Einstein--Langevin source correlations in closed non-relativistic systems
Abstract
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.
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BibTeX
@misc{xu2026einsteinlangevin,
title = {{Einstein--Langevin source correlations in closed non-relativistic systems}},
author = {Peng Xu and Li-E Qiang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02980},
eprint = {2610.02980},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02980},
}
RIS
TY - UNPB
TI - Einstein--Langevin source correlations in closed non-relativistic systems
AU - Peng Xu
AU - Li-E Qiang
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.02980
UR - https://arxiv.org/abs/2610.02980
AB - 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.
ER -