Anderson localization for the unitary almost Mathieu operator. (English) Zbl 07885182
Summary: We prove Anderson localization for all Diophantine frequencies and all non-resonant phases for a model that arises from a 2D quantum walk model subject to an external magnetic field, also known as the unitary almost Mathieu operator. Our work provides the first localization results for all Diophantine frequencies in quasi-periodic quantum walk and CMV matrix setting. We also obtain sharp asymptotics of the localized eigenfunctions.
{© The Author(s). Published by IOP Publishing Ltd and the London Mathematical Society}
{© The Author(s). Published by IOP Publishing Ltd and the London Mathematical Society}
MSC:
| 47-XX | Operator theory |
References:
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