Fluctuations and Transients in Quantum-Resonant Evolution

Details Fluctuations and Transients in Quantum-Resonant Evolution Fluctuations and Transients in Quantum-Resonant Evolution

2006-08-10

arxiv.org/abs/nlin/0608022v1

Physical Review E 74, 045201(R) (2006).

Nonlinear Sciences

Chaotic Dynamics

REVTEX, 12 pages

Scientific paper

10.1103/PhysRevE.74.045201

The quantum-resonant evolution of the mean kinetic energy (MKE) of the kicked particle is studied in detail on different time scales for {\em general} kicking potentials. It is shown that the asymptotic time behavior of a wave-packet MKE is typically a linear growth with bounded fluctuations having a simple number-theoretical origin. For a large class of wave packets, the MKE is shown to be exactly the superposition of its asymptotic behavior and transient logarithmic corrections. Both fluctuations and transients can be significant for not too large times but they may vanish identically under some conditions. In the case of incoherent mixtures of plane waves, it is shown that the MKE never exhibits asymptotic fluctuations but transients usually occur.

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