发表机构
Université de Strasbourg, CNRS, Institut de Physique et Chimie des Matériaux de Strasbourg（斯特拉斯堡大学，法国国家科学研究中心，斯特拉斯堡材料物理与化学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究薛定谔-牛顿半经典引力模型中玻恩规则的动力学弛豫，发现波包有界或缓慢增长时弛豫发生，快速膨胀时偏离持续，数值模拟证实，为原始量子非平衡提供最小模型。
AI 中文摘要
我们研究了由薛定谔-牛顿方程描述的半经典引力模型中对玻恩规则的动力学弛豫。利用自引力波包的Gaussian变分解，结合Nelson的量子动力学随机表示，我们追踪了初始概率分布不同于$|\Psi|^2$的粒子系综的演化。当波包保持有界或随时间增长足够缓慢时，会发生对玻恩规则的弛豫（“量子平衡”）；相反，对于薛定谔-牛顿方程的快速膨胀解，对玻恩规则的偏离可以无限期持续。数值模拟证实了这一分析图像。这些结果表明，半经典自引力既可以促进也可以抑制向玻恩规则的弛豫，为Underwood和Valentini [Phys. Rev. D 92, 063531 (2015)]提出的原始量子非平衡提议提供了一个最小模型。
英文摘要
We investigate dynamical relaxation to the Born rule in a semiclassical gravity model described by the Schrödinger-Newton equations. Using a Gaussian variational solution for the self-gravitating wave packet, combined with Nelson's stochastic representation of quantum dynamics, we track the evolution of particle ensembles whose initial probability distribution differs from $|Ψ|^2$. Relaxation to the Born rule ("quantum equilibrium") occurs when the wave packet remains bounded, or grows sufficiently slowly in time; in contrast, for rapidly expanding solutions of the Schrödinger-Newton equations, deviations from the Born rule can persist indefinitely. Numerical simulations confirm this analytical picture. These results show that semiclassical self-gravity can either enable or inhibit relaxation towards the Born rule, providing a minimal model relevant to proposals of primordial quantum non-equilibrium, as suggested by Underwood and Valentini [Phys. Rev. D 92, 063531 (2015)].
