爱因斯坦-朗之万源关联在封闭非相对论系统中的研究
Einstein--Langevin source correlations in closed non-relativistic systems
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- Center for Gravitational Wave Experiment, National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences（中国科学院力学研究所微重力国家实验室引力波实验中心）
- Key Laboratory of Gravitational Wave Precision Measurement of Zhejiang Province, Hangzhou Institute for Advanced Study, UCAS（浙江大学引力波精密测量重点实验室杭州高等研究院（中国科学院大学））
- Taiji Laboratory for Gravitational Wave Universe (Beijing/Hangzhou), University of Chinese Academy of Sciences (UCAS)（中国科学院大学太极引力波宇宙实验室（北京/杭州））
- National Space Science Center, Chinese Academy of Sciences（中国科学院国家空间科学中心）
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中文总结 AI 辅助
本文研究封闭非相对论系统中爱因斯坦-朗之万源关联，区分源协方差与物质通道，证明其与迪奥西-彭罗斯模型不同，并分析退相干指数及无信号性。
中文摘要 AI 辅助
随机半经典引力通过爱因斯坦-朗之万噪声核来表示应力-能量涨落。我们考察了其在指定的、粒子数守恒的封闭非相对论源下的牛顿投影，并将源协方差与约化物质通道区分开来。连通单粒子协方差是依赖于状态的，并且不同于迪奥西-彭罗斯模型中假设的普适势噪声定律。为了将源谱与退相干联系起来，我们定义了一个独立的静态探针，该探针服从规定的高斯噪声定律。对于孤立非简并本征态中的有限方差源算符，完整的连通谱测度在零附近存在一个间隙。探针退相干指数因此是有界的，其长时间斜率趋于零。相反，平稳双重态可以携带静态或低频谱线，而指定的自由扩散高斯源给出有限的极限指数。连续谱结果依赖于制备、归一化、红外正则化以及极限的顺序。我们还比较了相干和非相干多体制备，并确立了固定经典噪声通道的无信号性。这些结果确定了将源涨落与物质退相干模型联系起来所需的空间、时间和动力学假设。它们并不排除在其他粒子数守恒的非相对论制备中的马尔可夫极限。
英文摘要
Stochastic semiclassical gravity represents stress--energy fluctuations through the Einstein--Langevin noise kernel. We examine its Newtonian projection for specified closed, particle-number-conserving non-relativistic sources and distinguish the source covariance from a reduced matter channel. The connected one-particle covariance is state dependent and differs from the universal potential-noise law postulated in the Diósi--Penrose model. To relate the source spectrum to dephasing, we define a separate static probe subject to a prescribed Gaussian noise law. For a finite-variance source operator in an isolated non-degenerate eigenstate, the full connected spectral measure has a gap around zero. The probe dephasing exponent is then bounded and its long-time slope vanishes. Stationary doublets can instead carry static or low-frequency spectral lines, while a specified freely spreading Gaussian source gives a finite limiting exponent. Continuum results depend on preparation, normalisation, infrared regularisation and the order of limits. We also compare coherent and incoherent many-body preparations and establish no-signalling for fixed classical-noise channels. These results identify the spatial, temporal and dynamical assumptions needed to relate source fluctuations to a matter-decoherence model. They do not exclude Markovian limits in other number-conserving non-relativistic preparations.
