Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Rate of Quantum Ergodicity on hyperbolic Surfaces and Billiards   The rate of quantum ergodicity is studied for three strongly chaotic (Anosov)
systems. The quantal eigenfunctions on a compact Riemannian surface of genus
g=2 and of two triangular billiards on a surface of constant negative curvature
are investigated. One of the triangular billiards belongs to the class of
arithmetic systems. There are no peculiarities observed in the arithmetic
system concerning the rate of quantum ergodicity. This contrasts to the
peculiar behaviour with respect to the statistical properties of the quantal
levels. It is demonstrated that the rate of quantum ergodicity in the three
considered systems fits well with the known upper and lower bounds.
Furthermore, Sarnak's conjecture about quantum unique ergodicity for hyperbolic
surfaces is confirmed numerically in these three systems.

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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: q-fin
2
The categories of this paper are: math
1
The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
3
The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg