Correlation functions for the diffusive motion of particles in a periodic potential

The diffusive motion of particles in a one-dimensional periodic potential is treated using the Fokker-Planck equation method. First, a concise form of the Fokker-Planck equation and of the correlation function for this problem is set up. By expanding the distribution function into suitable eigenfunctions, a general method for calculating the correlation functions is then given. Finally, explicit calculations are presented for the velocity correlation functions, some of these are compared with those which were obtained by continued fraction methods.     

Exciton-polariton absorption in periodic and disordered quantum-well chains

The exciton-polariton transfer and absorption in regular and disordered structures with a finite number of quantum wells are studied theoretically. The transfer matrix method is invoked in the exciton resonance region to calculate the reflectivity, transmissivity, and absorptivity spectra, as well as the integrated absorptivity as a function of the γ/Γ₀ ratio of the parameters of nonradiative and radiative damping of quasi-two-dimensional excitons. It is shown that the integrated absorptivity as a function of γ (temperature) follows a universal pattern, more specifically, it increases monotonically from zero at γ = 0 to saturate at γ/Γ₀ ? 1. Because the exciton-polariton absorption being single mode, the integrated absorptivity in Bragg quantum-well structures is substantially lower than that in short-period structures, in which absorption involves the whole spectral multitude of modes. The intrawell disorder associated with fluctuations in the frequencies of exciton excitation in quantum wells enhances the integrated absorptivity to the level typical of light absorption with no resonance among excitons of different quantum wells. The interwell disorder originating from fluctuations in quantum-well separation likewise leads to an increase in the integrated absorptivity.     

Bloch analysis of finite periodic microring chains

We apply Bloch analysis to the study of finite periodic cascading of microring resonators. Diagonalization of the standard transfer matrix approach not only allows one to find an exact analytic expression for transmission and reflection, but also to derive a closed form solution for the field in every point of the structure. To gain more physical insight we have analyzed the main features of the transmission resonances in a finite chain and we have given some hints for their experimental verification . PACS 42.70.Qs; 42.82.Gw; 42.60.Da     

Taming chaotic solitons in Frenkel-Kontorova chains by weak periodic excitations

We have proposed theoretically and confirmed numerically the possibility of controlling chaotic solitons in damped, driven Frenkel-Kontorova chains subjected to additive bounded noise by weak periodic excitations. Theoretically, we obtained an effective equation of motion governing the dynamics of the soliton center of mass for which we deduced Melnikov's method-based predictions concerning the regions in the control parameter space where homoclinic bifurcations are frustrated. Numerically, we found that such theoretical predictions can be reliably applied to the original Frenkel-Kontorova chains, even for the case of localized application of the soliton-taming excitations, and there is strikingly good agreement between analytical estimates and numerical results.     

周期型二元颗粒链中孤波传播的二体碰撞近似分析

本文运用二体碰撞近似理论研究了孤波在周期型二元颗粒链中的传播. 周期型二元颗粒链由N个大球和一个小球交替排列而成, 球的材质都相同. 将小球和与之相邻的大球等效成一个球, 形成一条等效链. 采用二体碰撞近似理论, 推导了孤波在颗粒链中传播的速度、通过颗粒链时间以及小球的振荡频率. 理论分析得到小球振荡频率随着半径的增大而减小, 该结果与计算机模拟结果符合得相当好. 二体碰撞近似理论给出的波通过整条颗粒链时间, 在N ≤ 2时与计算机模拟结果符合得很好. 理论计算的误差随链长的变化不大. 但随着N的增大, 理论得到的结果相对误差变大.     

Correlation functions in the Itzykson-Zuber model

Then-point function for the integral over unitary matrices with Itzykson-Zuber measure is reduced to the integral over the Gelfand-Tzetlin table; the integrand (for genericn) is given by linear exponential times the rational function. Forn=2 and in some cases forn>2 later in fast is the polynomial and this allows to give an explicit and simple expression for all 2-point and a set ofn-point functions. For the most generaln-point function a simple linear differential equation is constructed.     

Unstable and exact periodic solutions of three-particles time-dependent FPU chains

For lower dimensional Fermi–Pasta–Ulam(FPU) chains, the α-chain is completely integrable and the Hamiltonian of the β-chain can be identified with the H′enon–Heiles Hamiltonian. When the strengths α, β of the nonlinearities depend on time periodically with the same frequencies as the natural angular frequencies, the resonance phenomenon is inevitable. In this paper, for certain periodic functions α(t) and β(t) with resonance frequencies, we give the existence and stability of some nontrivial exact periodic solutions for a one-dimensional αβ-FPU model composed of three particles with periodic boundary conditions.     

Almost periodic functions on connected locally compact groups

Some automatic continuity conditions for almost periodic functions on connected Lie groups and connected locally compact groups are discussed.     

Correlation functions and computer simulations

If the equilibrium properties of a statistical system are obtained by solving numerically the associated Langevin equation describing the approach to equilibrium, the connected correlation functions can be computed directly with small effort and high precision.     

Plasmonic modes in periodic metal nanoparticle chains: a direct dynamic eigenmode analysis

We demonstrate an efficient eigendecomposition method for analyzing the guided modes in metal nanoparticle chains. The proposed method has the advantage of simultaneously showing the dispersion relation and the mode quality. It can also separate the material properties from the geometrical properties. Its efficiency therefore does not depend on the complexity of the material polarizability. We used the method to analyze the guided modes of a single and a pair of metal nanoparticle chains. The rigorous dynamic dipole polarizability typically gives a redshift compared with the results obtained from the broadly used quasi-static dipole polarizability with radiation correction.