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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics