Tests of quantum gravity-induced non-locality: Hamiltonian formulation of a non-local harmonic oscillator
Tests of quantum gravity-induced non-locality: Hamiltonian formulation of a non-local harmonic oscillator
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DOI：
10.1088/1361-6382/ab2c0a
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发表时间：
2019-08-08
影响因子：
3.5
通讯作者：
Liberati, S.
中科院分区：
文献类型：
--
作者：
Belenchia, A.;Benincasa, D.;Liberati, S.
为了约束某些量子引力场景下的非局域效应，本文研究了非局域谐振子的哈密顿公式及其与腔场模式的耦合。特别地，我们考虑先前得到的非局部振子模型作为一类非局部Klein-Gordon算子f（平方）的非相对论性极限，f是解析函数。以前的工作结果，其中不包括相互作用，是恢复和推广的标准摄动理论。同时，在此公式中得到了扰动能谱，得到了表征相互作用系统的朗之万方程。
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, arc 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.