On the spectrum of the Rayleigh piston

We make a rigorous study of the spectrum of the Rayleigh piston. Our main results are that one is dealing with a trace-class perturbation for all values of the mass ratio y between test particles and heat bath particles and that apart from the ground state the discrete spectrum is empty for y sufficiently near 1. We also show that the so-called Lorentz limit ( ) is mathematically well defined and derive a qualitative statement on the discrete spectrum of the scattering operator for 1.