Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dispersion for Schr\"odinger operators on regular trees   We prove dispersive estimates for two models~: the adjacency matrix on a
discrete regular tree, and the Schr\"odinger equation on a metric regular tree
with the same potential on each edge/vertex. The latter model can be thought of
as an extension of the case of periodic Schr\"odinger operators on the real
line. We establish a $t^{-3/2}$-decay for both models which is sharp, as we
give the first-order asymptotics.

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The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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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: mtrl-th
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The categories of this paper are: nucl-ex