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, Mukhiddin, Neidhardt, H., Rasulov, T.
Format:	Article
Published:	American Institute of Physics 2014
Subjects:	QC Physics
Online Access:	http://eprints.utm.my/id/eprint/59856/ http://dx.doi.org/10.1063/1.4921169
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Institution:	Universiti Teknologi Malaysia

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spelling	my.utm.598562022-04-24T05:01:16Z http://eprints.utm.my/id/eprint/59856/ On the spectrum of the lattice spin-boson hamiltonian for any coupling: 1d case Muminov, Mukhiddin 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, Mukhiddin 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, Mukhiddin 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, Mukhiddin Neidhardt, H. Rasulov, T.
author_facet	Muminov, Mukhiddin Neidhardt, H. Rasulov, T.
author_sort	Muminov, Mukhiddin
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/59856/ http://dx.doi.org/10.1063/1.4921169
_version_	1732945381530009600

On the spectrum of the lattice spin-boson hamiltonian for any coupling: 1d case

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