Delocalization of Slowly Damped Eigenmodes on Anosov Manifolds

We look at the properties of high frequency eigenmodes for the damped wave equation on a compact manifold with an Anosov geodesic flow. We study eigenmodes with damping parameters which are asymptotically close enough to the real axis. We prove that such modes cannot be completely localized on subsets satisfying a condition of negative topological pressure. As an application, one can deduce the existence of a ??strip?? of logarithmic size without eigenvalues below the real axis under this dynamical assumption on the set of undamped trajectories.     

Extended nature of coupled optical interface modes in Thue-Morse dielectric superlattices

We investigate coupled optical interface modes in Thue-Morse (TM) dielectric superlattices composed of two kinds of materials with frequency-dependent dielectric functions. Four basic transfer matrices are derived in the dielectric continuum approximation. By a standard matrix operation method, the trace map of the global transfer matrix in this configuration is obtained. Under Born-von Kármán boundary conditions, the frequency spectra are calculated and their branching rules together with the quartet property are elucidated. It is further proved rigorously that nearly all eigenmodes in this framework have extended nature. The quartet of the eigenmodes is illuminated analytically. The common features and pronounced differences compared with coupled optical interface modes in periodic and Fibonacci dielectric superlattices as well as with other collective elementary excitations in TM structures are also revealed. Received 24 September 2002 / Received in final form 11 January 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: gjin@nju.edu.cn     

Ab initio many-body treatment of the electronic structure of metals

We propose and apply a combination of an ab initio (band-structure) calculation with a many-body treatment including screening effects. We start from a linearized muffin-tin orbital (LMTO) calculation to determine the Bloch functions for the Hartree one-particle Hamiltonian, from which we calculate the static susceptibility and dielectric function within the standard random phase approximation (RPA). From the Bloch functions we obtain maximally localized Wannier functions, using a method proposed by Marzari and Vanderbilt. Within this Wannier basis all relevant one-particle and unscreened and screened Coulomb matrix elements are calculated. This yields a multi-band Hamiltonian in second quantization with ab initio parameters, for which screening has been taken into account within the simplest standard approximation. Then, established methods of many-body theory are used. We apply this concept to a simple metal, namely lithium (Li). Here the maximally localized Wannier functions turn out to be of the sp³-orbital kind. Furthermore, only the on-site contributions of the screened Coulomb matrix elements are relevant, and a generalized, four-band Hubbard model is justified. The screened on-site Coulomb matrix elements are considerably smaller than the band width because of which it is sufficient to calculate the selfenergy in weak-coupling approximation. We compare results obtained within the screened Hartree-Fock approximation (HFA) and within the second-order perturbation theory (SOPT) in the Coulomb matrix elements for Li and find that many-body effects are small but not negligible even for this simple metal.     

Spectral domain analysis of eigenmodes in a shielded multilayer coplanar waveguide for microwave and millimeter-wave integrated circuits

Coplanar waveguide has found increasing use in microwave and millimeter-wave integrated circuits, and a knowledge of its eigenmodes is very useful for circuit design. In this paper, we determine the dispersion properties of the eigenmodes in a shielded multilayer coplanar waveguide using the spectral domain approach. Numerical results of the propagation constants for different combinations of dielectric materials are presented to illustrate the behaviors of the eigenmodes.     

Dipolar correlations and the dielectric permittivity of water

The static dielectric properties of liquid and solid water are investigated within linear response theory in the context of ab initio molecular dynamics. Using maximally localized Wannier functions to treat the macroscopic polarization we formulate a first-principles, parameter-free, generalization of Kirkwood's phenomenological theory. Our calculated static permittivity is in good agreement with experiment. Two effects of the hydrogen bonds, i.e., a significant increase of the average local moment and a local alignment of the molecular dipoles, contribute in almost equal measure to the unusually large dielectric constant of water.     

Reaction matrix for Dirichlet billiards with attached waveguides

The reaction matrix of a cavity with attached waveguides connects scattering properties to properties of a corresponding closed billiard for which the waveguides are cut off by straight walls. On the one hand, this matrix is directly related to the S-matrix, on the other hand it can be expressed by a spectral sum over all eigenfunctions of the closed system. However, in the physically relevant situation where these eigenfunctions vanish on the impenetrable boundaries of the closed billiard, the spectral sum for the reaction matrix, as it was used before, fails to converge and does not reliably reproduce the scattering properties. We derive here a convergent representation of the reaction matrix in terms of eigenmodes satisfying Dirichlet boundary conditions and demonstrate its validity in the rectangular and the Sinai billiards.     

