Duke Mathematical Journal

Controlling strong scarring for quantized ergodic toral automorphisms

Francesco Bonechi and Stephan De Bièvre

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We show that in the semiclassical limit the eigenfunctions of quantized ergodic symplectic toral automorphisms cannot concentrate in measure on closed orbits of the dynamics. More generally, we show that the mass of the pure point component of the limit measure must be smaller than two thirds of the total mass. The proofs use only the algebraic (i.e., not the number-theoretic) properties of the toral automorphisms together with the exponential instability of the dynamics and therefore work in all dimensions.

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Duke Math. J., Volume 117, Number 3 (2003), 571-587.

First available in Project Euclid: 26 May 2004

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Zentralblatt MATH identifier

Primary: 81Q20: Semiclassical techniques, including WKB and Maslov methods
Secondary: 37Axx: Ergodic theory [See also 28Dxx] 37N20: Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) 81Q50: Quantum chaos [See also 37Dxx]


Bonechi, Francesco; De Bièvre, Stephan. Controlling strong scarring for quantized ergodic toral automorphisms. Duke Math. J. 117 (2003), no. 3, 571--587. doi:10.1215/S0012-7094-03-11736-6. https://projecteuclid.org/euclid.dmj/1085598405

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