Quenched Large Deviations for Interacting Diffusions in Random Media

The aim of the paper is to establish a large deviation principle (LDP) for the empirical measure of mean-field interacting diffusions in a random environment. The point is to derive such a result once the environment has been frozen (quenched model). The main theorem states that a LDP holds for every sequence of environment satisfying appropriate convergence condition, with a rate function that does not depend on the disorder and is different from the rate function in the averaged model. Similar results concerning the empirical flow and local empirical measures are provided.     

随机介质的相干背散射与局域化研究

研究了不同尺度参数和粒子浓度下的ZnO随机介质相干背散射强度的分布规律,采用时域有限差分法分析了不同浓度随机介质的光场能量空间分布,预测了随机激光器阈值的高低。结果表明:同一折射率的介质随着介质尺寸的增大,相干背散射的带宽变窄,局域化参量kl值相应增大,使得局域化程度呈较大幅度减弱趋势;并且随着介质浓度的增加,相干背散射的带宽变宽,局域化程度增强,阈值降低。相干背散射有着光子局域化的先期特征,现在已成为研究光子局域化出现与否的基本判断依据,对研究光子局域化以及随机激光器具有重要意义。     

磁电弹性体中螺型位错与唇口裂纹的相互作用

研究磁电弹性体中螺型位错与唇口裂纹的相互作用。结合Muskhelishvili方法和干扰技术, 在假定裂纹面具有不可渗透条件下得到磁电弹性体中由位错和唇口裂纹所诱导的应力场、电场和磁场的解析解。应用广义Peach-Koehler公式,得到作用在位错上的影像力。通过数值算例,得到场强度因子的变化规律及影像力和广义力随位错位置的变化规律。     

Self-Averaging of Wigner Transforms in Random Media

We establish the self-averaging properties of the Wigner transform of a mixture of states in the regime when the correlation length of the random medium is much longer than the wave length but much shorter than the propagation distance. The main ingredients in the proof are the error estimates for the semiclassical approximation of the Wigner transform by the solution of the Liouville equations, and the limit theorem for two-particle motion along the characteristics of the Liouville equations. The results are applied to a mathematical model of the time-reversal experiments for the acoustic waves, and self-averaging properties of the re-transmitted wave are proved.     

Diffusive Fluctuations for One-Dimensional Totally Asymmetric Interacting Random Dynamics

We study central limit theorems for a totally asymmetric, one-dimensional interacting random system. The models we work with are the Aldous–Diaconis–Hammersley process and the related stick model. The A-D-H process represents a particle configuration on the line, or a 1-dimensional interface on the plane which moves in one fixed direction through random local jumps. The stick model is the process of local slopes of the A-D-H process, and has a conserved quantity. The results describe the fluctuations of these systems around the deterministic evolution to which the random system converges under hydrodynamic scaling. We look at diffusive fluctuations, by which we mean fluctuations on the scale of the classical central limit theorem. In the scaling limit these fluctuations obey deterministic equations with random initial conditions given by the initial fluctuations. Of particular interest is the effect of macroscopic shocks, which play a dominant role because dynamical noise is suppressed on the scale we are working. Received: 4 October 2001 / Accepted: 12 March 2002     

On the Partial Connection Between Random Matrices and Interacting Particle Systems

In the last decade there has been increasing interest in the fields of random matrices, interacting particle systems, stochastic growth models, and the connections between these areas. For instance, several objects appearing in the limit of large matrices arise also in the long time limit for interacting particles and growth models. Examples of these are the famous Tracy-Widom distribution functions and the Airy₂ process.     

Boundary Driven Zero-Range Processes in Random Media

The stationary states of boundary driven zero-range processes in random media with quenched disorder are examined, and the motion of a tagged particle is analyzed. For symmetric transition rates, also known as the random barrier model, the stationary state is found to be trivial in absence of boundary drive. Out of equilibrium, two further cases are distinguished according to the tail of the disorder distribution. For strong disorder, the fugacity profiles are found to be governed by the paths of normalized α-stable subordinators. The expectations of integrated functions of the tagged particle position are calculated for three types of routes.     

