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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Fluctuations in radioactive decays. I. Nonequilibrium effects and noise

Roberto Boscaino, G. Concas, M. Lissia, S. Serci

Published Jan 1, 1994• 5 citations
Publisher

Abstract

Radioactive decay is a nonequilibrium process. For most practical purposes it can be modeled as a steady-state process, but there are instances where counting statistics should not be assumed constant; this remark is particularly relevant for long counting intervals. We give explicit formulas for the probability distribution of counts, the expected values of the mean, the variance, and the Allan variance. These formulas, rather than the Poissonian ones, should be used as benchmark for experiments aimed at revealing exotic effects. Formulas are compared to numerical simulations and actual experiments.

DOI
10.1103/physreve.49.333

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Radioactive decay is a nonequilibrium process. For most practical purposes it can be modeled as a steady-state process, but there are instances where counting statistics should not be assumed constant; this remark is particularly relevant for long counting intervals. We give explicit formulas for the probability distribution of counts, the expected values of the mean, the variance, and the Allan variance. These formulas, rather than the Poissonian ones, should be used as benchmark for experiments aimed at revealing exotic effects. Formulas are compared to numerical simulations and actual experiments.
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Exact photocounting distributions are obtained for a pulse of light whose intensity is exponentially decaying in time, when the underlying photon statistics are Poisson. It is assumed that the starting time for the sampling interval (which is of arbitrary duration) is uniformly distributed. The probability of registering n counts in the fixed time T is given in terms of the incomplete gamma function for n >/= 1 and in terms of the exponential integral for n = 0. Simple closed-form expressions are obtained for the count mean and variance. The results are expected to be of interest in certain studies involving spontaneous emission, radiation damage in solids, and nuclear counting. They will also be useful in neurobiology and psychophysics, since habituation and sensitization processes may sometimes be characterized by the same stochastic model.
The evolution of views on the possibility of external influence on the process of radioactive decay is briefly presented. Such an effect can lead to the appearance of periods in the time series of the radioactive decay rate fluctuations, which have been the subject of intensive study in the last decade. Two mechanisms for identifying periods are considered: the study of deviations from the theoretical curve of the radioactive decay law and the study of the properties of fluctuations. It is shown that the latter method leads to a universal spectrum of periods observed not only in the time series of the radioactive decay rate fluctuations, but also in the time series of fluctuations of processes of various nature. The main object of our study are periods in the radioactive decay rate fluctuations. The presence of such periods suggests the possibility of external influence on the process of radioactive decay. Therefore, we briefly consider the evolution of views on the possibility of such an effect. To do this, we distinguish several stages. The division into stages is only partially historical, but, mainly, each stage characterizes a certain ideas that is implemented in it.
We theoretically investigate the quantum statistical properties of a two-mode cavity light generated by a ∨ -type three-level atom interacting with nondegenerate subharmonic light and coupled to a two-mode squeezed vacuum reservoir. Using the master equation, we obtain steady-state expectation values for the atomic and cavity-mode operators. Based on these results, we analyze the global and local photon number variances, intensity fluctuation spectrum, joint photon number distribution, and photon count statistics. Our results reveal that squeezing parameter and subharmonic generation significantly enhance intensity fluctuations, as well as the mean and variance of photon counts, whereas atom-field coupling and cavity decay suppress them. The system exhibits super-Poissonian photon statistics, indicating that photon number fluctuations exceed the mean photon number. Furthermore, the photon count variance, which incorporates intracavity transmission and input noise, increases with detector efficiency. These results provide a comprehensive picture of photon statistics in atom-photon systems and guide the design of advanced quantum optical devices.