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arXiv · 2110.15301

Pointwise Weyl law for graphs from quantized interval maps

Laura Shou
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Abstract

We prove an analogue of the pointwise Weyl law for families of unitary matrices obtained from quantization of one-dimensional interval maps. This quantization for interval maps was introduced by Pako\'nski et al. [J. Phys. A: Math. Gen. 34 9303-9317 (2001)] as a model for quantum chaos on graphs. Since we allow shrinking spectral windows in the pointwise Weyl law, as a consequence we obtain for these models a strengthening of the quantum ergodic theorem from Berkolaiko et al. [Commun. Math. Phys. 273 137-159 (2007)], and show in the semiclassical limit that a family of randomly perturbed quantizations has approximately Gaussian eigenvectors. We also examine further the specific case where the interval map is the doubling map.

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Laura Shou. 2021-10-28. Pointwise Weyl law for graphs from quantized interval maps. https://doi.org/10.1007/s00023-023-01276-3

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