Matrix elements for the quantum cat map: Fluctuations in short windows

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dc.creatorKurlberg, P.
dc.creatorRosenzweig, L.
dc.creatorRudnick, Z.
dc.date2007-01-24
dc.date2007-07-08
dc.date.accessioned2026-07-07T08:14:14Z
dc.date.available2026-07-07T08:14:14Z
dc.descriptionWe study fluctuations of the matrix coefficients for the quantized cat map. We consider the sum of matrix coefficients corresponding to eigenstates whose eigenphases lie in a randomly chosen window, assuming that the length of the window shrinks with Planck's constant. We show that if the length of the window is smaller than the square root of Planck's constant, but larger than the separation between distinct eigenphases, then the variance of this sum is proportional to the length of the window, with a proportionality constant which coincides with the variance of the individual matrix elements corresponding to Hecke eigenfunctions.
dc.description18 pages. Introduction revised/expanded, added references, corrected typos
dc.identifierhttps://arxiv.org/abs/math/0701685
dc.identifierhttp://arxiv.org/abs/math/0701685
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/133049
dc.subjectNumber Theory
dc.subjectMathematical Physics
dc.subject11
dc.titleMatrix elements for the quantum cat map: Fluctuations in short windows
dc.typetext

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