Ericson fluctuations constitute one of the most characteristic features of quantum chaotic scattering in the regime of strongly overlapping resonances such as a compound nucleus.[1][2][3] These fluctuations were predicted in 1960 by Torleif Ericson in two seminal articles,[4][5][6][7] further developed in 1963,[8] based on the same statistical assumptions as those used by E. Wigner, C. E. Porter and R. G. Thomas to describe generic properties of resonances in long-lived compound nuclear systems.[9][10][11] In the present case the fluctuations occur in the "continuum" regime for which a large number of such resonances overlap coherently, owing to the short lifetime of the compound nucleus. At the time it was believed that this would lead to a structure-less behavior. Ericson realized that the opposite was the case with strong, random fluctuations.[12][7]

The Ericson fluctuations were first observed in 1964 by P. Von Brentano et al.[13] in nuclear physics giving rise to a vigorous theoretical and experimental programme.[3] They have the curious feature of being both reproducible and random at the same time.[14] The fluctuations are universal and have later been observed in many other areas such as photoionization of hydrogen, uni-molecular dissociation (physical chemistry),[15] perturbed atomic and molecular systems and micro wave billiards.[3][16][17]

Present theoretical descriptions of chaotic quantum scattering confirm the predicted properties of the Ericson fluctuations.[9] The universality of the Ericson fluctuations are thus very well established.[3]

References

  1. ↑ Borisenko, Victor E.; Ossicini, Stefano (2013). What is What in the Nanoworld: A Handbook on Nanoscience and Nanotechnology. John Wiley & Sons. ISBN 978-3-527-64838-2.
  2. ↑ ""Compound-nucleus model". Encyclopedia Britannica". www.britannica.com. Retrieved 2021-11-16.
  3. 1 2 3 4 Mitchell, G. E.; Richter, A.; Weidenmüller, H. A. (2010). "Random matrices and chaos in nuclear physics: Nuclear reactions". Reviews of Modern Physics. 82 (4): 2845–2901. arXiv:1001.2422. Bibcode:2010RvMP...82.2845M. doi:10.1103/RevModPhys.82.2845. ISSN 0034-6861. S2CID 118607709.
  4. ↑ Ericson, Torleif (1960). "Fluctuations of Nuclear Cross Sections in the "Continuum" Region". Physical Review Letters. 5 (9): 430–431. Bibcode:1960PhRvL...5..430E. doi:10.1103/PhysRevLett.5.430. ISSN 0031-9007.
  5. ↑ Stroke, H. Henry (1999). The Physical Review: The first hundred years. Springer Science & Business Media. p. 249. ISBN 978-1-56396-188-5.
  6. ↑ Ericson, Torleif (1960). "The statistical model and nuclear level densities". Advances in Physics. 9 (36): 425–511. Bibcode:1960AdPhy...9..425E. doi:10.1080/00018736000101239. ISSN 0001-8732.
  7. 1 2 "This week's citation classic" (PDF). garfield.library.upenn.edu. Retrieved 2021-11-16.
  8. ↑ Ericson, Torleif (1963). "A theory of fluctuations in nuclear cross sections". Annals of Physics. 23 (3): 390–414. Bibcode:1963AnPhy..23..390E. doi:10.1016/0003-4916(63)90261-6.
  9. 1 2 Weidenmüller, H. A.; Mitchell, G. E. (2009). "Random matrices and chaos in nuclear physics: Nuclear structure". Reviews of Modern Physics. 81 (2): 539–589. arXiv:0807.1070. Bibcode:2009RvMP...81..539W. doi:10.1103/RevModPhys.81.539. ISSN 0034-6861. S2CID 16847809.
  10. ↑ Porter, C. E.; Thomas, R. G. (1956). "Fluctuations of Nuclear Reaction Widths". Physical Review. 104 (2): 483–491. Bibcode:1956PhRv..104..483P. doi:10.1103/PhysRev.104.483. ISSN 0031-899X.
  11. ↑ Ericson, T; Mayer-Kuckuk, T (1966). "Fluctuations in Nuclear Reactions". Annual Review of Nuclear Science. 16 (1): 183–206. Bibcode:1966ARNPS..16..183E. doi:10.1146/annurev.ns.16.120166.001151. ISSN 0066-4243. PMID 5334731.
  12. ↑ Blatt, John M.; Weisskopf, Victor F. (1979). Theoretical Nuclear Physics. New York, NY: Springer New York. doi:10.1007/978-1-4612-9959-2. ISBN 978-1-4612-9961-5.
  13. ↑ Von Brentano, P.; Ernst, J.; Häusser, O.; Mayer-Kuckuk, T.; Richter, A.; Von Witsch, W. (1964). "Statistical fluctuations in the cross sections of the reactions Cl35 (p, α)S32 and Cl37 (p, α)S34". Physics Letters. 9 (1): 48–51. Bibcode:1964PhL.....9...48V. doi:10.1016/0031-9163(64)90210-0. ISSN 0031-9163.
  14. ↑ Weidenmüller, Hans A. (1990). "Ericson fluctuations versus conductance fluctuations". Nuclear Physics A. 518 (1–2): 1–12. doi:10.1016/0375-9474(90)90531-P.
  15. ↑ Reid, Scott; Reisler, Hanna (1996). "Unimolecular Reaction of NO2: Overlapping Resonances, Fluctuations, and the Transition State". Journal of Chemical Physics. 100 (2): 474-487. doi:10.1021/jp952843w.
  16. ↑ Guhr, Thomas; Müller–Groeling, Axel; Weidenmüller, Hans A. (1998). "Random-matrix theories in quantum physics: common concepts". Physics Reports. 299 (4–6): 189–425. arXiv:cond-mat/9707301. Bibcode:1998PhR...299..189G. doi:10.1016/S0370-1573(97)00088-4. S2CID 119052579.
  17. ↑ Stöckmann, Hans-Jürgen (2010). "Microwave billiards and quantum chaos". Scholarpedia. 5 (10): 10243. Bibcode:2010SchpJ...510243S. doi:10.4249/scholarpedia.10243. ISSN 1941-6016.{{cite journal}}: CS1 maint: date and year (link)
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