Spontaneous decay of level from spectral theory point of view

• Autorzy: Ianovich Eduard

Identyfikatory

DOI

10.7494/OpMath.2021.41.6.849

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

spectral theory; quantum field theory; self-adjoint operators; absolutely continuous spectrum; spontaneous decay

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2021
• Tom: Vol. 41, no. 6
• Strony: 849--–859
• Opis fizyczny: BIbliogr. 7 poz.

Twórcy

autor

Ianovich Eduard

• Saint Petersburg, Russia

Bibliografia

• [1] A.I. Akhiezer, V.B. Berestetskiy, Quantum Field Theory, Nauka, Moscow, 1969 [in Russian].
• [2] P.A.M. Dirac, Lectures on Quantum Field Theory, Belfer Graduate School of Science, Academic Press, New York, 1966.
• [3] R.P. Feynman, Quantum Electrodynamics, W.A. Benjamin, Inc., New York, 1961.
• [4] V.A. Fock, A.V. Tulub, Application of Laplace transformation to the problems of radiation theory, Vestnik of Leningrad State University, Physics and Chemistry Series 3 (1965), no. 16, p. 7 [in Russian].
• [5] W. Heitler, The Quantum Theory of Radiation, Clarendon Press, Oxford, 1954.
• [6] E.A. Ianovich, Approximation of “fixed field” in the problem of interaction of excited atom with quantized electromagnetic field in free space, preprint, 2018 [in Russian].
• [7] B.S. Pavlov, S.V. Petras, The singular spectrum of a weakly perturbed multiplication operator, Funct. Anal. Appl. 4 (1970), no. 2, 136-142.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).