Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Absence of Absolutely Continuous Spectrum for Generic Quasi-Periodic
  Schr\"odinger Operators on the Real Line   We show that a generic quasi-periodic Schr\"odinger operator in
$L^2(\mathbb{R})$ has purely singular spectrum. That is, for any minimal
translation flow on a finite-dimensional torus, there is a residual set of
continuous sampling functions such that for each of these sampling functions,
the Schr\"odinger operator with the resulting potential has empty absolutely
continuous spectrum.

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics