Abstract
We study the anomalous diffusion resulting from the standard map. The quantum mechanical breakdown of this property occurs in a time depending logarithmically on the inverse of the Planck constant and implies a coherence among so small regions of phase-space as to be robust against environment fluctuations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
M. Hillery, R.F. O’Connell, M.O. Scully, and E.P. Wigner, Phys. Rep. 106, 121 (1984).
For the sake of simplicity we restrict ourself to the case of a particle moving in a one-dimensional potential V(q,t).
G.P. Berman and G.M. Zaslavsky, Physica A 91, 450 (1978); M.V. Berry, Ann. Phys. 131, 163 (1981); G.M. Zaslavsky, Phys. Rep. 80, 157 (1981);W.H. Zurek and J.P. Paz, Phys. Rev. Lett. 72, 2508 (1994).
M. Tabor, Chaos and Integrability in Nonlinear Dynamics (Wiley, New York, 1989).
G. Casati, B.V. Chirikov, F.M. Izrailev, and J. Ford in Stochastic Behavior in Classical and Hamiltonian Systems (Lectures Notes in Physics, Vol. 3), G. Casati and J. Ford, eds. (Springer, Berlin, 1979).
R. Ishizaki, H. Hata. T. Horita, and H. Mori, Prog. Theor. Phys. 84, 179 (1990).
G. Zumofen and J. Klafter, Europhys. Lett. 25, 565 (1994); Gy. Trefán, E. Floriani, B.J. West, and P. Grigolini, Phys. Rev. E 50, 2564 (1994).
R. Roncaglia, L. Bonci, B.J. West, and P. Grigolini, Phys. Rev. E 51, 5524 (1995).
J.C. Robinson, C. Bharucha, F.L. Moore, R. Jahnke, G.A. Georgakis, Q. Niu, M.G. Raizen, B. Sundaram, Phys. Rev. Lett 74, 3963 (1995).
W.H. Zurek, Phys. Rev. D 24, 1516 (1981); E. Joos and H.D. Zeh, Z. Phys. B 59, 223 (1985); A.O. Caldeira and A.J. Leggett, Phys. Rev. A 31, 1059 (1985); W.G. Unruh and W.H. Zurek, Phys. Rev. D 40, 1071 (1989).
P. Grigolini, Quantum Irreversibility and Measurement (World Scientific, Singapore, 1993).
L. Bonci, P. Grigolini, A. Laux, and R. Roncaglia, Phys. Rev. A. 54, 112 (1996).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Bonci, L. (1997). Superdiffusive Behavior in Weakly Chaotic Systems: A New Avenue to Quantum Macroscopic Manifestations. In: Ferrero, M., van der Merwe, A. (eds) New Developments on Fundamental Problems in Quantum Physics. Fundamental Theories of Physics, vol 81. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5886-2_7
Download citation
DOI: https://doi.org/10.1007/978-94-011-5886-2_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6487-3
Online ISBN: 978-94-011-5886-2
eBook Packages: Springer Book Archive