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SUMMARY:Pär Kurlberg
DTSTART:20210616T150000Z
DTEND:20210616T160000Z
DTSTAMP:20260418T064329Z
UID:LNTS/42
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LNTS/42/">Le
 vel repulsion for arithmetic toral point scatterers</a>\nby Pär Kurlberg 
 as part of London number theory seminar\n\n\nAbstract\nThe Seba billiard w
 as introduced to study the transition between\n    integrability and chaos
  in quantum systems. The model seem to exhibit\n    intermediate level sta
 tistics with strong repulsion between nearby\n    eigenvalues (consistent 
 with random matrix theory predictions for\n    spectra of chaotic systems)
 \, whereas large gaps seem to have "Poisson\n    tails" (as for spectra of
  integrable systems.)\n\n    We investigate the closely related "toral poi
 nt scatterer"-model\, i.e.\,\n    the Laplacian perturbed by a delta-poten
 tial\, on 3D tori of the form\n    R^3/Z^3.  This gives a rank one perturb
 ation of the original Laplacian\,\n    and it is natural to split the spec
 trum/eigenspaces into two parts: the\n    "old" (unperturbed) one spanned 
 by eigenfunctions vanishing at the\n    scatterer location\, and the "new"
  part (spanned by Green's functions).\n    We show that there is strong re
 pulsion between the new set of\n    eigenvalues.\n
LOCATION:https://researchseminars.org/talk/LNTS/42/
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