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Physics Letters A

Long-time deviations from exponential decay in atomic spontaneous emission theory

P. L. Knight, Peter W. Milonni

Published Apr 1, 1976• 79 citations
Publisher
DOI
10.1016/0375-9601(76)90306-6

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A mathematically rigorous treatment of the Weisskopf-Wigner model of atomic spontaneous emission is presented. For the first time to the authors' knowledge, it is shown that in the correct asymptotic treatment with a cutoff frequency at which the dipole approximation breaks down, the main contribution to the long-time deviation from the exponential decay is of the order of 1/(t ${\mathrm{ln}}^{2}$t). This contradicts the results of previous authors who have obtained a long-time behavior of the order of 1/${t}^{2}$ by nonrigorous mathematical treatment of the same model in the dipole approximation. However, we will show that the result 1/${t}^{2}$ can still be obtained if the retardation effects are taken into account, i.e., if no dipole approximation is made.

Physical Review A•Jul 1, 1988•49 citations
A mathematically rigorous treatment of the Weisskopf-Wigner model of atomic spontaneous emission is presented. For the first time to the authors' knowledge, it is shown that in the correct asymptotic treatment with a cutoff frequency at which the dipole approximation breaks down, the main contribution to the long-time deviation from the exponential decay is of the order of 1/(t ln2{\mathrm{ln}}^{2}ln2t). This contradicts the results of previous authors who have obtained a long-time behavior of the order of 1/t2{t}^{2}t2 by nonrigorous mathematical treatment of the same model in the dipole approximation. However, we will show that the result 1/t2{t}^{2}t2 can still be obtained if the retardation effects are taken into account, i.e., if no dipole approximation is made.