On the fluctuations of matrix elements of the quantum cat map - Mathematics > Number TheoryReport as inadecuate




On the fluctuations of matrix elements of the quantum cat map - Mathematics > Number Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: We study the fluctuations of the diagonal matrix elements of the quantum catmap about their limit. We show that after suitable normalization, the fifthcentered moment for the Hecke basis vanishes in the semiclassical limit,confirming in part a conjecture of Kurlberg and Rudnick.We also study sums of matrix elements lying in short windows. For observableswith zero mean, the first moment of these sums is zero, and the variance wasdetermined by the author with Kurlberg and Rudnick. We show that if the windowis sufficiently small in terms of Planck-s constant, the third moment vanishesif we normalize so that the variance is of order one.



Author: Lior Rosenzweig

Source: https://arxiv.org/







Related documents