AI 中文总结
研究泊松自发局域化模型的非马尔可夫版本，通过典型时间尺度$\tau_C$推导出长时间统计动力学，借助CPTP映射$\Phi_t$，经超累积量展开获无时间卷积主方程，刻画给定初始量子态时的坍缩事件过程。
AI 中文摘要
自发坍缩模型通过修改标准量子动力学为测量问题提供了一种可能的解决方案。修改包括添加诱导波函数在空间中坍缩的非线性和随机项。这些模型的非马尔可夫版本是出于物理原因、现象学一致性以及相对论扩展的潜力。本文研究了泊松自发局域化（PSL）模型的非马尔可夫版本，即一个以瞬时和局域坍缩事件为特征的模型。假设模型由典型时间尺度$\tau_C$表征，对于$t = 0$时标准量子物质的初始状态$\rho_0$，我们根据CPTP映射$\Phi_t$推导出有效的长时间（$t\gg \tau_C$）统计动力学。然后展示如何使$\Phi_t$等于非马尔可夫CSL模型得到的结果。此外，给定$\Phi_t$，通过超累积量展开获得相关的无时间卷积主方程。最后，在$t = 0$时给定初始量子态$\rho_0$，刻画坍缩事件过程（对于$t \gg \tau_C$的事件）。
英文摘要
Spontaneous collapse models provide a possible solution to the measurement problem by modifying standard quantum dynamics. The modification consists of adding non-linear and stochastic terms inducing wavefunction collapse in space. Non-Markovian versions of these models are motivated by physical reasons, phenomenological consistency, and potential for relativistic extensions. Here, we investigate a non-Markovian version of the Poissonian Spontaneous Localization (PSL) model, i.e., a model characterized by instantaneous and localized collapse events. We assume that our model is characterized by a typical time scale $τ_C$ so that, given an initial state $ρ_0$ of standard quantum matter at time $t=0$, we derive an effective long-time ($t\gg τ_C$) statistical dynamics in terms of a CPTP map $Φ_t$. We then show how $Φ_t$ can be made equal to that obtained by non-Markovian CSL models. Moreover, given $Φ_t$, we obtain the associated time-convolutionless master equation by means of a supercumulant expansion. Finally, we characterize the collapse events process (for events with $t \gg τ_C$) given an initial quantum state $ρ_0$ at $t=0$.
Comments8 pages plus appendices
