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Small Scale Equidistribution of Eigenfunctions on the Torus
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2017 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 350, no 1, 279-300 p.Article in journal (Refereed) Published
Abstract [en]

We study the small scale distribution of the L-2 mass of eigenfunctions of the Laplacian on the flat torus T-d. Given an orthonormal basis of eigenfunctions, we show the existence of a density one subsequence whose L-2 mass equidistributes at small scales. In dimension two our result holds all the way down to the Planck scale. For dimensions d = 3, 4 we can restrict to individual eigenspaces and show small scale equidistribution in that context. We also study irregularities of quantum equidistribution: We construct eigenfunctions whose L-2 mass does not equidistribute at all scales above the Planck scale. Additionally, in dimension d = 4 we show the existence of eigenfunctions for which the proportion of L-2 mass in small balls blows up at certain scales.

Place, publisher, year, edition, pages
Springer, 2017. Vol. 350, no 1, 279-300 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-203831DOI: 10.1007/s00220-016-2734-4ISI: 000393697400009Scopus ID: 2-s2.0-84981170244OAI: oai:DiVA.org:kth-203831DiVA: diva2:1083397
Note

QC 20170321

Available from: 2017-03-21 Created: 2017-03-21 Last updated: 2017-03-21Bibliographically approved

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