Magnetic response of planar dielectric rings

Magnetic response of a planar dielectric ring to an axially applied time-harmonic magnetic field is analyzed. We find the self-consistent distribution of the polarization current in the ring and its magnetic moment. It is shown that the magnetic moment exhibits multiple resonances corresponding to the excitation of different eigenmodes in the ring. The properties of the fundamental eigenmode are used to analyze the performance and limitations of an equivalent LCR circuit model.     

Chiral phase transition and Anderson localization in the instanton liquid model for QCD

We study the spectrum and eigenmodes of the QCD Dirac operator in a gauge background given by an instanton liquid model (ILM) at temperatures around the chiral phase transition. Generically we find the Dirac eigenvectors become more localized as the temperature is increased. At the chiral phase transition, both the low lying eigenmodes and the spectrum of the QCD Dirac operator undergo a transition to localization similar to the one observed in a disordered conductor. This suggests that Anderson localization is the fundamental mechanism driving the chiral phase transition. We also find an additional temperature dependent mobility edge (separating delocalized from localized eigenstates) in the bulk of the spectrum which moves toward lower eigenvalues as the temperature is increased. In both regions, the origin and the bulk, the transition to localization exhibits features of a 3D Anderson transition including multifractal eigenstates and spectral properties that are well described by critical statistics. Similar results are obtained in both the quenched and the unquenched case though the critical temperature in the unquenched case is lower. Finally we argue that our findings are not in principle restricted to the ILM approximation and may also be found in lattice simulations.     

线性电介质和中心对称光折变晶体界面表面波的研究

报道了中心对称光折变晶体与线性电介质界面表面波的形成及能量变化. 通过调节传播常数和波导参数的方法,可以得到非局域、振荡、局域三种类型的表面波. 波导参数和传播常数之差大于阈值时,线性电介质和中心对称光折变晶体界面可以形成局域表面波. 波导参数为正值时,局域表面波主要聚集在中心对称光折变晶体内,随着传播常数的增大,波能量随之单调递增,表面波可以稳定传播. 在给定的条件下,调节决定非线性作用强度的可变参量可以控制局域表面波模的阶数和传播波形. 关键词： 非线性光学 中心对称光折变晶体 表面波     

Statistics of the Jones matrix of fibers affected by polarization mode dispersion

We carry out a statistical characterization of Jones matrix eigenvalues and eigenmodes to gain deeper insight into recently proposed fiber models based on Jones matrix spectral decomposition. A set of linear dynamic equations for the Pauli coordinates of the Jones matrix is established. Using stochastic calculus, we determine the joint distribution of the retardation angle of the eigenmodes and, indirectly, their autocorrelation function. The correlation bandwidth of the eigenmodes is found to be radical2/3 that of the polarization mode dispersion vector. The results agree well with simulations performed with the standard retarded plate model.     

A dissipative network model with neighboring activation

We study the properties of spectrum and eigenstates of the Google matrix of a directed network formed by the procedure calls in the Linux Kernel. Our results obtained for various versions of the Linux Kernel show that the spectrum is characterized by the fractal Weyl law established recently for systems of quantum chaotic scattering and the Perron-Frobenius operators of dynamical maps. The fractal Weyl exponent is found to be ν ≈ 0.65 that corresponds to the fractal dimension of the network d ≈ 1.3. An independent computation of the fractal dimension by the cluster growing method, generalized for directed networks, gives a close value d ≈ 1.4. The eigenmodes of the Google matrix of Linux Kernel are localized on certain principal nodes. We argue that the fractal Weyl law should be generic for directed networks with the fractal dimension d < 2.     

介电界面系统的电-声子相互作用

本文应用体极化电荷和面极化电荷产生的宏观电势导出了极化本征矢量遵从的积分和微分方程。证明了极化本征矢量应按正文中的正交归一关系(18)归一化,并导出了双层界面系统的极化本征模的哈密顿量及其与荷电粒子相互作用哈密顿量的算符表示形式。证明了电子与P-偏振SO声子的相互作用可用电子与有效频率为ωeff,±SO的SO声子的相互作用耦合常数α±SO表征;电子与P-偏振LO声子相互作用在性质上是电子与它所在的介质的体LO声于的相互作用,但被面效应减弱了。     

Photonic Jet by a Near‐Unity‐Refractive‐Index Sphere on a Dielectric Substrate with High Index Contrast

