Subharmonic Resonance Behavior for the Classical Hydrogen Atomic System

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.

[1]  P. Koch,et al.  The importance of resonances in microwave “ionization” of excited hydrogen atoms , 1995 .

[2]  R. Ibrahim.  Book Reviews : Nonlinear Oscillations: A.H. Nayfeh and D.T. Mook John Wiley & Sons, New York, New York 1979, $38.50 , 1981 .

[3]  William H. Press,et al.  Numerical Recipes 3rd Edition: The Art of Scientific Computing , 2007 .

[4]  Yi Zou,et al.  Simulation Study of Aspects of the Classical Hydrogen Atom Interacting with Electromagnetic Radiation: Elliptical Orbits , 2004, J. Sci. Comput..

[5]  鈴木 増雄.  A. H. Nayfeh and D. T. Mook: Nonlinear Oscillations, John Wiley, New York and Chichester, 1979, xiv+704ページ, 23.5×16.5cm, 10,150円. , 1980 .

[6]  Akhlesh Lakhtakia,et al.  Essays on the formal aspects of electromagnetic theory , 1993 .

[7]  Daniel C. Cole,et al.  The quantum dice: An introduction to stochastic electrodynamics , 1996 .

[8]  Yi Zou,et al.  Simulation Study of Aspects of the Classical Hydrogen Atom Interacting with Electromagnetic Radiation: Circular Orbits , 2004, J. Sci. Comput..

[9]  Daniel C. Cole,et al.  Quantum mechanical ground state of hydrogen obtained from classical electrodynamics , 2003, quant-ph/0307154.

[10]  Yi Zou,et al.  Perturbation Analysis and Simulation Study of the Effects of Phase on the Classical Hydrogen Atom Interacting with Circularly Polarized Electromagnetic Radiation , 2004, J. Sci. Comput..

[11]  T. Gallagher,et al.  Classical subharmonic resonances in microwave ionization of lithium Rydberg atoms , 2000 .

[12]  C. Teitelboim,et al.  Classical electrodynamics of retarded fields and point particles , 1980 .

[13]  T. Gallagher,et al.  Microwave Manipulation of an Atomic Electron in a Classical Orbit , 2005, Science.

[14]  D. Cole.  REVIEWING AND EXTENDING SOME RECENT WORK ON STOCHASTIC ELECTRODYNAMICS , 1993 .

[15]  Cole.  Derivation of the classical electromagnetic zero-point radiation spectrum via a classical thermodynamic operation involving van der Waals forces. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[16]  D. Cole,et al.  Analysis of orbital decay time for the classical hydrogen atom interacting with circularly polarized electromagnetic radiation. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  T. H. Boyer,et al.  Random electrodynamics: The theory of classical electrodynamics with classical electromagnetic zero-point radiation , 1975 .

[18]  Luis de la Peña,et al.  The quantum dice : an introduction to stochastic electrodynamics , 1996 .

[19]  Cole.  Reinvestigation of the thermodynamics of blackbody radiation via classical physics. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[20]  W. Press,et al.  Numerical Recipes: The Art of Scientific Computing , 1987 .