## Abstract

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 language | English |
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Article number | 106 |

Number of pages | 23 |

Journal | Letters in Mathematical Physics |

Volume | 111 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2021 |

## Keywords

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