Spontaneous decay of level from spectral theory point of view

In quantum field theory it is believed that the spontaneous decay of excited atomic or molecular level is due to the interaction with continuum of field modes. Besides, the atom makes a transition from upper level to lower one so that the probability to find the atom in the excited state tends to ze...

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Autor principal:	Eduard Ianovich
Formato:	article
Lenguaje:	EN
Publicado:	AGH Univeristy of Science and Technology Press 2021
Materias:	spectral theory quantum field theory self-adjoint operators absolutely continuous spectrum spontaneous decay Applied mathematics. Quantitative methods T57-57.97
Acceso en línea:	https://doi.org/10.7494/OpMath.2021.41.6.849 https://doaj.org/article/bb139bce960e4e25894d44aef91130aa
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spelling	oai:doaj.org-article:bb139bce960e4e25894d44aef91130aa2021-11-29T22:51:48ZSpontaneous decay of level from spectral theory point of view1232-9274https://doi.org/10.7494/OpMath.2021.41.6.849https://doaj.org/article/bb139bce960e4e25894d44aef91130aa2021-11-01T00:00:00Zhttps://www.opuscula.agh.edu.pl/vol41/6/art/opuscula_math_4140.pdfhttps://doaj.org/toc/1232-9274In quantum field theory it is believed that the spontaneous decay of excited atomic or molecular level is due to the interaction with continuum of field modes. Besides, the atom makes a transition from upper level to lower one so that the probability to find the atom in the excited state tends to zero. In this paper it will be shown that the mathematical model in single-photon approximation may predict another behavior of this probability generally. Namely, the probability to find the atom in the excited state may tend to a nonzero constant so that the atom is not in the pure state finally. This effect is due to that the spectrum of the complete Hamiltonian is not purely absolutely continuous and has a discrete level outside the continuous part. Namely, we state that in the corresponding invariant subspace, determining the time evolution, the spectrum of the complete Hamiltonian when the field is considered in three dimensions may be not purely absolutely continuous and may have an eigenvalue. The appearance of eigenvalue has a threshold character. If the field is considered in two dimensions the spectrum always has an eigenvalue and the decay is absent.Eduard IanovichAGH Univeristy of Science and Technology Pressarticlespectral theoryquantum field theoryself-adjoint operatorsabsolutely continuous spectrumspontaneous decayApplied mathematics. Quantitative methodsT57-57.97ENOpuscula Mathematica, Vol 41, Iss 6, Pp 849-859 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	spectral theory quantum field theory self-adjoint operators absolutely continuous spectrum spontaneous decay Applied mathematics. Quantitative methods T57-57.97
spellingShingle	spectral theory quantum field theory self-adjoint operators absolutely continuous spectrum spontaneous decay Applied mathematics. Quantitative methods T57-57.97 Eduard Ianovich Spontaneous decay of level from spectral theory point of view
description	In quantum field theory it is believed that the spontaneous decay of excited atomic or molecular level is due to the interaction with continuum of field modes. Besides, the atom makes a transition from upper level to lower one so that the probability to find the atom in the excited state tends to zero. In this paper it will be shown that the mathematical model in single-photon approximation may predict another behavior of this probability generally. Namely, the probability to find the atom in the excited state may tend to a nonzero constant so that the atom is not in the pure state finally. This effect is due to that the spectrum of the complete Hamiltonian is not purely absolutely continuous and has a discrete level outside the continuous part. Namely, we state that in the corresponding invariant subspace, determining the time evolution, the spectrum of the complete Hamiltonian when the field is considered in three dimensions may be not purely absolutely continuous and may have an eigenvalue. The appearance of eigenvalue has a threshold character. If the field is considered in two dimensions the spectrum always has an eigenvalue and the decay is absent.
format	article
author	Eduard Ianovich
author_facet	Eduard Ianovich
author_sort	Eduard Ianovich
title	Spontaneous decay of level from spectral theory point of view
title_short	Spontaneous decay of level from spectral theory point of view
title_full	Spontaneous decay of level from spectral theory point of view
title_fullStr	Spontaneous decay of level from spectral theory point of view
title_full_unstemmed	Spontaneous decay of level from spectral theory point of view
title_sort	spontaneous decay of level from spectral theory point of view
publisher	AGH Univeristy of Science and Technology Press
publishDate	2021
url	https://doi.org/10.7494/OpMath.2021.41.6.849 https://doaj.org/article/bb139bce960e4e25894d44aef91130aa
work_keys_str_mv	AT eduardianovich spontaneousdecayoflevelfromspectraltheorypointofview
_version_	1718406886784499712

Spontaneous decay of level from spectral theory point of view

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