Duke Mathematical Journal

Controlling strong scarring for quantized ergodic toral automorphisms

Francesco Bonechi and Stephan De Bièvre

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 26 May 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1085598405

Digital Object Identifier
doi:10.1215/S0012-7094-03-11736-6

Mathematical Reviews number (MathSciNet)
MR1979054

Zentralblatt MATH identifier
1049.81028

Subjects
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]

Citation

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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