Advertisement

Chaos pp 137-156 | Cite as

Fermi Acceleration

Abstract

The so-called Fermi acceleration — the acceleration of a particle through collision with an oscillating wall — is one of the most famous model systems for understanding nonlinear Hamiltonian dynamics. The problem was introduced by Fermi [1] in connection with studies of the acceleration mechanism of cosmic particles through fluctuating magnetic fields. Similar mechanisms have been studied for accelerating cosmic rockets by planetary or stellar gravitational fields. One of the most interesting aspects of such models is the determination of criteria for stochastic (statistical) behavior, despite the strictly deterministic dynamics.

Keywords

Phase Space Rotation Number Mouse Button Wall Velocity Invariant Curf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    E. Fermi, On the origin of cosmic radiation, Phys. Rev. 75 (1949) 1169 see also Collected Works 2, 978zbMATHCrossRefADSGoogle Scholar
  2. 2.
    S. Ulam, On some statistical properties of dynamical systems, 4th Berkeley Symp. on Math. Stat. and Probabil. 3 (1961) 315MathSciNetADSGoogle Scholar
  3. 3.
    G. M. Zaslavskii and B. V. Chirikov, Fermi acceleration mechanism in the one-dimensional case, Sov. Phys. Dokl. 9 (1965) 989ADSGoogle Scholar
  4. 4.
    A. Brahic, Numerical study of a simple dynamical system, Astron. Astrophys. 12 (1971) 98ADSGoogle Scholar
  5. 5.
    A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion, Springer, New York, 1983zbMATHGoogle Scholar
  6. 6.
    M. A. Lieberman and A. J. Lichtenberg, Stochastic and adiabatic behaviour of particles accelerated by periodic forces, Phys. Rev. A 5 (1972) 1852CrossRefADSGoogle Scholar
  7. 7.
    A. J. Lichtenberg, M. A. Lieberman, and R. H. Cohen, Fermi acceleration revisited, Physica D 1 (1980) 291CrossRefMathSciNetADSzbMATHGoogle Scholar
  8. 8.
    J. E. Howard, A. J. Lichtenberg, and M. A. Lieberman, Two-frequency Fermi mapping, Physica D 5 (1982) 243CrossRefMathSciNetADSGoogle Scholar
  9. 9.
    A. B. Pippard, Response and Stability, Cambridge Press, Cambridge, 1985zbMATHGoogle Scholar
  10. 10.
    K. Briggs, Simple experiments in chaotic dynamics, Am. J. Phys. 55 (1987 1083CrossRefADSGoogle Scholar
  11. 11.
    N. M. Tufillaro and A. M. Albano, Chaotic dynamics of a bouncing ball, Am. J. Phys. 54 (1986) 939CrossRefADSGoogle Scholar
  12. 12.
    R. L. Zimmermann, The electronic bouncing ball, Am. J. Phys. 60 (1992) 378CrossRefADSGoogle Scholar
  13. 13.
    P. J. Holmes, The dynamics of repeated impacts with a sinusoidally vibrating table, J. Sound Vib. 84 (1982) 173zbMATHADSGoogle Scholar
  14. 14.
    J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer, New York, 1983zbMATHGoogle Scholar
  15. 15.
    E. D. Leonel and P. V. E. McClintock, A hybrid Fermi-Ulam-bouncer model, J. Phys. A 38 (2005) 823zbMATHCrossRefMathSciNetADSGoogle Scholar
  16. 16.
    J. V. José, Study of a quantum Fermi-acceleration model, Phys. Rev. Lett. 56 (1986) 290CrossRefADSGoogle Scholar
  17. 17.
    G. Karner, On the quantum Fermi accelerator and its relevance to “quantum chaos”, Lett. Math. Phys. 17 (1989) 329zbMATHCrossRefMathSciNetADSGoogle Scholar
  18. 18.
    C. Scheininger and M. Kleber, Quantum to classical correspondence for the Fermi-acceleration model, Physica D 50 (1991) 391zbMATHCrossRefMathSciNetADSGoogle Scholar
  19. 19.
    J. V. José, Quasi energy and eigenfunctions of time-dependent periodic Hamiltonians, in H. A. Cerdeira, R. Ramaswamy, M. C. Gutzwiller, and G. Casati, editors, Quantum chaos. World Scientific, Singapore, 1991Google Scholar
  20. 20.
    T. M. Mello and N. M. Tufillaro, Strange attractors of a bouncing ball, Am. J. Phys. 55 (1987) 316CrossRefADSGoogle Scholar
  21. 21.
    F. C. Moon, Chaotic Vibrations, John Wiley, New York, 1987zbMATHGoogle Scholar
  22. 22.
    R. Keolian, L. A. Turkevich, S. J. Putterman, I. Rudnick, and J. A. Rudnick, Subharmonic sequences in the Faraday experiment: Departures from period doubling, Phys. Rev. Lett. 47 (1981) 1133, reprinted in: Hao Bai-Lin, Chaos, World Scientific, Singapore, 1984CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Personalised recommendations