The role of pseudo-eigenvalues of the Boltzmann collision operator in thermalization problems

Abstract

The calculation of the eigenvalues of the hard sphere Boltzmann collision operator using discrete matrix methods yields discrete eigenvalues, a large fraction of which are unconverged and lie in the continuum spectrum of the operator. The role of these pseudo-eigenvalues is examined. The results strongly suggest that for practical calculations the rigorous treatment of the continuum is not necessary provided that a moderately large number of pseudo-eigenvalues are included.