Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact eigenfunction amplitude distributions of integrable quantum
  billiards   The exact probability distributions of the amplitudes of eigenfunctions,
$\Psi(x, y)$, of several integrable planar billiards are analytically
calculated and shown to possess singularities at $\Psi = 0$; the nature of this
singularity is shape-dependent. In particular, we prove that the distribution
function for a rectangular quantum billiard is proportional to the complete
elliptic integral, ${\bf K}(1 - \Psi ^2)$, and demonstrate its universality,
modulo a weak dependence on quantum numbers. On the other hand, we study the
low-lying states of nonseparable, integrable triangular billiards and find the
distributions thereof to be described by the Meijer G-function or certain
hypergeometric functions. Our analysis captures a marked departure from the
Gaussian distributions for chaotic billiards in its survey of the fluctuations
of the eigenfunctions about $\Psi = 0$.

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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
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The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: physics
25
The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
37
The categories of this paper are: supr-con