Abstract
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 (γ → ∞) is mathematically well defined and derive a qualitative statement on the discrete spectrum of the scattering operator for γ ≫ 1.
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Driessler, W. On the spectrum of the Rayleigh piston. J Stat Phys 24, 595–606 (1981). https://doi.org/10.1007/BF01011377
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DOI: https://doi.org/10.1007/BF01011377