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 nonrelativistic limit of a class of non-local Klein-Gordon operators, f, 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.
Belenchia A., Benincasa D., Marin F., Marino F., Ortolan A., Paternostro M., et al. (2019). Tests of quantum gravity-induced non-locality: Hamiltonian formulation of a non-local harmonic oscillator. CLASSICAL AND QUANTUM GRAVITY, 36(15), 155006 [10.1088/1361-6382/ab2c0a].
Tests of quantum gravity-induced non-locality: Hamiltonian formulation of a non-local harmonic oscillator
Paternostro M.Co-ultimo
Membro del Collaboration Group
;
2019-07-12
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 nonrelativistic limit of a class of non-local Klein-Gordon operators, f, 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.File | Dimensione | Formato | |
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