Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T13:43:43.115Z Has data issue: false hasContentIssue false
  • English
  • Français

The evolution and measurement of a population of pairs

Part of: Markov processes Optics, electromagnetic theory - General

Published online by Cambridge University Press:  14 July 2016

Eric Jakeman ,
Sean Phayre  and
Eric Renshaw
Eric Jakeman*
Affiliation:
Defence Research Agency, Malvern
Sean Phayre*
Affiliation:
University of Strathclyde
Eric Renshaw*
Affiliation:
University of Strathclyde
*
∗Postal address: Defence Research Agency, Malvern, Worcs WR14 3PS, UK.
∗∗Postal address: Department of Statistics and Modelling Science, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, UK.
∗∗Postal address: Department of Statistics and Modelling Science, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, UK.
Get access Rights & Permissions [Opens in a new window]

Abstract

The statistical properties of a population of immigrant pairs of individuals subject to loss through emigration are calculated. Exact analytical results are obtained which exhibit characteristic even–odd effects. The population is monitored externally by counting the number of emigrants leaving in a fixed time interval. The integrated statistics for this process are evaluated and it is shown that under certain conditions only even numbers of individuals will be observed.

Keywords

COUNTING PROCESSDEATHEMIGRATIONEVEN–ODD EFFECTSPHOTON PAIRSQUANTUM OPTICSSUPER/SUB-POISSONIANTELEGRAPH WAVEWAITING TIMES

MSC classification

Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 78A10: Physical optics
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 4 , December 1995 , pp. 1048 - 1062
Copyright
Copyright © Applied Probability Trust 1995 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Bedard, G. (1966) Photon counting statistics of Gaussian light. Phys. Rev. 151, 1038–1039.Google Scholar
[2] Burnham, D. C. and Weinberg, D. L. (1970) Observation of simultaneity in parametric production of optical photon pairs. Phys. Rev. Lett. 25, 84–87.Google Scholar
[3] Cox, D. R. and Lewis, P. A. W. (1966) The Statistical Analysis of Series of Events. Methuen, London.Google Scholar
[4] Erdélyi, A. (1953) Higher Transcendental Functions, Vol. II. McGraw-Hill, New York.Google Scholar
[5] Ghielmetti, F. (1976) Some comments on the relation between photo-electron and photon statistics and on the scaling properties of laser light. Nuovo Cimento B35, 243–247.Google Scholar
[6] Jakeman, E. (1990) Generation, detection and applications of sub-Poissonian light. In Coherence and Quantum Optics VI, ed. Eberly, V. H., Mandel, L. and Wolf, E., Plenum Press, New York.Google Scholar
[7] Jakeman, E. (1990) Statistics of binomial number fluctuations. J. Phys. A23, 2815–2825.Google Scholar
[8] Jakeman, E. and Renshaw, E. (1987) Correlated random walk model for scattering. J. Opt. Soc. Amer. A4, 1206–1212.Google Scholar
[9] Jakeman, E. and Shepherd, T. J. (1984) Population statistics and the counting process. J. Phys. A17, L745–L750.Google Scholar
[10] Loudon, R. and Knight, P. L. (1987) Squeezed light. J. Mod. Opt. 34, 709–759.Google Scholar
[11] Mandel, L. (1959) Fluctuations of photon beams: the distribution of the photo-electrons. Proc. Phys. Soc. 74, 233–243.Google Scholar
[12] Middleton, D. (1960) Statistical Communication Theory. McGraw-Hill, New York.Google Scholar
[13] Paul, H. (1982) Photon antibunching. Rev. Mod. Phys. 54, 1061–1102.Google Scholar
[14] Renshaw, E. (1988) The high-order autocovariance structure of the telegraph wave. J. Appl. Prob. 25, 744–751.Google Scholar
[15] Saleh, B. E. A. (1978) Photoelectron Statistics. Springer-Verlag, Berlin.Google Scholar
[16] Shepherd, T. J. (1984) Photoelectron counting — semiclassical and population monitoring approaches. Optica Acta 31, 1399–1407.Google Scholar
[17] Shepherd, T. J. and Jakeman, E. (1987) Statistical analysis of an incoherently coupled, steady-state optical amplifier. J. Opt. Soc. Amer. B4, 1860–1869.Google Scholar
[18] Shimoda, K., Takahasi, H. and Townes, C. H. (1957) Fluctuations in amplification of quanta with application to maser amplifiers. J. Phys. Soc. Jap. 12, 686–700.Google Scholar
[19] Srinivasan, S. K. (1988) Point Process Models of Cavity Radiation and Detection. Oxford University Press.Google Scholar
[20] Teich, M. C. and Saleh, B. E. A. (1989) Squeezed states of light. Quant. Opt. 1, 153–191.Google Scholar
[21] Walls, D. F. (1983) Squeezed states of light. Nature 306, 141–148.Google Scholar