Abstract
We present a comprehensive account of the special ‘Rayleigh piston’ model for the spatial and velocity relaxation of an ensemble of labelled test-particles in a one-dimensional heat-bath of particles with identical mass. This model, originally formulated by Rayleigh in 1891 but since largely neglected, is in effect a prototype for all later models in singular particle transport theory and serves to illustrate the mathematical problems associated with the occurrence of singular eigenfunctions and continuous spectra of a scattering operator. Although other idealized scattering models are known, the Rayleigh model remains a unique example of an exactly soluble singular system which, in including conservation laws and time-reversal symmetry in scattering, retains a degree of mechanical realism.
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