Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantitative continuity of singular continuous spectral measures and
  arithmetic criteria for quasiperiodic Schr\"odinger operators   We introduce a notion of $\beta$-almost periodicity and prove quantitative
lower spectral/quantum dynamical bounds for general bounded $\beta$-almost
periodic potentials. Applications include a sharp arithmetic criterion of full
spectral dimensionality for analytic quasiperiodic Schr\"odinger operators in
the positive Lyapunov exponent regime and arithmetic criteria for families with
zero Lyapunov exponents, with applications to Sturmian potentials and the
critical almost Mathieu operator.

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The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc