Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exponential Lower Bounds for Quasimodes of Semiclassical Schr\"{o}dinger
  Operators   We prove quantitative unique continuation results for the semiclassical
Schrodinger operator on smooth, compact domains. These take the form of
exponentially decreasing (in h) local L^{2} lower bounds for exponentially
precise quasimodes. We also show that these lower bounds are sharp in h, and
that, moreover, the hypothesized quasimode accuracy is also sharp.

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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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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: patt-sol