Communications in Mathematical Physics

, Volume 194, Issue 2, pp 323–341

Dynamical Localization for Discrete and Continuous Random Schrödinger Operators


  • F. Germinet
    • UFR de Mathématiques et LPTMC, Université Paris VII – Denis Diderot, 75251 Paris Cedex 05, France. E-mail:
  • S. De Bièvre
    • UFR de Mathématiques et URA GAT, Université des Sciences et Technologies de Lille, 59655 Villeneuve d'Ascq Cedex, France. E-mail:

DOI: 10.1007/s002200050360

Cite this article as:
Germinet, F. & De Bièvre, S. Comm Math Phys (1998) 194: 323. doi:10.1007/s002200050360


We show for a large class of random Schrödinger operators Hο on \(\) and on \(\) that dynamical localization holds, i.e. that, with probability one, for a suitable energy interval I and for q a positive real,
Here ψ is a function of sufficiently rapid decrease, \(\) and PI(Hο) is the spectral projector of Hο corresponding to the interval I. The result is obtained through the control of the decay of the eigenfunctions of Hο and covers, in the discrete case, the Anderson tight-binding model with Bernoulli potential (dimension ν = 1) or singular potential (ν > 1), and in the continuous case Anderson as well as random Landau Hamiltonians.

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© Springer-Verlag Berlin Heidelberg 1998