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Session S30 - Mathematical Methods in Quantum Mechanics

Friday, July 16, 17:15 ~ 17:40 UTC-3

Spectral Theory of the Thermal Hamiltonian

Giuseppe De Nittis

Pontificia Universidad Católica de Chile, Chile   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

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 to 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 result about the perturbation by potential and the related scattering theory. We will finish with some hints to the classic problem (which is completely solved) and the comparison between classical and quantum behavior.

Joint work with Vicente Lenz (Delft University of Technology).

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