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Poisson distributio...
Poisson distribution for gaps between sums of two squares and level spacings for toral point scatterers
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Freiberg, Tristan (author)
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- Kurlberg, Pär (author)
- KTH,Matematik (Avd.)
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Rosenzweig, Lior (author)
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KTH Matematik (Avd) (creator_code:org_t)
- 2017
- 2017
- English.
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In: Communications in Number Theory and Physics. - 1931-4523 .- 1931-4531. ; 11:4, s. 837-877
- Related links:
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https://urn.kb.se/re...
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https://doi.org/10.4...
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Abstract
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Publication and Content Type
- ref (subject category)
- art (subject category)
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