Abstract
Wave packets in a system governed by a Hamiltonian with a generic nonlinear spectrum typically exhibit both full and fractional revivals. It is shown that, by varying the parameters in the Hamiltonian cyclically with a period T and thus inducing suitable geometric phases in the states, fractional revivals can be eliminated at the relevant times T, 2T,... . Further, with the introduction of this time step T, the occurrence of near full revivals can be mapped onto that of Poincaré recurrences in an irrational rotation map of the circle. The distinctive recurrence statistics of the latter can thus serve as a clear signature of the dynamics of wave packet revivals.
Similar content being viewed by others
REFERENCES
E. Schrödinger, Naturwiss. 14:664 (1926).
B. Kohler, V. V. Yakovlev, J. Che, J. L. Krause, M. Messina, K. R. Wilson, N. Schwentner, R. M. Whitnell, and Y. J. Yan, Phys. Rev. Lett. 74:3360 (1995); C. J. Bardeen, Q. Wang, and C. V. Shank, Phys. Rev. Lett. 75:3410 (1995).
Z. D. Gaeta and C. R. Stroud, Jr., Phys. Rev. A 42:6308 (1990); O. Knospe and R. Schmidt, Phys. Rev. A 54:1154 (1996).
K. Leo, J. Shah, E. O. Gobel, T. C. Damen, S. Schmitt-Rink, W. Scafer, and K. Kohler, Phys. Rev. Lett. 66:201 (1991).
M. J. J. Vrakking, D. M. Villeneuve, and A. Stolow, Phys. Rev. A 54:R37 (1996).
J. Parker and C. R. Stroud, Jr., Phys. Rev. Lett. 56:716 (1986).
M. Nauenberg, J. Phys. B 23:L385 (1990).
I. Sh. Averbukh and N. F. Perelman, Phys. Lett. A 139:449 (1989).
A. Zewail, Femtochemistry: Ultrafast Dynamics of the Chemical Bond (World Scientific, Singapore, 1994).
Ch. Meier, V. Engel, and J. S. Briggs, J. Chem. Phys. 95:7337 (1991).
M. V. Berry, J. Phys. A: Math. Gen. 18:15 (1985).
K. Tara, G. S. Agarwal, and S. Chaturvedi, Phys. Rev. A 47:5024 (1993).
S. Seshadri, Thesis, unpublished (Indian Institute of Technology—Madras, India, 1999).
S. Flügge, Practical Quantum Mechanics (Springer-Verlag, Berlin, 1971).
N. Datta and G. Ghosh, Phys. Rev. A 46:5358 (1992).
W. de Melo and S. van Strien, One-Dimensional Dynamics (Springer-Verlag, Berlin, 1993).
N. B. Slater, Proc. Camb. Phil. Soc. 63:1115 (1967); G. Rauzy, Acta Arith. 34:315 (1979).
A. Pandey and R. Ramaswamy, Phys. Rev. A 43:4237 (1991).
M. Theunissen, C. Nicolis, and G. Nicolis, J. Stat. Phys. 94:437 (1999).
S. Seshadri, S. Lakshmibala, and V. Balakrishnan, Phys. Lett. A 256:15 (1999).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Seshadri, S., Lakshmibala, S. & Balakrishnan, V. Control of Wave Packet Revivals Using Geometric Phases. Journal of Statistical Physics 101, 213–223 (2000). https://doi.org/10.1023/A:1026488815731
Issue Date:
DOI: https://doi.org/10.1023/A:1026488815731