Quantum filter processes driven by Markovian white noises have classical versions

具有马尔可夫嵌入的连续监测非马尔可夫量子系统的物理约化随机方程

Physical Reduced Stochastic Equations for Continuously Monitored Non-Markovian Quantum Systems with a Markovian Embedding

本文针对具有马尔可夫嵌入的连续监测非马尔可夫量子系统，通过精确消除耦合随机微分方程中的非对角块，推导出仅含对角块的闭合约化随机方程，从而得到主系统约化条件态的随机Nakajima-Zwanzig型描述。

量子随机过程中的Ito-Stratonovich争论的解决

A Resolution of the Ito-Stratonovich Debate in Quantum Stochastic Processes

本文提出了一种量子噪声同质化方案，解决了乘法有色噪声驱动的量子随机过程中Ito-Stratonovich约定的歧义问题，通过重整化系数和修正项实现一致的马尔可夫极限。

Non-Markovian Quantum Feedback Networks II: Controlled Flows

The concept of a controlled flow of a dynamical system, especially when the controlling process feeds information back about the system, is of central importance in control engineering. In this paper we build on the ideas presented by Bouten and van Handel (L. Bouten, R. van Handel, "On the separation principle of quantum control", in Quantum Stochastics and Information: Statistics, Filtering and Control, World Scientific, 2008) and develop a general theory of quantum feedback. We elucidate the relationship between the controlling processes $Z$ and the measured process $Y$, and to this end mak…

二维湍流中傅里叶模的随机建模

Stochastic modeling of Fourier modes in two-dimensional turbulence via filtered white noise

本文通过滤波白噪声建模二维湍流的傅里叶模，发现典型时间相关长度并提出随机模型，利用直接数值模拟比较被动示踪物的输运与随机模型的有效扩散。

Transport of a quantum particle in a time-dependent white-noise potential

We show that a quantum particle in $\mathbb{R}^d$, for $d \geq 1$, subject to a white-noise potential, moves super-ballistically in the sense that the mean square displacement $\int \|x\|^2 \langle ρ(x,x,t) \rangle ~dx$ grows like $t^{3}$ in any dimension. The white noise potential is Gaussian distributed with an arbitrary spatial correlation function and a delta correlation function in time. This is a known result in one dimension (see refs. Fischer, Leschke, Müller and Javannar, Kumar}. The energy of the system is also shown to increase linearly in time. We also prove that for the same white…

The Rotating-Wave Approximation: Consistency and Applicability from an Open Quantum System Analysis

We provide an in-depth and thorough treatment of the validity of the rotating-wave approximation (RWA) in an open quantum system. We find that when it is introduced after tracing out the environment, all timescales of the open system are correctly reproduced, but the details of the quantum state may not be. The RWA made before the trace is more problematic: it results in incorrect values for environmentally-induced shifts to system frequencies, and the resulting theory has no Markovian limit. We point out that great care must be taken when coupling two open systems together under the RWA. Thou…