Tests of Quantum Gravity-Induced Non-Locality: Hamiltonian formulation of a non-local harmonic oscillator

Abstract

Motivated by the development of on-going optomechanical experiments aimed at constraining non-local effects inspired by some quantum gravity scenarios, the Hamiltonian formulation of a non-local harmonic oscillator, and its coupling to a cavity field mode(s), is investigated. In particular, we consider the previously studied model of non-local oscillators obtained as the non-relativistic limit of a class of non-local Klein-Gordon operators, $f(\square )$, with $f$ an analytical function. The results of previous works, in which the interaction was not included, are recovered and extended by way of standard perturbation theory. At the same time, the perturbed energy spectrum becomes available in this formulation, and we obtain the Langevin's equations characterizing the interacting system.

7+3 pages, 2 figures. This version matches the published one

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Cited by in corpus (6)

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• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Quantum gravitational decoherence of a mechanical oscillator from spacetime fluctuations
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• Quantum gravity inspired nonlocal quantum dynamics preserving the classical limit
• Classifying deviation from standard quantum behavior using Kullback Leibler divergence