Exact Large Deviation Functional of a Stationary Open Driven Diffusive System: The Asymmetric Exclusion Process

We consider the asymmetric exclusion process (ASEP) in one dimension on sites i=1,...,N, in contact at sites i=1 and i=N with infinite particle reservoirs at densities _a and _b . As _a and _b are varied, the typical macroscopic steady state density profile ¯(x), x[a,b], obtained in the limit N=L(b–a), exhibits shocks and phase transitions. Here we derive an exact asymptotic expression for the probability of observing an arbitrary macroscopic profile , so that is the large deviation functional, a quantity similar to the free energy of equilibrium systems. We find, as in the symmetric, purely diffusive case q=1 (treated in an earlier work), that is in general a non-local functional of (x). Unlike the symmetric case, however, the asymmetric case exhibits ranges of the parameters for which is not convex and others for which has discontinuities in its second derivatives at (x)=¯(x). In the latter ranges the fluctuations of order in the density profile near ¯(x) are then non-Gaussian and cannot be calculated from the large deviation function.     

Why Do the Quantum Observables Form a Jordan Operator Algebra?

The Jordan algebra structure of the bounded real quantum observables was recognized already in the early days of quantum mechanics. While there are plausible reasons for most parts of this structure, the existence of the distributive nonassociative multiplication operation is hard to justify from a physical or statistical point of view. Considering the non-Boolean extension of classical probabilities, presented in a recent paper, it is shown in this paper that such a multiplication operation can be derived from certain properties of the conditional probabilities and the observables, i.e., from postulates with a clear statistical interpretation. The well-known close relation between Jordan operator algebras and C*-algebras then provides the connection to the quantum-mechanical Hilbert space formalism, thus resulting in a novel axiomatic approach to general quantum mechanics that includes the types II and III von Neumann algebras.     

Stationary Coverage of a Stochastic Adsorption–Desorption Process with Diffusional Relaxation

We show that it is possible to derive the stationary coverage of an adsorption–desorption process of dimers with diffusional relaxation with a very simple ansatz for the stationary distribution of the process supplemented by a hypothesis of global balance. Our approach is compared to the exact result and we seek to understand its validity within an instance of the model.     

Stationary Scattering Theory for a Charged Particles Transport Problem

We consider a nonautonomous transport problem, the modelization of the charge exchange dynamics in a monoatomic ionized gas, and apply scattering theory to its dynamics. The free dynamics corresponds to the evolution of the total distribution of particles (neutral plus ionized particles) and the perturbed dynamics corresponds to the evolution of the neutral particles, which is the solution of a nonautonomous transport problem. The existence of the time-dependent wave operators was proved by the first author. In the present paper we follow Howland's formalism in constructing a stationary scattering theory for this nonautonomous transport problem by studying the evolution equation. We prove the existence of the wave operators and by using the smooth perturbation technique we obtain the similarity between perturbed and unperturbed operators.     

Stationary states for a mechanical system with stochastic boundary conditions

We consider a system of Newtonian particles, with a long-range repulsive pair potential, moving in a cavity whose surface temperature is spatially varying. When a particle hits the surface, it is thermalized at the temperature of the collision point. We prove that this system has a unique stationary ensemble, to which any initial distribution converges for large times. We show that this stationary ensemble depends continuously on the surface temperature profile.     

经高斯函数光滑的Wigner算符的性质

鉴于通常的Wigner算符是不正定的,我们提出将其经过以参数k表征的高斯函数光滑以后的广义Wigner算符,在证明其正定和完备性以后,将它发展为量子光场密度算符及其经典对应的新理论,特别地当k=1时,它退化为了在相干态表象中的p-表示.     

Conversion of Gyrotron Output into a Gaussian Beam Using the Far-Field

A compact system to convert gyrotron output into an intense gaussian beam has been designed by introducing an intermediate focusing element into the quasi-optical system. The design is significantly simplified by applying gaussian optics and confirmed by application of the Huygens equation. The beam quality is improved by truncating the sidelobes of the far-field. In spite of the beam truncation, only a small fraction (11 %) of the beam power is sacrificed.     

Exact Stationary States of a Two-Dimensional Transport Model

Previous calculations of transport coefficients of particle systems in two or more dimensions have used computer simulations or various approximations, like those implicit in the Boltzmann equation or in the standard probability theory of diffusion. Here an exactly solved model of crystal growth in three dimensions is transformed into a 2D model of steady particle transport. Then the exact, many-body stationary distribution and exact transport coefficients can be found as well as correlation functions. The model is highly asymmetric. In the transverse direction, particles are strongly attracted, so that long transverse rows of particles tend to form at low temperature. Kinks in these rows are rare, so the transverse positions of kinks effectively move continuously on a large distance scale.     

