The Spectrum of Period-Doubling Hamiltonian

Qinghui Liu; Yanhui Qu; Xiao Yao

doi:10.1007/s00220-022-04417-7

The Spectrum of Period-Doubling Hamiltonian

Qinghui Liu, Yanhui Qu^*, Xiao Yao

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In this paper, we show the following: the Hausdorff dimension of the spectrum of period-doubling Hamiltonian is bigger than log α/ log 4 , where α is the Golden number; there exists a dense uncountable subset of the spectrum such that for each energy in this set, the related trace orbit is unbounded, which is in contrast with a recent result of Carvalho (Nonlinearity 33, 2020); we give a complete characterization for the structure of gaps and the gap labelling of the spectrum. All of these results are consequences of an intrinsic coding of the spectrum we construct in this paper.

Original language	English
Pages (from-to)	1039-1100
Number of pages	62
Journal	Communications in Mathematical Physics
Volume	394
Issue number	3
DOIs	https://doi.org/10.1007/s00220-022-04417-7
Publication status	Published - Sept 2022

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Liu, Q., Qu, Y., & Yao, X. (2022). The Spectrum of Period-Doubling Hamiltonian. Communications in Mathematical Physics, 394(3), 1039-1100. https://doi.org/10.1007/s00220-022-04417-7

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AB - In this paper, we show the following: the Hausdorff dimension of the spectrum of period-doubling Hamiltonian is bigger than log α/ log 4 , where α is the Golden number; there exists a dense uncountable subset of the spectrum such that for each energy in this set, the related trace orbit is unbounded, which is in contrast with a recent result of Carvalho (Nonlinearity 33, 2020); we give a complete characterization for the structure of gaps and the gap labelling of the spectrum. All of these results are consequences of an intrinsic coding of the spectrum we construct in this paper.

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The Spectrum of Period-Doubling Hamiltonian

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