Quantum Resonances and Regularity Islands in Quantum Maps

Details Quantum Resonances and Regularity Islands in Quantum Maps Quantum Resonances and Regularity Islands in Quantum Maps

1999-12-07

arxiv.org/abs/chao-dyn/9912009v1

Nonlinear Sciences

Chaotic Dynamics

28 pages (LaTeX), 11 ps figures, submitted to PRE

Scientific paper

10.1103/PhysRevE.61.5057

We study analytically as well as numerically the dynamics of a quantum map near a quantum resonance of an order q. The map is embedded into a continuous unitary transformation generated by a time-independent quasi-Hamiltonian. Such a Hamiltonian generates at the very point of the resonance a local gauge transformation described the unitary unimodular group SU(q). The resonant energy growth of is attributed to the zero Liouville eigenmodes of the generator in the adjoint representation of the group while the non-zero modes yield saturating with time contribution. In a vicinity of a given resonance, the quasi-Hamiltonian is then found in the form of power expansion with respect to the detuning from the resonance. The problem is related in this way to the motion along a circle in a (q^2-1)-component inhomogeneous "magnetic" field of a quantum particle with $q$ intrinsic degrees of freedom described by the SU(q) group. This motion is in parallel with the classical phase oscillations near a non-linear resonance. The most important role is played by the resonances with the orders much smaller than the typical localization length, q << l. Such resonances master for exponentially long though finite times the motion in some domains around them. Explicit analytical solution is possible for a few lowest and strongest resonances.

Affiliated with

Also associated with

No associations

Rating

Quantum Resonances and Regularity Islands in Quantum Maps does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quantum Resonances and Regularity Islands in Quantum Maps, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Resonances and Regularity Islands in Quantum Maps will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-282025