Communications in Mathematical Physics

, Volume 221, Issue 1, pp 27-56

First online:

How to Prove Dynamical Localization

  • Serguei TcheremchantsevAffiliated withMAPMO-CNRS, Département des Mathématiques, Université d'Orléans, BP 6759, 45067 Orléans Cedex 2, France. e-mail:

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Let H be a self-adjoint operator on l 2(Z d ) or L 2(R d ) with pure point spectrum on some interval I. We establish general necessary and sufficient conditions for dynamical localization for a given vector and on the interval of energies I. The sufficient conditions we obtain improve the existing ones such as SULE or WULE and can be useful in applications.