Fractal Weyl laws in discrete models of chaotic scattering

Details Fractal Weyl laws in discrete models of chaotic scattering Fractal Weyl laws in discrete models of chaotic scattering

2005-06-17

arxiv.org/abs/math-ph/0506045v2

Journal of Physics A 38 (2005) 10683-10702

Physics

Mathematical Physics

Invited article in the Special Issue of Journal of Physics A on "Trends in Quantum Chaotic Scattering"

Scientific paper

10.1088/0305-4470/38/49/014

We analyze simple models of quantum chaotic scattering, namely quantized open baker's maps. We numerically compute the density of quantum resonances in the semiclassical r\'{e}gime. This density satisfies a fractal Weyl law, where the exponent is governed by the (fractal) dimension of the set of trapped trajectories. This type of behaviour is also expected in the (physically more relevant) case of Hamiltonian chaotic scattering. Within a simplified model, we are able to rigorously prove this Weyl law, and compute quantities related to the "coherent transport" through the system, namely the conductance and "shot noise". The latter is close to the prediction of random matrix theory.

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