Hyperbolic Scar Patterns in Phase Space

Details Hyperbolic Scar Patterns in Phase Space Hyperbolic Scar Patterns in Phase Space

2001-04-27

arxiv.org/abs/nlin/0104068v1

Nonlinear Sciences

Chaotic Dynamics

12 pages, 10 figures, Submited to Phys. Rev. E

Scientific paper

10.1088/0951-7715/15/3/309

We develop a semiclassical approximation for the spectral Wigner and Husimi functions in the neighbourhood of a classically unstable periodic orbit of chaotic two dimensional maps. The prediction of hyperbolic fringes for the Wigner function, asymptotic to the stable and unstable manifolds, is verified computationally for a (linear) cat map, after the theory is adapted to a discrete phase space appropriate to a quantized torus. The characteristic fringe patterns can be distinguished even for quasi-energies where the fixed point is not Bohr-quantized. The corresponding Husimi function dampens these fringes with a Gaussian envelope centered on the periodic point. Even though the hyperbolic structure is then barely perceptible, more periodic points stand out due to the weakened interference.

Affiliated with

Also associated with

No associations

Rating

Hyperbolic Scar Patterns in Phase Space 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 Hyperbolic Scar Patterns in Phase Space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hyperbolic Scar Patterns in Phase Space will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-437027