短脉冲高斯光束的时空形式

考虑到腔模光腰尺寸的频率依赖性，得到了一短脉冲高斯光束在自由空间传播的时域解析形式，发现其可由一复时间变量来描述，复时间变量的实部给出了脉冲的传输时间，其与波前曲率有关，虚部给出了空间量值，两者的交叉项称为时空耦合，并对傅里叶变换极限脉冲和啁啾脉冲的时空形式作了分析。     

有源RLC介观电路量子化过程中幺正算符的选择

采用正则变换和正变换方法对有源RLC介观电路实现了量子化,通过构造几种不同形式的幺正算,对介观电路实施量子化的计算过程的比较分析,得到了构造幺正算符的最佳方案,该方案能够使正则变换与幺正变换的结果完全吻合。     

Fluctuations in the Weakly Asymmetric Exclusion Process with Open Boundary Conditions

We investigate the fluctuations around the average density profile in the weakly asymmetric exclusion process with open boundaries in the steady state. We show that these fluctuations are given, in the macroscopic limit, by a centered Gaussian field and we compute explicitly its covariance function. We use two approaches. The first method is dynamical and based on fluctuations around the hydrodynamic limit. We prove that the density fluctuations evolve macroscopically according to an autonomous stochastic equation, and we search for the stationary distribution of this evolution. The second approach, which is based on a representation of the steady state as a sum over paths, allows one to write the density fluctuations in the steady state as a sum over two independent processes, one of which is the derivative of a Brownian motion, the other one being related to a random path in a potential.     

Stationary diffusion over a multidimensional potential barrier: A generalization of Kramers' formula

We consider diffusion over a potential barrier forn degrees of freedom. Generalizing the procedure of Kramers, we find a quasistationary solution to the associated Fokker-Planck equation. This yields an expression for the diffusion current over the barrier and, finally, a simple and elegant generalization of Kramers' formula for the diffusion rate.On leave from the Institute of Atomic Energy, Academia Sinica, Peking, People's Republic of China.     

多模海森堡代数的算符恒等式

利用算符代数中的分析方法,得到了多模海森堡(Heisenberg)代数中的BCH公式和压缩算符的展开式。     

Design of a Quasi-Optical System to Convert TE0n Mode Outputs of a Gyrotron into Gaussian Beams

In this paper we present a novel design of a quasi-optical system for conversion of gyrotron outputs into gaussian beams. It consists of a quasi-optical antenna, four focusing mirrors (parabolic cylinders) and a filter which removes the side lobes of the beam. The system is capable to convert three TE_0n mode outputs into gaussian beams with waist size of 16.7 mm as well as four TE_1n mode outputs into bi-gaussian beams with waist size of 10.9 mm in width and 16.5 mm in length.     

RLC串联电路暂态过程时间常数的测量与修正

本文分析了RLC串联电路暂态过程时间常数τ的实验测量值与理论值偏差的原因,以频率为振荡频率的正弦波代替欠阻尼振荡波,测出电路电容和电感上的损耗电阻,对时间常数的理论值进行修正,可使τ的理论修正值与实验测量值基本吻合。     

Time Jitters in Multiple-Core Fiber

Property of soliton propagation is analyzed by using self-companying operator method in every core of multiple-core fiber. The results show that the time jitters of soliton transmission in every core relate to the relative phase among the input solitons in multiple-core fiber.     

On Spectral Analysis of an Integral-Difference Operator

A complete spectral analysis of an integral-difference operator arising as a collision operator in some nonequilibrium statistical physics models is presented. Eigenfunctions of both discrete and continuous spectrum are constructed.     

Weighted Estimations from a Conjugate Operator

In this Letter we develop a general procedure leading from a Mourre-type estimation for a given self-adjoint operator H to a Hardy-type weighted inequality. We use this method in order to prove exponential decay for eigenvectors of a large class of perturbations of operators of convolution with bounded analytic functions.     

非共振条件下高斯光束斜入射法布里-珀罗干涉仪的透射特性

基于多光束干涉原理,研究了当高斯光束的载波频率与法布里—珀罗(F P)干涉仪的谐振频率存在偏差(即非共振)时,高斯光束斜入射F P干涉仪的透射特性。结果表明,与共振情况相比,非共振条件下透射光束的峰值强度及其所对应的位置、以及光斑的大小随入射角的变化都发生了显著的改变。     

Condensation in the Zero Range Process: Stationary and Dynamical Properties

The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between particles. We rigorously prove that for the stationary probability measure there is a background phase at some critical density and for large system size essentially all excess particles accumulate at a single, randomly located site. Using random walk arguments supported by Monte Carlo simulations, we also study the dynamics of the clustering process with particular attention to the difference between symmetric and asymmetric jump rates. For the late stage of the clustering we derive an effective master equation, governing the occupation number at clustering sites.