Quantum Chaos,Random Matrices,and Irreversibility in Interacting Many-Body Quantum Systems

The Pauli master equation describes the statistical equilibration of a closed quantum system. Simplifying and generalizing an approach developed in two previous papers, we present a derivation of that equation using concepts developed in quantum chaos and random-matrix theory. We assume that the system consists of subsystems with strong internal mixing. We can then model the system as an ensemble of random matrices. Equilibration results from averaging over the ensemble. The direction of the arrow of time is determined by an (ever-so-small) coupling to the outside world. The master equation holds for sufficiently large times if the average level densities in all subsystems are sufficiently smooth. These conditions are quantified in the text, and leading-order correction terms are given.     

Perturbation of Transmission Matrices in Nonlinear Random Media

Random media with tailored optical properties are attracting burgeoning interest for applications in imaging, biophysics, energy, nanomedicine, spectroscopy, cryptography, and telecommunications. A key paradigm for devices based on this class of materials is the transmission matrix, the tensorial link between the input and the output signals, that describes in full their optical behavior. The transmission matrix has specific statistical properties, such as the existence of lossless channels, that can be used to transmit information, and are determined by the disorder distribution. In nonlinear materials, these channels may be modulated and the transmission matrix tuned accordingly. Here, the direct measurement of the nonlinear transmission matrix of complex materials is reported, exploiting the strong optothermal nonlinearity of scattering silica aerogel (SA). It is shown that the dephasing effects due to nonlinearity are both controllable and reversible, opening the road to applications based on the nonlinear response of random media.     

Long Term Behaviour of a Reversible System of Interacting Random Walks

This paper studies the long-term behaviour of a system of interacting random walks labelled by vertices of a finite graph. We show that the system undergoes phase transitions, with different behaviour in various regions, depending on model parameters and properties of the underlying graph. We provide the complete classification of the long-term behaviour of the corresponding continuous time Markov chain, identifying whether it is null recurrent, positive recurrent, or transient. The proofs are partially based on the reversibility of the model, which allows us to use the method of electric networks. We also provide some alternative proofs (based on the Lyapunov function method and the renewal theory), which are of interest in their own right, since they do not require reversibility and can be applied to more general situations.

     

Auto-correlation Properties of Scattering Light in Ultrasound-modulated Random Media

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Auto-correlation Properties of Scattering Light in Ultrasound-modulated Random Media

In this paper, the auto-correlation properties of scattering light in random media modulated by ultrasound were studied. The expression of temporal auto-correlation function of scattering light amplitude in the ultrasound-modulated media was presented. The results show that the auto-correlation function is modulated as the ultrasound is introduced into the media and the modulation amplitude decays with correlation time. The influences of ultrasound amplitude, Brownian diffusion coefficient, scattering and absorption coefficients on auto-correlation function were discussed. The auto-correlation imaging of an object hidden in random media was also studied by the use of Monte Carlo simulations.     

A Solvable Model of Interface Depinning in Random Media

We study the mean-field version of a model proposed by Leschhorn to describe the depinning transition of interfaces in random media. We show that evolution equations for the distribution of forces felt by the interface sites can be written directly for an infinite system. For a flat distribution of random local forces the value of the depinning threshold can be obtained exactly. In the case of parallel dynamics (all unstable sites move simultaneously), due to the discrete character of the interface heights allowed in the model, the motion of the center of mass is non-uniform in time in the moving phase close to the threshold, and the mean interface velocity vanishes with a square-root singularity.     

本征态的局域化与增益介质中局域态的放大

用时域有限差分方法(FDTD)模拟了二维增益、非增益随机介质中的光学现象。在非增益介质中，观察到了局域态空间分布及其频率特征。在增益介质中，观察到局域态的放大过程。模拟结果显示非增益介质中的局域态相当于传统激光腔的腔模，随机激光是由局域态谐振产生的。     

A Pearson Random Walk with Steps of Uniform Orientation and Dirichlet Distributed Lengths

A constrained diffusive random walk of n steps in ℝ ^d and a random flight in ℝ ^d , which are equivalent, were investigated independently in recent papers (J. Stat. Phys. 127:813, 2007; J. Theor. Probab. 20:769, 2007, and J. Stat. Phys. 131:1039, 2008). The n steps of the walk are independent and identically distributed random vectors of exponential length and uniform orientation. Conditioned on the sum of their lengths being equal to a given value l, closed-form expressions for the distribution of the endpoint of the walk were obtained altogether for any n for d=1,2,4. Uniform distributions of the endpoint inside a ball of radius l were evidenced for a walk of three steps in 2D and of two steps in 4D.