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arXiv · 1610.06472

The Berry-Keating operator on a lattice

Jens Bolte·Sebastian Egger·Stefan Keppeler
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Abstract

We construct and study a version of the Berry-Keating operator with a built-in truncation of the 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 a specific combination of the limits leads to a logarithmic mean spectral density as it was anticipated by Berry and Keating.

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Jens Bolte, Sebastian Egger, Stefan Keppeler. 2016-10-20. The Berry-Keating operator on a lattice. https://doi.org/10.1088/1751-8121%2Faa5844

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