Scarring on invariant manifolds for perturbed quantized hyperbolic toral automorphisms

Details Scarring on invariant manifolds for perturbed quantized hyperbolic toral automorphisms Scarring on invariant manifolds for perturbed quantized hyperbolic toral automorphisms

2006-07-18

arxiv.org/abs/math-ph/0607033v2

Physics

Mathematical Physics

17 pages

Scientific paper

10.1007/s00220-007-0331-2

We exhibit scarring for certain nonlinear ergodic toral automorphisms. There are perturbed quantized hyperbolic toral automorphisms preserving certain co-isotropic submanifolds. The classical dynamics is ergodic, hence in the semiclassical limit almost all eigenstates converge to the volume measure of the torus. Nevertheless, we show that for each of the invariant submanifolds, there are also eigenstates which localize and converge to the volume measure of the corresponding submanifold.

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