Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The defect of toral Laplace eigenfunctions and Arithmetic Random Waves   We study the defect (or "signed area") distribution of toral Laplace
eigenfunctions restricted to shrinking balls of radius above the Planck scale,
in either random Gaussian scenario ("Arithmetic Random Waves"), or
deterministic eigenfunctions averaged w.r.t. the spatial variable. In either
scenario we exploit the associated symmetry of the eigenfunctions to show that
the expectation (Gaussian or spatial) vanishes. Our principal results concern
the high energy limit behaviour of the defect variance.

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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin