Long time propagation and control on scarring for perturbed quantized hyperbolic toral automorphisms

Details Long time propagation and control on scarring for perturbed quantized hyperbolic toral automorphisms Long time propagation and control on scarring for perturbed quantized hyperbolic toral automorphisms

2004-09-24

arxiv.org/abs/math-ph/0409069v1

Ann. Henri Poincare, 6, (2005) 885-913

Physics

Mathematical Physics

Scientific paper

10.1007/s00023-005-0228-6

We show that on a suitable time scale, logarithmic in $\hbar$, the coherent states on the two-torus, evolved under a quantized perturbed hyperbolic toral automorphism, equidistribute on the torus. We then use this result to obtain control on the possible strong scarring of eigenstates of the perturbed automorphisms by periodic orbits. Our main tool is an adapted Egorov theorem, valid for logarithmically long times.

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