Abstract
We investigate possible ways in which a quantum wavepacket spreads. We show that in a general class of double kicked rotor system, a wavepacket may undergo superballistic spreading; i.e., its variance increases as the cubic of time. The conditions for the observed superballistic spreading and two related characteristic time scales are studied. Our results suggest that the symmetry of the studied model and whether it is a Kolmogorov-Arnold-Moser system are crucial to its wavepacket spreading behavior. Our study also sheds new light on the exponential wavepacket spreading phenomenon previously observed in the double kicked rotor system.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
R. Ketzmerick, K. Kruse, S. Kraut, and T. Geisel, Phys. Rev. Lett. 79, 1959 (1997).
I. Guarneri, Europhys. Lett. 10, 95 (1989).
I. Guarneri, Europhys. Lett. 21, 729 (1993).
L. Hufnagel, R. Ketzmerick, T. Kottos, and T. Geisel, Phys. Rev. E 64, 012301 (2001).
Z. J. Zhang, P. Q. Tong, J. B. Gong, and W. B. Li, Phys. Rev. Lett. 108, 070603 (2012).
J. Wang, I. Guarneri, G. Casati, and J. B. Gong, Phys. Rev. Lett. 107, 234104 (2011).
G. Casati, B. V. Chirikov, F. M. Izrailev, and J. Ford, in Stochastic behavior in classical and quantum Hamiltonian systems (Lecture Notes in Physics Vol.93) (Springer, Berlin, 1979), pp. 334–352.
F. L. Moore, J. C. Robinson, C. F. Bharucha, B. Sundaram, and M. G. Raizen, Phys. Rev. Lett. 75, 4598 (1995).
J. Chabe, G. Lemarie, B. Gremaud, D. Delande, P. Szriftgiser, and J. C. Garreau, Phys. Rev. Lett. 101, 255702 (2008).
H. L.Wang, J. Wang, I. Guarneri, G. Casati, and J. B. Gong, Phys. Rev. E 88, 052919 (2013).
S. Fishman, I. Guarneri, and L. Rebuzzini, Phys. Rev. Lett. 89, 084101 (2002).
F. M. Izrailev, and D. L. Shepelyanskii, Theor. Math. Phys. 43, 553 (1980).
I. Dana, E. Eisenberg, and N. Shnerb, Phys. Rev. E 54, 5948 (1996).
L. Chierchia, and J. N. Mather, Scholarpedia 5, 2123 (2010).
P. X.Wang, J. X. Wang, Y. K. Huo, W. Scheid, and H. Hora, Chin. Sci. Bull. 57, 1494 (2012).
A. Shapira, L. Naor, and A. Arie, Sci. Bull. 60, 1403 (2015).
P. F. Sui, and Z. H. Dai, Sci. China-Phys. Mech. Astron. 58, 052002 (2015).
B. Chirikov, and D. Shepelyansky, Scholarpedia 3, 3550 (2008).
W. Li, S. G. Chen, and G. R. Wang, Phys. Lett. A 281, 334 (2001).
P. H. Jones, M. M. Stocklin, G. Hur, and T. S. Monteiro, Phys. Rev. Lett. 93, 223002 (2004).
J. Wang, T. S. Monteiro, S. Fishman, J. P. Keating, and R. Schubert, Phys. Rev. Lett. 99, 234101 (2007).
W. Lawton, A. S. Mouritzen, J. Wang, and J. B. Gong, J. Math. Phys. 50, 032103 (2009).
J. Wang, and J. B. Gong, Phys. Rev. A 77, 031405(R) (2008).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Fang, P., Wang, J. Superballistic wavepacket spreading in double kicked rotors. Sci. China Phys. Mech. Astron. 59, 680011 (2016). https://doi.org/10.1007/s11433-016-0076-y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11433-016-0076-y