Stochastic spikes and Poisson Approximation of one-dimensional stochastic differential equations with applications to continuously measured Quantum Systems

泊松量子轨迹中的尖峰现象

Spikes in Poissonian quantum trajectories

本研究证明泊松噪声量子轨迹中也会出现尖峰现象，通过分析三种破坏非破坏性的情形，利用随机重置等效性给出了尖峰与跳跃的完整统计，并辅以数值验证。

量子轨道中的尖峰

Spikes in quantum trajectories

受到强连续监控的量子系统经历量子跳跃。这一众所周知的事实隐藏着一个被忽视的微妙之处：即使在测量速率非常大的极限下，跳跃过程也总是受到标度不变的剧烈波动的修饰。这篇文章致力于定量研究这些剩余的波动，我们称之为尖峰，并讨论他们的物理状态。我们首先介绍一个经典模型，其中这些波动的起源更直观，然后跳到量子领域，它们的存在不那么直观。我们计算了连续监测量子比特的尖峰的精确分布。最后，我们讨论其物理和业务相关性。

Stochastic spikes and strong noise limits of stochastic differential equations

Motivated by studies of indirect measurements in quantum mechanics, we investigate stochastic differential equations with a fixed point subject to an additional infinitesimal repulsive perturbation. We conjecture, and prove for an important class, that the solutions exhibit a universal behavior when time is rescaled appropriately: by fine-tuning of the time scale with the infinitesimal repulsive perturbation, the trajectories converge in a precise sense to spiky trajectories that can be reconstructed from an auxiliary time-homogeneous Poisson process. Our results are based on two main tools. T…

Vlasov-Poisson方程谱方法的反对称与保正性构造

Anti-symmetric and Positivity Preserving Formulation of a Spectral Method for Vlasov-Poisson Equations

本研究针对一维Vlasov-Poisson方程提出一种基于对称加权Hermite基谱展开、中心有限差分和隐式Runge Kutta积分的离散格式，证明其保反对称结构与稳定性，推导两种形式的守恒律并通过多类基准问题验证。