Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Localization and Cantor spectrum for quasiperiodic discrete
  Schr\"odinger operators with asymmetric, smooth, cosine-like sampling
  functions   We prove Cantor spectrum and almost-sure Anderson localization for
quasiperiodic discrete Schr\"odinger operators $H = \varepsilon\Delta + V$ with
potential $V$ sampled with Diophantine frequency $\alpha$ from an asymmetric,
smooth, cosine-like function $v \in C^2(\mathbb{T},[-1,1])$ for sufficiently
small interaction $\varepsilon \leq \varepsilon_0(v,\alpha)$. We prove this
result via an inductive analysis on scales, whereby we show that locally the
Rellich functions of Dirichlet restrictions of $H$ inherit the cosine-like
structure of $v$ and are uniformly well-separated.

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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex