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Poisson distribution for gaps between sums of two squares and level spacings for toral point scatterers
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2017 (English)In: Communications in Number Theory and Physics, ISSN 1931-4523, E-ISSN 1931-4531, Vol. 11, no 4, p. 837-877Article in journal (Refereed) Published
Abstract [en]

We investigate the level spacing distribution for the quantum spectrum of the square billiard. Extending work of Connors-Keating, and Smilansky, we formulate an analog of the Hardy-Littlewood prime k-tuple conjecture for sums of two squares, and show that it implies that the spectral gaps, after removing degeneracies and rescaling, are Poisson distributed. Consequently, by work of Rud-nick and Ueberschar, the level spacings of arithmetic toral point scatterers, in the weak coupling limit, are also Poisson distributed. We also give numerical evidence for the conjecture and its implications.

Place, publisher, year, edition, pages
2017. Vol. 11, no 4, p. 837-877
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-220308DOI: 10.4310/CNTP.2017.v11.n4.a3ISI: 000416453300003Scopus ID: 2-s2.0-85035755443OAI: oai:DiVA.org:kth-220308DiVA, id: diva2:1168834
Funder
Swedish Research Council, 621-2011-5498
Note

QC 20171221

Available from: 2017-12-21 Created: 2017-12-21 Last updated: 2017-12-21Bibliographically approved

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