Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decay rates at infinity for solutions to periodic Schr\"{o}dinger
  equations   We consider the equation $\Delta u=Vu$ in exterior domains in $\mathbb{R}^2$
and $\mathbb{R}^3$, where $V$ has certain periodicity properties. In particular
we show that such equations cannot have non-trivial superexponentially decaying
solutions. As an application this leads to a new proof for the absolute
continuity of the spectrum of particular periodic Schr\"{o}dinger operators.
The equation $\Delta u=Vu$ is studied as part of a broader class of elliptic
evolution equations.

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The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph