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Quantum Ergodicity for Point Scatterers on Arithmetic Tori
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-4734-5092
2014 (English)In: Geometric and Functional Analysis, ISSN 1016-443X, E-ISSN 1420-8970, Vol. 24, no 5, 1565-1590 p.Article in journal (Refereed) Published
Abstract [en]

We prove an analogue of Shnirelman, Zelditch and Colin de VerdiS- re's quantum ergodicity Theorems in a case where there is no underlying classical ergodicity. The system we consider is the Laplacian with a delta potential on the square torus. There are two types of wave functions: old eigenfunctions of the Laplacian, which are not affected by the scatterer, and new eigenfunctions which have a logarithmic singularity at the position of the scatterer. We prove that a full density subsequence of the new eigenfunctions equidistribute in phase space. Our estimates are uniform with respect to the coupling parameter, in particular the equidistribution holds for both the weak and strong coupling quantizations of the point scatterer.

Place, publisher, year, edition, pages
2014. Vol. 24, no 5, 1565-1590 p.
National Category
URN: urn:nbn:se:kth:diva-154745DOI: 10.1007/s00039-014-0275-6ISI: 000342429700006ScopusID: 2-s2.0-84907698217OAI: diva2:761074
Swedish Research Council
Available from: 2014-11-05 Created: 2014-10-27 Last updated: 2014-11-05Bibliographically approved

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Kurlberg, Pär
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