Spectral Theory of the Thermal Hamiltonian

In 1964 J. M. Luttinger introduced a model for the quantum thermal transport. In this paper we study the spectral theory of the Hamiltonian operator associated with the Luttinger's model, with a special focus at the one-dimensional case. It is shown that the so-called thermal Hamiltonian has a one-parameter family of self-adjoint extensions and the spectrum, the time-propagator group and the Green function are explicitly computed. We also describe some results about the perturbation by potential and the related scattering theory. We will finish with some hints to the classic problem and the comparison between classical and quantum behavior.
Joint work with: Vicente Lenz (Delft University of Technology).