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

Pär Kurlberg*, Lior Rosenzweig, Zeév Rudnick

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We 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.

Original languageEnglish
Article number001
Pages (from-to)2289-2304
Number of pages16
JournalNonlinearity
Volume20
Issue number10
DOIs
StatePublished - 1 Oct 2007

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