The continued fraction representation of the evolution matrix for the Lorentz gas with planar symmetry in k-space (Q1118779)

The solution of the Fourier-Laplace transform of the Boltzmann equation for the Lorentz gas in infinite three-dimensional space and in absence of external forces is studied. Assuming that the Fourier transform of the initial distribution function depends on the wave vector k, the modulus of the velocity v and the cosinus of the angle between them, the Fourier- Laplace transform of the distribution is expanded into a series of Legendre functions. The coefficients of this series are calculated using the Mori-Zwanzig projection method. An approximate method of calculating these coefficients is discussed.