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Inicio » Actividades I+D > Publicaciones 2002 > Hyperbolic Scar Patterns in Phase Space
artículo con referato
"Hyperbolic Scar Patterns in Phase Space"
A.M.F. Rivas and A.M. Ozorio de Almeida
Nonlinearity 15(3) (2002) 681-693
We develop a semiclassical approximation for the spectral Wigner and Husimi functions in the neighborhood 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 quantified torus. The characteristic fringe patterns can be distinguished even for quasi-energies where the fixed point is not Bohr-quantified. 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.
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