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Quantum chaos concerns eigenfunctions of the Laplace operator in a domain
where a billiard ball would bounce chaotically. Such chaotic eigenfunctions
have been conjectured to share statistical properties of their nodal domains
with a simple percolation model, from which many interesting quantities can
be computed analytically. We numerically test conjectures on the number and
size of nodal domains of quantum chaotic eigenfunctions at very high energies,
approaching the semiclassical limit. We use a highly efficient scaling method
to quickly compute eigenfunctions at low resolution and interpolate to higher
resolution. We computed 10^5 eigenfunctions and counted 10^9 nodal domains.
Our results agree with the conjectured size nodal domains but disagree with the
conjectured mean and variance of the number of nodal domains.
Senior Honors Thesis. Advisor: Alex Barnett.
Bibliographic citation for this report: [plain text] [BIB] [BibTeX] [Refer]
Or copy and paste:
Kyle T. Konrad, "Asymptotic Statistics of Nodal Domains of Quantum Chaotic Billiards in the Semiclassical Limit." Dartmouth Computer Science Technical Report TR2012-723, May 2012.
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