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Title: Ballistic Transport for One‐Dimensional Quasiperiodic Schrödinger Operators
In this paper, we show that one-dimensional discrete multifrequency quasiperiodic Schrödinger operators with smooth potentials demonstrate ballistic motion on the set of energies on which the corresponding Schrödinger cocycles are smoothly reducible to constant rotations. The proof is performed by establishing a local version of strong ballistic transport on an exhausting sequence of subsets on which reducibility can be achieved by a conjugation uniformly bounded in the Cℓ-norm. We also establish global strong ballistic transport under an additional integral condition on the norms of conjugation matrices. The latter condition is quite mild and is satisfied in many known examples.  more » « less
Award ID(s):
1846114
PAR ID:
10438991
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Communications on Pure and Applied Mathematics
Volume:
LXXV
ISSN:
0010-3640
Page Range / eLocation ID:
0001-0036
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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