Photonic jets are normally generated in transmission mode and are represented as a spatially localized high‐intensity region on the shadow side of a particle‐lens, with a background to medium refractive index contrast of 1.3–1.7 while illuminated by a plane wave. Here, a photonic jet is discovered in the opposing plane wave propagation direction and lies in the area in the upper boundary of a near‐unity refractive index sphere on a high refractive index dielectric substrate. The redistribution of the power flow is inhibited during the reflected wave passing the near‐unity refractive index sphere. This has led to a unique effect on the focus position and shape of the produced photonic jet in reflection mode which can be maximally maintained near the sphere regardless of the modulation of the refractive index for the dielectric substrate material.     

Plasmon spectroscopy of metallic nanoparticles above flat dielectric substrates

We numerically analyze the spectral properties of localized plasmon resonances in metal nanoparticles when these are above a dielectric substrate. This analysis is performed as a function of the various parameters involved in the problem (relative optical properties, particle-substrate separation, angle of incidence, etc.). It can be shown that from the spectral behavior of the resonance in the far field, information about particle near-field interactions can be obtained.     

外磁场作用下一维光子晶体的光传输特性

采用光学传输矩阵方法,研究了外磁场作用下一维光子晶体的光传输特性.在外磁场作用下,介质介电函数在回旋频率ω.附近受到强烈的调制,使组分材料的色散关系发生明显改变,导致光子晶体的能带发生变化,透射谱出现复杂结构.在光子带隙中出现窄通带,窄带中的光是局域的.这表明,在不改变光子晶体组分材料的条件下,可以通过改变外磁场的大小,调制光子晶体的能带及其光传输性质.     

Construction of maximally localized Wannier functions

We present a general method for constructing maximally localized Wannier functions. It consists of three steps: (i) picking a localized trial wave function, (ii) performing a full band projection, and (iii) orthonormalizing with the Löwdin method. Our method is capable of producing maximally localized Wannier functions without further minimization, and it can be applied straightforwardly to random potentials without using supercells. The effectiveness of our method is demonstrated for both simple bands and composite bands.     

Distribution of the Field of Whispering-Gallery Modes in a Radially Nonuniform Two-Layer Cylindrical Dielectric Resonator

We study eigenmodes of a radially nonuniform two-layer cylindrical dielectric resonator bounded by two perfectly conducting planes at its ends. Formulas for the electromagnetic-field components of the modes and the characteristic equation of the resonator made of anisotropic dielectrics and immersed in an anisotropic medium are obtained. Resonators with various whispering-gallery modes are studied numerically in the 8-mm wavelength range. The distributions of the axial field component of the eigenmodes over the radial coordinate are given for various values of the radius, dielectric permittivity, and loss tangent of the inner layer of the resonator. The influence of the inner-layer parameters on the behavior of field distribution over the radius and on the spectral and energy characteristics of the resonator are analyzed. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 7, pp. 622–632, July 2008.     

Propagation and stability of kinks in driven and damped nonlinear klein-gordon chains1

We consider the propagation of kinks in an elastic chain in a bistable or multistable potential under the action of a driving force [M. Büttiker and H. Thomas,Phys. Rev. A 37:235 (1988)]. Each element of the chain is subject to a damping force proportional to its velocity. We show that both the propagation velocity of the kinks as a function of the driving field, and the kink width as a function of propagation velocity, are determined by characteristic functions which depend only on the form of the potential. These functions can be found by considering a single particle moving in the upside-down potential of the chain. The general properties of these functions are studied and illustrated by several examples. The stability of these driven kinks is discussed. Interestingly, we find in addition to the expected discrete localized eigenmodes a two-dimensional continuum of oscillatory modes with a localized envelope.This paper will appear in a forthcoming issue of theJournal of Statistical Physics.     

Role of spatial mode function in the presence of two-atom events in a micromaser

In this paper, we discuss the effects of spatial mode function in an one-photon micromaser in the presence of two-atom events. It is shown that two-atom events allow us a possibility to study the effects of different cavity eigenmodes in a micromaser. We find that squeezing properties of the radiation field depend upon the parity (odd or even) and order (lower or higher) of cavity eigenmodes. For example, squeezing can be obtained for odd-order cavity eigenmodes which completely vanishes for even-order modes. Our results also show that effects similar to self-induced transparency are never obtained in the presence of two-atom events. Finally, we consider the effect of pump fluctuations and cavity losses in our system.