The Berry-Keating operator on a lattice

Jens Bolte, Sebastian Egger, Keppeler Stefan

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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.
Original languageEnglish
Article number105201
Pages (from-to)1-17
Number of pages17
JournalJournal of Physics A: Mathematical and Theoretical
Volume50
Issue number10
Early online date10 Jan 2017
DOIs
Publication statusPublished - 2 Feb 2017

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