The Schrödinger–Newton (SN) model is a semi-classical theory in which, in addition to mutual attraction, massive quantum particles interact with their own gravitational fields. While there are many studies on the phenomenology of single particles, correlation dynamics in multipartite systems is largely unexplored. Here, we show that the SN interactions preserve the product form of the initial state of a many-body system, yet on average agreeing with classical mechanics of continuous mass distributions. This leads to a simple test of the model, based on verifying bipartite gravitational evolution towards non-product states. We show using standard quantum mechanics that, with currently accessible single-particle parameters, two masses released from harmonic traps get correlated well before any observable entanglement is accumulated. Therefore, the SN model can be tested with setups aimed at observation of gravitational entanglement with significantly relaxed requirements on coherence time. We also present a mixed-state extension of the model that avoids superluminal signaling.

中文翻译：

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薛定谔-牛顿模型中的相关性和信号传导


薛定谔-牛顿 （SN） 模型是一种半经典理论，其中除了相互吸引之外，大质量量子粒子还与它们自己的引力场相互作用。虽然有许多关于单粒子现象学的研究，但多部分系统中的相关动力学在很大程度上尚未得到探索。在这里，我们表明 SN 相互作用保留了多体系统初始状态的乘积形式，但平均而言与连续质量分布的经典力学一致。这导致了对模型的简单测试，基于验证向非乘积状态的二分引力演化。我们使用标准量子力学表明，使用目前可访问的单粒子参数，从谐波陷阱释放的两个质量在任何可观察到的纠缠累积之前就已经很好地相关了。因此，SN 模型可以使用旨在观测引力纠缠的装置进行测试，对相干时间的要求明显放宽。我们还提出了该模型的混合状态扩展，它避免了超光速信号传导。