Ballistic transport for limit-periodic Schrödinger operators in one dimension
Giorgio Young
University of Michigan, Ann Arbor, USA
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Abstract
In this paper, we consider the transport properties of the class of limit-periodic continuum Schrödinger operators whose potentials are approximated exponentially quickly by a sequence of periodic functions. For such an operator , and the Heisenberg evolution of the position operator, we show the limit of as exists and is nonzero for belonging to a dense subspace of initial states which are sufficiently regular and of suitably rapid decay. This is viewed as a particularly strong form of ballistic transport, and this is the first time it has been proven in a continuum almost periodic non-periodic setting. In particular, this statement implies that for the initial states considered, the second moment grows quadratically in time.
Cite this article
Giorgio Young, Ballistic transport for limit-periodic Schrödinger operators in one dimension. J. Spectr. Theory 13 (2023), no. 2, pp. 451–489
DOI 10.4171/JST/463