The spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space

The singular continuous spectrum of the Liouville operator of quantum stati stical physics is, in general, properly included in the difference of the s pectral values of the singular continuous spectrum of the associated Hamilt onian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying state s of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian. (C) 1 999 American Institute of Physics. [S0022-2488(99)00208-X].