On the Phase-Space Distribution of Bloch Eigenmodes for Periodic Point Scatterers

Jory Griffin

Research output: Contribution to journalArticle (Academic Journal)peer-review

1 Citation (Scopus)
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Abstract

Consider the 3-dimensional Laplacian with a potential described by point scatterers placed on the integer lattice. We prove that for Floquet-Bloch modes with fixed quasi-momentum satisfying a certain Diophantine condition, there is a subsequence of eigenvalues of positive density whose eigenfunctions exhibit equidistribution in position space and localisation in momentum space. This result complements the result of Ueberschaer and Kurlberg, J. Eur. Math. Soc. (JEMS) (to
appear); [e-print arXiv:1409.6878 (2014)] who show momentum localisation for zero quasi-momentum in 2-dimensions, and is the first result in this direction in 3-dimensions.
Original languageEnglish
Article number082101
Number of pages13
JournalJournal of Mathematical Physics
Volume57
DOIs
Publication statusPublished - 9 Aug 2016

Bibliographical note

16 pages, 2 figures

Keywords

  • math-ph
  • math.MP

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