Log-Scale Equidistribution of Zeros of Quantum Ergodic Eigensections

Robert Chang, Steve Zelditch*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Under suitable hypotheses, a symplectic map can be quantized as a sequence of unitary operators acting on the Nth powers of a positive line bundle over a Kähler manifold. We show that if the symplectic map has sufficiently fast polynomial decay of correlations, then there exists a density one subsequence of eigensections whose masses and zeros become equidistributed in balls of logarithmically shrinking radii of lengths | log N| - γ for some constant γ> 0 independent of N.

Original languageEnglish (US)
Pages (from-to)3783-3814
Number of pages32
JournalAnnales Henri Poincare
Volume19
Issue number12
DOIs
StatePublished - Dec 1 2018

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics

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