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Communications in Mathematical Physics

, Volume 354, Issue 1, pp 85–113 | Cite as

Ballistic Transport for the Schrödinger Operator with Limit-Periodic or Quasi-Periodic Potential in Dimension Two

  • Yulia Karpeshina
  • Young-Ran Lee
  • Roman Shterenberg
  • Günter Stolz
Article

Abstract

We prove the existence of ballistic transport for the Schrödinger operator with limit-periodic or quasi-periodic potential in dimension two. This is done under certain regularity assumptions on the potential which have been used in prior work to establish the existence of an absolutely continuous component and other spectral properties. The latter include detailed information on the structure of generalized eigenvalues and eigenfunctions. These allow one to establish the crucial ballistic lower bound through integration by parts on an appropriate extension of a Cantor set in momentum space, as well as through stationary phase arguments.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Campbell HallUniversity of Alabama at BirminghamBirminghamUSA
  2. 2.Department of MathematicsSogang UniversitySeoulSouth Korea

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