Spectral theory of the thermal Hamiltonian: 1D case

  • Giuseppe De Nittis

    Pontificia Universidad Católica de Chile, Santiago, Chile
  • Vicente Lenz

    TUDelft, Netherlands
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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 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. Moreover, the scattering by convolution-type potentials is analyzed. Finally, also the associated classical problem is completely solved, thus providing a comparison between classical and quantum behavior. This article aims to be a first contribution in the construction of a complete theory for the thermal Hamiltonian.

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Giuseppe De Nittis, Vicente Lenz, Spectral theory of the thermal Hamiltonian: 1D case. J. Spectr. Theory 11 (2021), no. 4, pp. 1415–1469

DOI 10.4171/JST/376