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On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case

A lattice model of radiative decay (so-called spin-boson model) of a two level atom and at most two photons is considered. The location of the essential spectrum is described. For any coupling constant, the finiteness of the number of eigenvalues below the bottom of its essential spectrum is proved....

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Main Authors: Muminov, M., Neidhardt, H., Rasulov, T.
Format: Article
Published: American Institute of Physics 2014
Subjects:
QC Physics
Online Access:http://eprints.utm.my/id/eprint/58686/
http://dx.doi.org/10.1063/1.4921169
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spelling my.utm.586862022-04-24T05:00:36Z http://eprints.utm.my/id/eprint/58686/ On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case Muminov, M. Neidhardt, H. Rasulov, T. QC Physics A lattice model of radiative decay (so-called spin-boson model) of a two level atom and at most two photons is considered. The location of the essential spectrum is described. For any coupling constant, the finiteness of the number of eigenvalues below the bottom of its essential spectrum is proved. The results are obtained by considering a more general model H for which the lower bound of its essential spectrum is estimated. Conditions which guarantee the finiteness of the number of eigenvalues of H below the bottom of its essential spectrum are found. It is shown that the discrete spectrum might be infinite if the parameter functions are chosen in a special form. American Institute of Physics 2014-10 Article PeerReviewed Muminov, M. and Neidhardt, H. and Rasulov, T. (2014) On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case. Journal of Mathematical Physics, 56 (5). pp. 1-29. ISSN 0022-2461 http://dx.doi.org/10.1063/1.4921169 DOI: 10.1063/1.4921169
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
topic QC Physics
spellingShingle QC Physics
Muminov, M.
Neidhardt, H.
Rasulov, T.
On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case
description A lattice model of radiative decay (so-called spin-boson model) of a two level atom and at most two photons is considered. The location of the essential spectrum is described. For any coupling constant, the finiteness of the number of eigenvalues below the bottom of its essential spectrum is proved. The results are obtained by considering a more general model H for which the lower bound of its essential spectrum is estimated. Conditions which guarantee the finiteness of the number of eigenvalues of H below the bottom of its essential spectrum are found. It is shown that the discrete spectrum might be infinite if the parameter functions are chosen in a special form.
format Article
author Muminov, M.
Neidhardt, H.
Rasulov, T.
author_facet Muminov, M.
Neidhardt, H.
Rasulov, T.
author_sort Muminov, M.
title On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case
title_short On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case
title_full On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case
title_fullStr On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case
title_full_unstemmed On the spectrum of the lattice spin-boson Hamiltonian for any coupling: 1D case
title_sort on the spectrum of the lattice spin-boson hamiltonian for any coupling: 1d case
publisher American Institute of Physics
publishDate 2014
url http://eprints.utm.my/id/eprint/58686/
http://dx.doi.org/10.1063/1.4921169
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score 13.211869

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