Ballistic Transport in Periodic and Random Media

Anne BoutetdeMonvel, Mostafa Sabri

Research output: Chapter in Book/Report/Conference proceedingChapter


We prove ballistic transport of all orders, that is, ∥ xme i t Hψ∥ ≍ tm, for the following models: the adjacency matrix on ℤd, the Laplace operator on ℝd, periodic Schrödinger operators on ℝd, and discrete periodic Schrödinger operators on periodic graphs. In all cases we give the exact expression of the limit of ∥ xme i t Hψ∥ ∕ tm as t→ + ∞. We then move to universal covers of finite graphs (these are infinite trees) and prove ballistic transport in mean when the potential is lifted naturally, giving a periodic model, and when the tree is endowed with random i.i.d. potential, giving an Anderson model. The limiting distributions are then discussed, enriching the transport theory. Some general upper bounds are detailed in the appendix.

Original languageEnglish (US)
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages54
StatePublished - 2023

Publication series

NameOperator Theory: Advances and Applications
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878


  • Ballistic transport
  • Delocalization
  • Periodic Schrödinger operators
  • Periodic graphs
  • Trees

ASJC Scopus subject areas

  • Analysis


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