The Berry-Keating operator on a lattice. / Bolte, Jens; Egger, Sebastian; Stefan, Keppeler.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 50, No. 10, 105201, 02.02.2017, p. 1-17.

Research output: Contribution to journalArticlepeer-review

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The Berry-Keating operator on a lattice. / Bolte, Jens; Egger, Sebastian; Stefan, Keppeler.

In: Journal of Physics A: Mathematical and Theoretical, Vol. 50, No. 10, 105201, 02.02.2017, p. 1-17.

Research output: Contribution to journalArticlepeer-review

Harvard

Bolte, J, Egger, S & Stefan, K 2017, 'The Berry-Keating operator on a lattice', Journal of Physics A: Mathematical and Theoretical, vol. 50, no. 10, 105201, pp. 1-17. https://doi.org/10.1088/1751-8121/aa5844

APA

Bolte, J., Egger, S., & Stefan, K. (2017). The Berry-Keating operator on a lattice. Journal of Physics A: Mathematical and Theoretical, 50(10), 1-17. [105201]. https://doi.org/10.1088/1751-8121/aa5844

Vancouver

Bolte J, Egger S, Stefan K. The Berry-Keating operator on a lattice. Journal of Physics A: Mathematical and Theoretical. 2017 Feb 2;50(10):1-17. 105201. https://doi.org/10.1088/1751-8121/aa5844

Author

Bolte, Jens ; Egger, Sebastian ; Stefan, Keppeler. / The Berry-Keating operator on a lattice. In: Journal of Physics A: Mathematical and Theoretical. 2017 ; Vol. 50, No. 10. pp. 1-17.

BibTeX

@article{99df613cc5114534b4963c83acc4123e,
title = "The Berry-Keating operator on a lattice",
abstract = "We construct and study a version of the Berry-Keating operator corresponding to a classical Hamiltonian on a compact phase space, which we choose to be a two-dimensional torus. The operator is a Weyl quantisation of the classical Hamiltonian for an inverted harmonic oscillator, producing a difference operator on a finite, periodic lattice. We investigate the continuum and the infinite-volume limit of our model in conjunction with the semiclassical limit. Using semiclassical methods, we show that only a specific combination of the limits leads to a logarithmic mean spectral density as it was anticipated by Berry and Keating.",
author = "Jens Bolte and Sebastian Egger and Keppeler Stefan",
year = "2017",
month = feb,
day = "2",
doi = "10.1088/1751-8121/aa5844",
language = "English",
volume = "50",
pages = "1--17",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "1751-8113",
publisher = "IOP Publishing Ltd.",
number = "10",

}

RIS

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T1 - The Berry-Keating operator on a lattice

AU - Bolte, Jens

AU - Egger, Sebastian

AU - Stefan, Keppeler

PY - 2017/2/2

Y1 - 2017/2/2

N2 - We construct and study a version of the Berry-Keating operator corresponding to a classical Hamiltonian on a compact phase space, which we choose to be a two-dimensional torus. The operator is a Weyl quantisation of the classical Hamiltonian for an inverted harmonic oscillator, producing a difference operator on a finite, periodic lattice. We investigate the continuum and the infinite-volume limit of our model in conjunction with the semiclassical limit. Using semiclassical methods, we show that only a specific combination of the limits leads to a logarithmic mean spectral density as it was anticipated by Berry and Keating.

AB - We construct and study a version of the Berry-Keating operator corresponding to a classical Hamiltonian on a compact phase space, which we choose to be a two-dimensional torus. The operator is a Weyl quantisation of the classical Hamiltonian for an inverted harmonic oscillator, producing a difference operator on a finite, periodic lattice. We investigate the continuum and the infinite-volume limit of our model in conjunction with the semiclassical limit. Using semiclassical methods, we show that only a specific combination of the limits leads to a logarithmic mean spectral density as it was anticipated by Berry and Keating.

U2 - 10.1088/1751-8121/aa5844

DO - 10.1088/1751-8121/aa5844

M3 - Article

VL - 50

SP - 1

EP - 17

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 10

M1 - 105201

ER -