Fluctuations and Transients in Quantum-Resonant Evolution

Abstract

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.

REVTEX, 12 pages

References in corpus (5)

• Quantum resonances and decoherence for delta-kicked atoms
• A classical scaling theory of quantum resonances
• General Quantum Resonances of the Kicked Particle
• Gravity-Sensitive Quantum Dynamics in Cold Atoms
• General Approach to the Quantum Kicked Particle in a Magnetic Field: Quantum-Antiresonance Transition

Cited by in corpus (7)

• Experimental Realization of Quantum-Resonance Ratchets
• Quantum Ratchet Accelerator without a Bichromatic Lattice Potential
• Quantum Resonances and Ratchets in Free-Falling Frames
• The manifestation of quantum resonances and antiresonances in a finite temperature dilute atomic gas
• Pseudo-classical theory for fidelity of nearly resonant quantum rotors
• Power-law behavior in the quantum-resonant evolution of the delta-kicked accelerator
• Fractional resonances in the atom-optical delta-kicked accelerator