Several approaches to quantum gravity lead to nonlocal modifications of fields’ dynamics. This, in turn, can give rise to nonlocal modifications of quantum mechanics at non-relativistic energies. Here, we analyze the nonlocal Schrödinger evolution of a quantum harmonic oscillator in one such scenario, where the problem can be addressed without the use of perturbation theory. We demonstrate that although deviations from standard quantum predictions occur at low occupation numbers, where they could potentially be detected or constrained by high-precision experiments, the classical limits of quantum probability densities and free energy remain unaffected up to energies comparable with the nonlocality scale. These results provide an example of nonlocal quantum dynamics compatible with classical predictions, suggesting massive quantum objects as a promising avenue for testing some phenomenological aspects of quantum gravity.

中文翻译：

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量子引力启发非局域量子动力学保持经典极限


量子引力的几种方法导致场动力学的非局部修改。反过来，这可以引起量子力学在非相对论能量下的非局域修改。在这里，我们分析了在这种情况下量子谐振子的非局域薛定谔演化，该问题可以在不使用微扰理论的情况下得到解决。我们证明，尽管在低占据数时会出现与标准量子预测的偏差，它们可能会被高精度实验检测到或限制，但量子概率密度和自由能的经典极限在与非定域尺度相当的能量范围内仍然不受影响。这些结果提供了与经典预测兼容的非局域量子动力学的例子，表明大质量量子物体是测试量子引力的某些现象学方面的有希望的途径。