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Subharmonic Resonance Behavior for the Classical Hydrogen Atomic System

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Abstract

Previously unexplored resonance conditions are shown to exist for the classical hydrogen atomic system, where the electron is treated as a classical charged point particle following the nonrelativistic Lorentz-Dirac equation of motion about a stationary nucleus of opposite charge. For circularly polarized (CP) light directed normal to the orbit, very pronounced subharmonic resonance behavior is shown to occur with a variety of interesting properties. In particular, only if the amplitude of the CP light exceeds a critical value, will the resonance continue without radius and energy decay. A perturbation analysis is carried out to illustrate the main features of the behavior. The present phenomena adds to a growing list of other nonlinear dynamical behaviors of this simple system, that may well be important for more deeply understanding classical and quantum connections.

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References

  1. Cole, D.C., Zou, Y.: Simulation study of aspects of the classical hydrogen atom interacting with electromagnetic radiation: Circular orbits. J. Sci. Comput. 20(1), 43–68 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. Cole, D.C., Zou, Y.: Simulation study of aspects of the classical hydrogen atom interacting with electromagnetic radiation: Elliptical orbits. J. Sci. Comput. 20(3), 379–404 (2004). Preprint available at http://www.bu.edu/simulation/publications/dcole/publications.html

    Article  MATH  MathSciNet  Google Scholar 

  3. Cole, D.C., Zou, Y.: Perturbation analysis and simulation study of the effects of phase on the classical hydrogen atom interacting with circularly polarized electromagnetic radiation. J. Sci. Comput. 21(2), 145–172 (2004). Preprint available at http://www.bu.edu/simulation/publications/dcole/publications.html

    Article  MATH  MathSciNet  Google Scholar 

  4. Cole, D.C., Zou, Y.: Analysis of orbital decay time for the classical hydrogen atom interacting with circularly polarized electromagnetic radiation. Phys. Rev. E 69(1), 16601 (2004)

    Article  MathSciNet  Google Scholar 

  5. Cole, D.C., Zou, Y.: Quantum mechanical ground state of hydrogen obtained from classical electrodynamics. Phys. Lett. A 317(1–2), 14–20 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  6. de la Peña, L., Cetto, A.M.: The Quantum Dice—An Introduction to Stochastic Electrodynamics. Kluwer Academic, Dordrecht (1996)

    Google Scholar 

  7. Cole, D.C.: Reviewing and extending some recent work on stochastic electrodynamics. In: Lakhtakia, A. (ed.) Essays on the Formal Aspects of Electromagnetic Theory, pp. 501–532. World Scientific, Singapore (1993)

    Google Scholar 

  8. Noel, M.W., Griffith, W.M., Gallagher, T.F.: Classical subharmonic resonances in microwave ionization of lithium Rydberg atoms. Phys. Rev. A 62, 063401 (2000)

    Article  Google Scholar 

  9. Koch, P.M., van Leeuwen, K.A.H.: The importance of resonances in microwave “ionization” of excited hydrogen atoms. Phys. Rep. 255, 289–403 (1995)

    Article  Google Scholar 

  10. Maeda, H., Norum, D.V.L., Gallagher, T.F.: Microwave manipulation of an atomic electron in a classical orbit. Science 307, 1757–1760 (2005)

    Article  Google Scholar 

  11. Teitelboim, C., Villarroel, D., van Weert, Ch.G.: Classical electrodynamics of retarded fields and point particles. Riv. Nuovo Cim. 3(9), 1–64 (1980)

    Article  Google Scholar 

  12. Boyer, T.H.: Random electrodynamics: The theory of classical electrodynamics with classical electromagnetic zero–point radiation. Phys. Rev. D 11(4), 790–808 (1975)

    Article  Google Scholar 

  13. Cole, D.C.: Derivation of the classical electromagnetic zero–point radiation spectrum via a classical thermodynamic operation involving van der Waals forces. Phys. Rev. A 42, 1847–1862 (1990)

    Article  Google Scholar 

  14. Cole, D.C.: Reinvestigation of the thermodynamics of blackbody radiation via classical physics. Phys. Rev. A 45, 8471–8489 (1992)

    Article  Google Scholar 

  15. Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley, New York (1979)

    MATH  Google Scholar 

  16. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes: The Art of Scientific Computing, 3rd edn. Cambridge University Press, Cambridge (2007)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Dept. of Manufacturing Engineering, Boston University, 15 St. Mary’s Street, Brookline, MA, 02446, USA

    Daniel C. Cole

  2. One AMD Place, P.O. Box 3453, MS 78, Sunnyvale, CA, 94088-3453, USA

    Yi Zou

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  1. Daniel C. Cole
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  2. Yi Zou
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Correspondence to Daniel C. Cole.

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Cole, D.C., Zou, Y. Subharmonic Resonance Behavior for the Classical Hydrogen Atomic System. J Sci Comput 39, 1–27 (2009). https://doi.org/10.1007/s10915-008-9248-y

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  • DOI: https://doi.org/10.1007/s10915-008-9248-y

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