Hölder Continuity of the Spectra for Aperiodic Hamiltonians

Horia Cornean, Jean Bellissard, Siegfried Beckus

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Resumé

We study the spectral location of a strongly pattern equivariant Hamiltonians arising through configurations on a colored lattice. Roughly speaking, two configurations are “close to each other” if, up to a translation, they “almost coincide” on a large fixed ball. The larger this ball, the more similar they are, and this induces a metric on the space of the corresponding dynamical systems. Our main result states that the map which sends a given configuration into the spectrum of its associated Hamiltonian, is Hölder (even Lipschitz) continuous in the usual Hausdorff metric. Specifically, the spectral distance of two Hamiltonians is estimated by the distance of the corresponding dynamical systems.

OriginalsprogEngelsk
TidsskriftAnnales Henri Poincare
Vol/bind20
Udgave nummer11
Sider (fra-til)3603-3631
ISSN1424-0637
DOI
StatusUdgivet - 2019

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continuity
dynamical systems
Configuration
balls
Ball
configurations
Dynamical system
Hausdorff Metric
Equivariant
Lipschitz
Metric

Citer dette

Cornean, Horia ; Bellissard, Jean ; Beckus, Siegfried. / Hölder Continuity of the Spectra for Aperiodic Hamiltonians. I: Annales Henri Poincare. 2019 ; Bind 20, Nr. 11. s. 3603-3631.
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abstract = "We study the spectral location of a strongly pattern equivariant Hamiltonians arising through configurations on a colored lattice. Roughly speaking, two configurations are “close to each other” if, up to a translation, they “almost coincide” on a large fixed ball. The larger this ball, the more similar they are, and this induces a metric on the space of the corresponding dynamical systems. Our main result states that the map which sends a given configuration into the spectrum of its associated Hamiltonian, is H{\"o}lder (even Lipschitz) continuous in the usual Hausdorff metric. Specifically, the spectral distance of two Hamiltonians is estimated by the distance of the corresponding dynamical systems.",
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Hölder Continuity of the Spectra for Aperiodic Hamiltonians. / Cornean, Horia; Bellissard, Jean ; Beckus, Siegfried.

I: Annales Henri Poincare, Bind 20, Nr. 11, 2019, s. 3603-3631.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - Hölder Continuity of the Spectra for Aperiodic Hamiltonians

AU - Cornean, Horia

AU - Bellissard, Jean

AU - Beckus, Siegfried

PY - 2019

Y1 - 2019

N2 - We study the spectral location of a strongly pattern equivariant Hamiltonians arising through configurations on a colored lattice. Roughly speaking, two configurations are “close to each other” if, up to a translation, they “almost coincide” on a large fixed ball. The larger this ball, the more similar they are, and this induces a metric on the space of the corresponding dynamical systems. Our main result states that the map which sends a given configuration into the spectrum of its associated Hamiltonian, is Hölder (even Lipschitz) continuous in the usual Hausdorff metric. Specifically, the spectral distance of two Hamiltonians is estimated by the distance of the corresponding dynamical systems.

AB - We study the spectral location of a strongly pattern equivariant Hamiltonians arising through configurations on a colored lattice. Roughly speaking, two configurations are “close to each other” if, up to a translation, they “almost coincide” on a large fixed ball. The larger this ball, the more similar they are, and this induces a metric on the space of the corresponding dynamical systems. Our main result states that the map which sends a given configuration into the spectrum of its associated Hamiltonian, is Hölder (even Lipschitz) continuous in the usual Hausdorff metric. Specifically, the spectral distance of two Hamiltonians is estimated by the distance of the corresponding dynamical systems.

KW - spectrum location

KW - aperiodic Hamiltonians

KW - operator theory

U2 - 10.1007/s00023-019-00848-6

DO - 10.1007/s00023-019-00848-6

M3 - Journal article

VL - 20

SP - 3603

EP - 3631

JO - Annales Henri Poincare

JF - Annales Henri Poincare

SN - 1424-0637

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