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Simple dynamical system with discrete bound states

De Luca J1

  • 1Departamento de Fisica, Universidade Federal de Sao Carlos, Rodovia Washington Luiz, km 235, Caixa Postal 676, Sao Carlos, Sao Paulo 13565-905, Brazil.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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We numerically investigated a two-electron atom model with Darwin interaction, revealing scale-dependent stability. Stable nonionizing orbits emerge only at specific resonant energies within the quantum atomic range.

Area of Science:

  • Atomic Physics
  • Quantum Electrodynamics
  • Computational Physics

Background:

  • Studying the two-electron atom provides insights into complex atomic systems.
  • Coulomb dynamics exhibit unique chaotic behavior and scale-invariance symmetry.
  • Relativistic corrections, like the Darwin interaction, introduce scale-dependent effects.

Purpose of the Study:

  • To investigate the scale-dependent effects of relativistic electrodynamics in a two-electron atom model.
  • To explore the interplay between chaotic dynamics and relativistic corrections.
  • To identify conditions for stable nonionizing orbits in this system.

Main Methods:

  • Numerical simulations of the two-electron atom dynamical system.
  • Incorporation of the Darwin interaction as a relativistic perturbation.

Related Experiment Videos

  • Analysis of phase space, orbit stability, and scale-invariance properties.

    • Main Results:

    • The combination of chaotic dynamics and Darwin interaction leads to scale-dependent stability.
    • Stable nonionizing orbits were found to exist only at a discrete set of resonant energies.
    • Fourier transforms of these orbits revealed sharp frequency spectra.

    Conclusions:

    • Scale-dependent stability is a key phenomenon arising from relativistic corrections in atomic systems.
    • The identified resonant energies and frequencies are relevant to the quantum atomic range.
    • Numerical findings provide evidence for the existence of stable orbits under specific relativistic conditions.