatio ns in real gases (with many moving particles) and the random Lorentz gas (w ith one moving particle and fixed scatterers) are expected to cause the sup er-Burnett coefficient to diverge in most cases. Here, we show that the exp ression for the super-Burnett coefficient of the periodic Lorentz gas conve rges as a result of exponential decay of correlations and a nontrivial canc ellation of divergent contributions. (C) 2000 Elsevier Science B.V. All rig hts reserved.