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Distribution of Resonances for Open Quantum Maps

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Abstract

We analyze a simple model of quantum chaotic scattering system, namely the quantized open baker’s map. This model provides a numerical confirmation of the fractal Weyl law for the semiclassical density of quantum resonances. The fractal exponent is related to the dimension of the classical repeller. We also consider a variant of this model, for which the full resonance spectrum can be rigorously computed, and satisfies the fractal Weyl law. For that model, we also compute the shot noise of the conductance through the system, and obtain a value close to the prediction of random matrix theory.

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Authors and Affiliations

  1. Service de Physique Théorique, CEA/DSM/PhT, Unité de Recherche Associée au CNRS, CEA/Saclay, 91191, Gif-sur-Yvette, France

    Stéphane Nonnenmacher

  2. Mathematics Department, University of California, Evans Hall, Berkeley, CA, 94720, USA

    Maciej Zworski

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  1. Stéphane Nonnenmacher
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  2. Maciej Zworski
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Correspondence to Maciej Zworski.

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Communicated by P. Sarnak

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Nonnenmacher, S., Zworski, M. Distribution of Resonances for Open Quantum Maps. Commun. Math. Phys. 269, 311–365 (2007). https://doi.org/10.1007/s00220-006-0131-0

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