Abstract
We explain Fermi acceleration of particles bouncing in a gravitational field and experiencing a force due to a modulated evanescent laser field. The acceleration strongly depends upon the initial conditions in the phase space and certain modulation amplitude. We study the accelerated modes by the Poincaré surface of sections and Lyapunov exponents. Furthermore, we identify the initial areas of the phase space that support accelerated dynamics and write a mapping for accelerated dynamics. We show that a distinction between accelerated and chaotic evolutions can be made with the help of the aspect ratio. The Lyapunov exponent shows that the accelerated mode supports ordered evolution.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. Fermi, Phys. Rev., 75, 1169 (1949).
M. Lieberman and A. J. Lichtenberg, Phys. Rev. A, 5, 1852 (1972).
A. J. Lichtenberg and M. A. Lieberman, Regular and Chaotic Dynamics, Springer, New York (1992).
E. D. Leonel, J. K. L. da Silva, and S. O. Kamphorst, Physica A, 331, 435 (2004).
E. D. Leonel, P. V. E. McClintock, and J. K. L. da Silva, Phys. Rev. Lett., 93, 014101 (2004).
E. D. Leonel and P. V. E. McClintock, J. Phys. A: Math. Gen., 38, 425 (2005).
R. E. de Carvalho, F. C. Souza, and E. D. Leonel, Phys. Rev. E, 73, 066229 (2006).
A. K. Karlis, P. K. Papachristou, F. K. Diakonos, et al., Phys. Rev. Lett., 97, 194102 (2006).
A. K. Karlis, P. K. Papachristou, F. K. Diakonos, et al., Phys. Rev. E, 76, 016214 (2007).
A. Steane, P. Szriftgiser, P. Desbiolles, and J. Dalibard, Phys. Rev. Lett., 74, 4972 (1995).
F. Saif, I. Bialynicki-Birula, M. Fortunato, and W. P. Schleich, Phys. Rev. A, 58, 4779 (1998).
F. Saif, Phys. Rev. E, 62, 6308 (2000).
F. Saif, Phys. Lett. A, 274, 98 (2000).
F. Saif, G. Alber, V. Savichev, and W. P. Schleich, J. Optics B, 2, 668 (2000).
F. Saif, Phys. Rep., 419, 207 (2005).
F. Saif and I. Rehman, Phys. Rev. A, 75, 043610 (2007).
A. V. Milovanov and L. M. Zeleny, Phys. Rev. E, 64, 052101 (2001).
A. Veltri and V. Carbone, Phys. Rev. Lett., 92, 143901 (2004).
K. Kobayakawa, Y. S. Honda, and T. Tamura, Phys. Rev. D, 66, 083004 (2002).
M. A. Malkov, Phys. Rev. E, 58, 4911 (1998).
S. Ulam, in: Proceedings of the 4th Berkeley Symposium on Mathematics, Statistics, and Probability (Berkeley, CA), California University Press (1961), Vol. 3, p. 315.
L. D. Pustylnikov, Trans. Moscow Math. Soc., 2 (1978)
L. D. Pustylnikov, Theor. Math. Phys., 57, 1035 (1983).
L. D. Pustylnikov, Sov. Math. Dokl., 35, 88 (1987).
L. D. Pustylnikov, Russ. Acad. Sci. Sb. Math., 82, 231 (1995).
B. V. Chirikov, Phys. Rep., 52, 263 (1979).
G. M. Zaslavsky and U. Frish (Eds.), Levy Flights and Related Topics in Physics, Springer-Verlag (1995).
C. G. Aminoff, A. M. Steane, P. Bouyer, et al., Phys. Rev. Lett., 71, 3083 (1993).
A. Steane, P. Szriftgiser, P. Desbiolles, et al., Phys. Rev. Lett., 74, 4972 (1995).
Javed Akram, Khalid Naseer, Inam-ur Rehman, and Farhan Saif, Math. Probl. Eng., 2009, 246438 (2009).
J. Greene, J. Math. Phys., 20, 1183 (1979).
Edson D. Leonel, Juliano A. de Oliveira, Farhan Saif, J. Phys. A: Math. Gen., 44, 302001 (2011).
Farhan Saif and Pierre Meystre, Int. J. Mod. Phys. D, 16, 2593 (2007).
Itzhack Dana and Shmuel Fishman, Physica D, 17, 63 (1985).
Author information
Authors and Affiliations
Corresponding author
Additional information
Manuscript submitted by the authors in English on August 9, 2013.
Rights and permissions
About this article
Cite this article
Saif, F., Rehman, I.U. Acceleration Modes in Fermi Accelerator. J Russ Laser Res 34, 515–522 (2013). https://doi.org/10.1007/s10946-013-9383-2
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10946-013-9383-2