Spectral geometry of flat tori with random impurities
Journées équations aux dérivées partielles (2015), article no. 11, 7 p.

We discuss new results on the geometry of eigenfunctions in disordered systems. More precisely, we study tori d /L d , d=2,3, with uniformly distributed Dirac masses. Whereas at the bottom of the spectrum eigenfunctions are known to be localized, we show that for sufficiently large eigenvalue there exist uniformly distributed eigenfunctions with positive probability. We also study the limit L with a positive density of random Dirac masses, and deduce a lower polynomial bound for the localization length in terms of the eigenvalue for Poisson distributed Dirac masses on d . Finally, we discuss some results on the breakdown of localization in random displacement models above a certain energy threshold.

DOI: 10.5802/jedp.640
Ueberschär, Henrik 1

1 Max Planck Institute of Mathematics Vivatsgasse 7 53111 Bonn, Germany and Laboratoire Paul Painlevé (UMR CNRS 8524) Université Lille 1 59655 Villeneuve d’Ascq, France
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Ueberschär, Henrik. Spectral geometry of flat tori  with random impurities. Journées équations aux dérivées partielles (2015), article  no. 11, 7 p. doi : 10.5802/jedp.640. http://www.numdam.org/articles/10.5802/jedp.640/

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