Perturbation Theory for the Thermal Hamiltonian: 1D Case

Giuseppe De Nittis*, Vicente Lenz

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review


This work continues the study of the thermal Hamiltonian, initially proposed by J. M. Luttinger in 1964 as a model for the conduction of thermal currents in solids. The previous work (De Nittis and Lenz in Spectral theory of the thermal Hamiltonian, 1D case, 2020) contains a complete study of the “free” model in one spatial dimension along with a preliminary scattering result for convolution-type perturbations. This work complements the results obtained in De Nittis and Lenz (2020) by providing a detailed analysis of the perturbation theory for the one-dimensional thermal Hamiltonian. In more detail, the following results are established: the regularity and decay properties for elements in the domain of the unperturbed thermal Hamiltonian; the determination of a class of self-adjoint and relatively compact perturbations of the thermal Hamiltonian; the proof of the existence and completeness of wave operators for a subclass of such potentials.

Original languageEnglish
Article number106
Number of pages23
JournalLetters in Mathematical Physics
Issue number4
Publication statusPublished - 2021


  • Scattering theory
  • Self-adjoint extensions
  • Spectral theory
  • Thermal Hamiltonian


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