Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pointwise Weyl law for graphs from quantized interval maps   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 (2001)] as a model for quantum chaos on graphs. Since we
allow shrinking spectral windows in the pointwise Weyl law analogue, we obtain
a strengthening of the quantum ergodic theorem for these models, 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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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph