Distributional Modes for Scalar Field Quantization

We propose a mode-sum formalism for the quantization of the scalar field based on distributional modes, which are naturally associated with a slight modification of the standard plane-wave modes. We show that this formalism leads to the standard Rindler temperature result, and that these modes can be canonically defined on any Cauchy surface.     

Berezin quantization of gauged WZW and coset models

Gauged WZW and coset models are known to be useful to prove holomorphic factorization of the partition function of WZW and coset models. In this note we show that these gauged models can be also important to quantize the theory in the context of the Berezin formalism. For gauged coset models Berezin quantization procedure also admits a further holomorphic factorization in the complex structure of the moduli space.This work is dedicated to Professor Michel Ryan on the occasion of his 60th birthday.     

Fractional Brownian Motion and Sheet as White Noise Functionals

In this short note, we show that it is more natural to look the fractional Brownian motion as functionals of the standard white noises, and the fractional white noise calculus developed by Hu and Фksendal follows directly from the classical white noise functional calculus. As examples we prove that the fractional Girsanov formula, the Ito type integrals and the fractional Black-Scholes formula are easy consequences of their classical counterparts. An extension to the fractional Brownian sheet is also briefly discussed.     

环形激光陀螺随机误差测试中的计数误差

详细讨论了环形激光陀螺（RLG）误差测试中的计数误差。首先提出了在角度随机游走为主要误差源的情况下，RLG的离散输出模型。在假设累积角度量化误差为白噪声的前提下推导了方差（或AIlan方差）分析中的量化误差模型。接着指出白噪声假设并不总能成立，特别是对于由计数器只能计整数引致的量化误差（特称为“计数误差”），由于量化间隔很大，这一假设通常不能成立。最后，给出了一种白噪声假设不能成立时的处理方法及仿真数据分析结果。     

力学系统的扩散运动及量子化

研究位形由扩散过程定义的力学系统．利用变分的路径计算给出系统广义坐标表示的动力学方程，该方程连同连续方程描述系统量子波动随时间演化的概率进程．文末的表示定理指出，在满足适当正规条件的扩散过程和Ｓｃｈｒｄｉｎｇｅｒ方程的解（波函数）之间存在一一对应关系     

Edge agreement of second-order multi-agent system with dynamic quantization via the directed edge Laplacian

This work explores the edge agreement problem of second-order multi-agent systems with dynamic quantization under directed communication. To begin with, by virtue of the directed edge Laplacian, we propose a model reduction representation of the closed-loop multi-agent system depending on the spanning tree subgraph. Considering the limitations of the finite bandwidth channels, the quantization effects of second-order multi-agent systems under directed graph are considered. The static quantizers generally contain a fixed quantization interval and infinite quantization level, which are, to some extent, inefficient and impractical. To further reduce the bit depth (number of bits available) and to obtain better precision, the dynamic quantized communication strategy referring to zooming in-zooming out scheme is required. Based on the reduced model associated with the essential edge Laplacian, the asymptotic stability of second-order multi-agent systems under dynamic quantized effects with only finite quantization level can be guaranteed. Finally, the simulation of altitude alignment of micro air vehicles is provided to verify the theoretical results.     

Distributed subgradient method for multi‐agent optimization with quantized communication

This paper focuses on a distributed optimization problem associated with a time‐varying multi‐agent network with quantized communication, where each agent has local access to its convex objective function, and cooperatively minimizes a sum of convex objective functions of the agents over the network. Based on subgradient methods, we propose a distributed algorithm to solve this problem under the additional constraint that agents can only communicate quantized information through the network. We consider two kinds of quantizers and analyze the quantization effects on the convergence of the algorithm. Furthermore, we provide explicit error bounds on the convergence rates that highlight the dependence on the quantization levels. Finally, some simulation results on a l₁‐regression problem are presented to demonstrate the performance of the algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

悬链曲面上的点粒子动力学及扩展空间约束系统量子化

扩张型正则量子化方案的核心内容是位置、动量以及哈密顿量同时量子化. 通过分析悬链面上粒子的扩张型正则量子化方案, 并且与薛定谔理论进行比较, 发现内禀几何中二维悬链面给不出与薛定谔理论相一致的结果, 而考虑将二维悬链面嵌入在三维欧氏空间之后, 还需要将正则量子化方案进行扩张, 可以得到体系的几何势能和几何动量, 并与薛定谔理论相一致.     

有限空间中经典场的正则量子化

从离散的角度研究带边界的1+1维经典标量场和Dirac场的正则量子化问题. 与以往不同的是, 这里将时间和空间两个变量同时进行变步长的离散, 应用变步长离散的变分原理, 得到离散形式的运动方程、边界条件和能量守恒的表达式. 然后, 根据Dirac理论, 将边界条件当作初级约束, 将边界条件和内在约束统一处理. 研究表明, 采用此方法, 不仅在每个离散的时空格点上能够建立起Dirac括号, 从而可以完成该模型的正则量子化;而且, 该方法还保持了离散情况下的能量守恒.