Probabilistic Weyl laws for quantized tori

For the Toeplitz quantization of complex-valued functions on a \(2n\)-dimensional torus we prove that the expected number of eigenvalues of small random perturbations of a quantized observable satisfies a natural Weyl law. In numerical experiments the same Weyl law also holds for ``false''...

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Bibliographic Details
Published in:arXiv.org 2009-09
Main Authors: Christiansen, T J, Zworski, M
Format: Article
Language:English
Subjects:
Eigenvalues
Legislation
Perturbation
Toruses
Online Access:Get full text
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Summary:For the Toeplitz quantization of complex-valued functions on a \(2n\)-dimensional torus we prove that the expected number of eigenvalues of small random perturbations of a quantized observable satisfies a natural Weyl law. In numerical experiments the same Weyl law also holds for ``false'' eigenvalues created by pseudospectral effects.
ISSN:2331-8422
DOI:10.48550/arxiv.0909.2014