Arithmetic Spectral Transitions for the Maryland Model Academic Article

abstract

• AbstractWe give a precise description of spectra of the Maryland model urn:x-wiley:0010-3640:media:cpa21688:cpa21688-math-0001 for all values of parameters. We introduce an arithmetically defined index and show that for , urn:x-wiley:0010-3640:media:cpa21688:cpa21688-math-0004 and urn:x-wiley:0010-3640:media:cpa21688:cpa21688-math-0005 Since , this gives a complete description of the spectral decomposition for all values of parameters , , and , making it the first case of a family where arithmetic spectral transition is described without any parameter exclusion. The set of eigenvalues can be explicitly identified for all parameters, using the quantization condition. We also establish, for the first time for this or any other model, a quantization condition for singular continuous spectrum (an arithmetically defined measure zero set that supports singular continuous measures) for all parameters. 2017 Wiley Periodicals, Inc.

authors

• Liu, Wencai

published proceedings

• COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS

altmetric score

• 1

author list (cited authors)

• Jitomirskaya, S., & Liu, W.

citation count

• 29

complete list of authors

• Jitomirskaya, Svetlana||Liu, Wencai

publication date

• June 2017

publisher

• Wiley  Publisher

keywords

• 49 Mathematical Sciences
• 4901 Applied Mathematics
• 4904 Pure Mathematics

Digital Object Identifier (DOI)

• 10.1002/cpa.21688

start page

• 1025

end page

• 1051

volume

• 70

issue

• 6

URL

• http://dx.doi.org/10.1002/cpa.21688