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。     

具有随机节点结构的复杂网络同步研究

针对具有随机节点结构的复杂网络, 研究其同步问题. 基于Lyapunov稳定性理论和线性矩阵不等式技术给出了复杂网络同步稳定的充分性条件, 该充分性条件不仅与复杂网络的状态时延有关, 还与节点结构的概率分布有关. 数值仿真表明本文方法的有效性. 关键词： 复杂网络 随机节点 同步稳定 时滞     

Generic replica symmetric field-theory for short range Ising spin glasses

Symmetry considerations and a direct, Hubbard-Stratonovich type, derivation are used to construct a replica field-theory relevant to the study of the spin glass transition of short range models in a magnetic field. A mean-field treatment reveals that two different types of transitions exist, whenever the replica number n is kept larger than zero. The Sherrington-Kirkpatrick critical point in zero magnetic field between the paramagnet and replica magnet (a replica symmetric phase with a nonzero spin glass order parameter) separates from the de Almeida-Thouless line, along which replica symmetry breaking occurs. We argue that for studying the de Almeida-Thouless transition around the upper critical dimension d = 6, it is necessary to use the generic cubic model with all the three bare masses and eight cubic couplings. The critical role n may play is also emphasized. To make perturbative calculations feasible, a new representation of the cubic interaction is introduced. To illustrate the method, we compute the masses in one-loop order. Some technical details and a list of vertex rules are presented to help future renormalisation-group calculations. Received 9 October 2001     

Random walks with imperfect trapping in the decoupled-ring approximation

We investigate random walks on a lattice with imperfect traps. In one dimension, we perturbatively compute the survival probability by reducing the problem to a particle diffusing on a closed ring containing just one single trap. Numerical simulations reveal this solution, which is exact in the limit of perfect traps, to be remarkably robust with respect to a significant lowering of the trapping probability. We demonstrate that for randomly distributed traps, the long-time asymptotics of our result recovers the known stretched exponential decay. We also study an anisotropic three-dimensional version of our model. We discuss possible applications of some of our findings to the decay of excitons in semiconducting organic polymer materials, and emphasize the crucial influence of the spatial trap distribution on the kinetics. Received 23 July 2001 / Received in final form 14 May 2002 Published online 13 August 2002     

Model-dependent nature of blowtorch effect on the escape and equilibration rates

We analyze the relaxation behavior of a bistable system when the background temperature profile is inhomogeneous due to the presence of a localized hot region (blowtorch) on one side of the potential barrier. Since the diffusion equation for inhomogeneous medium is model-dependent, we consider two physical models to study the kinetics of such system. Using a conventional stochastic method, we obtain the escape and equilibration rates of the system for the two physical models. For both models, we find that the hot region enhances the escape rate from the well where it is placed while it retards the escape rate from the other well. However, the value of the escape rate from the well where the hot region is placed differs for the two models while that of the escape rate from the other well is identical for both. This work, for the first time, gives a detailed report of the similarities and differences of the escape rates and, hence, exposes the common and distinct features of the two known physical models in determining the way the bistable system relaxes. Received 25 September 2001     

Unitary Correlations and the Fejér Kernel

Let M be a unitary matrix with eigenvalues t _j , and let f be a function on the unit circle. Define X _f (M)=f(t _j ). We derive exact and asymptotic formulae for the covariance of X _f and X _g with respect to the measures |(M)|²dM where dM is Haar measure and an irreducible character. The asymptotic results include an analysis of the Fejér kernel which may be of independent interest.     

Decay of the remanent magnetization in the asymmetric spin chain

The dynamics of the one-dimensional spin glass with asymmetric interactions between neighboring spins is considered. We confine ourselves to discrete couplings with values ±J. We show that the algebraic decay of the remanent magnetization of the infinite ±J-spin chain at zero temperature is only valid for symmetric couplings. Our analytical investigations as well as computer simulations show stretched exponential decay for any finite concentration of antisymmetric bonds. Thus, the asymmetric ±J-spin chain shows an asymmetry-induced phase transition at zero temperature.     

Diffusion from sessile droplets through membranes

We analyze diffusion from a periodic array of hemispherical droplets through a membrane. We find that the multiple sources do not interact strongly, even when the droplets are closely spaced, so that the flux through the membrane appears nearly additive.     

High-density properties of hard spheres within a modified Percus-Yevick theory: The role of thermodynamic consistency

Using an integral-equation approach based upon an approximation for the tail function, the equilibrium properties of a system of hard spheres are studied with special concern for the behavior in the region of close packing. The closure adopted is such that full, internal consistency is ensured in the thermodynamics of the model with respect to both the two zero-separation theorems as well as to the more standard virial and fluctuation routes to the equation of state. The scheme also makes use of the continuity properties of the tail function and of the cavity distribution function at contact. These properties are explictly tested in the low-density limit up to the fourth derivative. The theory generates an equilibrium branch bounded on the high-density side by a point corresponding to a packing fraction0.78, a value which closely matches Rogers' least upper bound for the densest packing of spheres. The pair structure of the fluid in the state of random close packing is also compared to the type of local order predicted by the theory at similar densities.     

Statistics of transfer matrices for disordered quantum thin metallic slabs

In the quantum transport problem of a tight-binding Anderson model, the statistics of eigenvalues for the transfer matrices of thin disordered slabs is studied. Numerical simulations indicate that the probability distribution of nearest neighbor eigenvalue spacing and the ₃ statistics have already become close to that of the Gaussian orthogonal ensemble for sample lengths of the order of the mean free path, provided that transverse localization effects are not important. An intuitive argument is given why this should occur independently of the size of the matrix. Therefore, good mixing of the channels is not essential for obtaining Gaussian orthogonal ensemble type statistics and universal conductance fluctuations.