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Volume 37, Issue 2
Spectral Properties of an Energy-Dependent Hamiltonian

Huu-Tai Pierre Chau & Bernard Ducomet

DOI: 10.4208/cmr.2020-0040

Commun. Math. Res., 37 (2021), pp. 141-179.

Published online: 2021-04

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  • Abstract

We study spectral properties of a quantum Hamiltonian with a complex-valued energy-dependent potential related to a model introduced in physics of nuclear reactions [30] and we prove that the principle of limiting absorption holds at any point of a large subset of the essential spectrum. When an additional dissipative or smallness hypothesis is assumed on the potential, we show that the principle of limiting absorption holds at any point of the essential spectrum.

  • Keywords

Non-self-adjoint, complex potential, dissipative, limiting absorption principle, spectral singularity, energy dependent potential.

  • AMS Subject Headings

35J10, 35P15, 35P35, 47A55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-37-141, author = {Pierre Chau , Huu-Tai and Ducomet , Bernard}, title = {Spectral Properties of an Energy-Dependent Hamiltonian}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {37}, number = {2}, pages = {141--179}, abstract = {

We study spectral properties of a quantum Hamiltonian with a complex-valued energy-dependent potential related to a model introduced in physics of nuclear reactions [30] and we prove that the principle of limiting absorption holds at any point of a large subset of the essential spectrum. When an additional dissipative or smallness hypothesis is assumed on the potential, we show that the principle of limiting absorption holds at any point of the essential spectrum.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2020-0040}, url = {http://global-sci.org/intro/article_detail/cmr/18736.html} }
TY - JOUR T1 - Spectral Properties of an Energy-Dependent Hamiltonian AU - Pierre Chau , Huu-Tai AU - Ducomet , Bernard JO - Communications in Mathematical Research VL - 2 SP - 141 EP - 179 PY - 2021 DA - 2021/04 SN - 37 DO - http://doi.org/10.4208/cmr.2020-0040 UR - https://global-sci.org/intro/article_detail/cmr/18736.html KW - Non-self-adjoint, complex potential, dissipative, limiting absorption principle, spectral singularity, energy dependent potential. AB -

We study spectral properties of a quantum Hamiltonian with a complex-valued energy-dependent potential related to a model introduced in physics of nuclear reactions [30] and we prove that the principle of limiting absorption holds at any point of a large subset of the essential spectrum. When an additional dissipative or smallness hypothesis is assumed on the potential, we show that the principle of limiting absorption holds at any point of the essential spectrum.

Pierre Chau Huu-Tai & Bernard Ducomet. (2021). Spectral Properties of an Energy-Dependent Hamiltonian. Communications in Mathematical Research . 37 (2). 141-179. doi:10.4208/cmr.2020-0040
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