Skip to content
DraconiticResearch
Search Sources API
203,948 studies31 sourcesUpdated 19 min ago
PreprintarXiv licencearXiv

A periodic Anderson--Bernoulli model with infinitely many spectral gaps

  • Jake Fillman
  • William Wood
Open at sourcePDFDOICite

Abstract

We prove that the (almost-sure) spectrum of a periodic Anderson--Bernoulli model may enjoy infinitely many gaps. In particular, this shows that Schrödinger operators associated with transitive subshifts of finite type do not necessarily have finite-gap spectra. This resolves a pair of open problems posed by Damanik and the first named author. The main mechanism is the construction of a transverse heteroclinic connection within the class of Schrödinger transfer matrices, together with a scale-matching argument to produce a sequence of invariant multicones.

Related

  1. Localization near the edge for the lattice Anderson-Bernoulli model on general dimension
    Linjun Li, Shihe Liu, Lingfu Zhang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsDynamical systemsarXiv
  2. Poisson statistics for one-dimensional Anderson--Bernoulli Schrödinger operators
    Yi Han
    arXivPreprintCC BY 4.0Full textMathematical physicsProbabilityarXiv
  3. Infinitely many finite simple groups of Lie type are not generated invariably by two elements of prime order
    Robert M. Guralnick, John Shareshian, Russ Woodroofe
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. Examples of Uniformly Quasiregular Mappings with Fatou Set Having Infinitely Many Components
    Gaven Martin, Kirsi Peltonen
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. Infinitely many normalized solutions of L2-supercritical NLS equations on noncompact metric graphs with localized nonlinearities
    Pablo Carrillo, Damien Galant, Louis Jeanjean +1
    Discrete and Continuous Dynamical Systems - Series APeer-reviewedCC BY 4.0Full text2 citedAnalysis & PDEsHAL

Cite

BibTeXRIS
BibTeX
@misc{fillman2026periodic,
  title = {{A periodic Anderson--Bernoulli model with infinitely many spectral gaps}},
  author = {Jake Fillman and William Wood},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27160},
  eprint = {2610.27160},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27160},
}
RIS
TY  - UNPB
TI  - A periodic Anderson--Bernoulli model with infinitely many spectral gaps
AU  - Jake Fillman
AU  - William Wood
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.27160
UR  - https://arxiv.org/abs/2610.27160
AB  - We prove that the (almost-sure) spectrum of a periodic Anderson--Bernoulli model may enjoy infinitely many gaps. In particular, this shows that Schrödinger operators associated with transitive subshifts of finite type do not necessarily have finite-gap spectra. This resolves a pair of open problems posed by Damanik and the first named author. The main mechanism is the construction of a transverse heteroclinic connection within the class of Schrödinger transfer matrices, together with a scale-matching argument to produce a sequence of invariant multicones.
ER  -