On First-order Corrections to the LSW Theory I: Infinite Systems

We present a new method to efficiently identify the first-order correction to the classical model by Lifshitz, Slyozov and Wagner (LSW). The latter describes the evolution of second phase particles embedded in a matrix during the last stage of a phase transformation and is valid in the regime of vanishing volume fraction of particles. We consider a statistically homogeneous (and thus infinite) system, where the first-order correction is of order ^1/2. The key idea is to relate the full system of particles to systems where a finite number of particles has been removed. This method decouples screening and correlation effects and allows to efficiently evaluate conditional expected values of the particle growth rates.     

Nonuniversality in Low-Volume-Fraction Ostwald Ripening

We study Ostwald ripening in the regime of small volume fraction and consider spatially periodic systems whose size is smaller than the screening length. Within the snapshot perspective we obtain an explicit characterization of the leading-order deviation to the classical mean-field theory by Lifshitz, Slyozov and Wagner (LSW). Using this representation, we show that the corrections are not universal, in the sense that the mean value has a strong dependence on geometry, and arbitrarily large fluctuations can happen with finite probability. AMS Subject classification: 35B27, 74N20, 82C26.     

The Becker-Döring equations at large times and their connection with the LSW theory of coarsening

A systematic procedure is given for obtaining the asymptotic late-time behavior of the Becker-Döring equations describing the time evolution of a population of clusters of particles. In lowest order of approximation, the distribution of the sizes of the largest clusters satisfies the equations of the Lifshitz-Slyozov-Wagner theory of coarsening.     

Heavy-ion scattering at low energies: First-order correction to the eikonal phase shift

The first-order non-eikonal correction has been applied to calculate heavy-ion reaction cross sections at low energies. The numerical investigations show that, for many heavy-ion systems, reaction cross sections and elastic scattering angular distributions thus calculated, are in good agreement with the optical model calculations.     

Weak-Coupling Theory for Semiclassical Periodically Driven Two-Level Systems: Beyond Rotating-Wave Approximation

We present a weak-coupling theory of semiclassical periodically driven two-level systems. The explicit analytical approximating solution is shown to reproduce highly accurately the exact results well beyond the regime of the rotating-wave approximation.     

On the dielectric properties of molecular crystals: II. First-order spatial dispersion and optical activity

The general formal expression for the wavevector- and frequency-dependent dielectric susceptibility tensor of a simple molecular crystal, derived in paper I, is applied to the case of a Bravais lattice with gyrotropic molecules. The dielectric susceptibility tensor is calculated with first-order spatial dispersion and from this an expression for the gyration tensor is derived. As an example the optical rotary power is calculated for light propagating along the optical axis of a gyrotropic tetragonal crystal.     

On the application of homogenization formalisms to active dielectric composite materials

The Maxwell Garnett and Bruggeman formalisms were applied to estimate the effective permittivity dyadic of active dielectric composite materials. The active nature of the homogenized composite materials (HCMs) arises from one of the component materials which takes the form of InAs/GaAs quantum dots. Provided that the real parts of the permittivities of the component materials have the same sign, the Maxwell Garnett and Bruggeman formalisms give physically plausible estimates of the HCM permittivity dyadic that are in close agreement. However, if the real parts of the permittivities of the component materials have different signs then there are substantial differences between the Bruggeman and Maxwell Garnett estimates. These differences are slightly less pronounced if the relative permittivity of the metallic component material is described by the extended version of the Drude formula appropriate to very small particles. However, these differences become enormous - with the Bruggeman estimate being physically implausible - as the imaginary parts of the permittivities of the component materials tend to zero.     

顶色辅助的人工色理论中荷电的Top介子在LC实验中对顶夸克产生的修正

讨论了顶色辅助的人工色理论预言的赝标量Goldstones粒子(TC介子和Top介子)在LC实验中对顶夸克产生的贡献,发现Top介子对顶夸克产生截面σ_tt的贡献是主要的,在大部分参数空间中荷电Top介子的贡献非常大.当取合理的参数时,荷电Top介子对的σ_tt贡献可以达到8%左右,能够被LC的实验探测到.     

The Duffing oscillator in the low-friction limit: Theory and analog simulation

By a joint use of theory and analog simulation the low-friction regime of the Duffing oscillator is explored. In the weak-temperature case it is shown that the low-friction regime, in turn, must be divided in two well-distinct subregimes. In the former one, characterized by the friction ranging from 2 ₀ ( ₀ is the harmonic frequency) up to a lower bound _T, the method of statistical linearization applies and a continued fraction procedure (CFP) generated by the Zwanzig-Mori projection techniques is shown to provide correct information for both the renormalized frequency of the oscillator and the corresponding line shape. The latter subregime, characterized by the friction ranging from = 0 to = _T , is fraught with the complete breakdown of the statistical linearization method. The CFP is shown to provide an incorrect picture of the line shape while suggesting a novel mean field approximation which is then proven analytically via an alternative method of calculation. This method consists of expressing the system in a form reminiscent of the model of Kubo's stochastic oscillator. By using this alternative approach we are in a position to account for the residual linewidth which is shown by the analog experiment to survive for 0.     

统一展开理论在激光系统中的应用

在统一展开理论的框架内，通过提高推导过程中的精度，得到了更精确的结果，且将其推广应用到激光系统中。具体研究两个激光模型，得到了它们的光强定态几率分布、光强平均值及相相对涨落，通过比较发现，本文所得到的结果明显的改善了用统一色噪声的似所得到的结果而与精确的数值结果和数值模拟结果符合更好。     

The Response of Glassy Systems to Random Perturbations: A Bridge Between Equilibrium and Off-Equilibrium

We discuss the response of aging systems with short-range interactions to a class of random perturbations. Although these systems are out of equilibrium, the limit value of the free energy at long times is equal to the equilibrium free energy. By exploiting this fact, we define a new order parameter function, and we relate it to the ratio between response and fluctuation, which is in principle measurable in an aging experiment. For a class of systems possessing stochastic stability, we show that this new order parameter function is intimately related to the static order parameter function, describing the distribution of overlaps between clustering states. The same method is applied to investigate the geometrical organization of pure states. We show that the ultrametric organization in the dynamics implies static ultrametricity, and we relate these properties to static separability, i.e., the property that the measure of the overlap between pure states is essentially unique. Our results, especially relevant for spin glasses, pave the way to an experimental determination of the order parameter function.     

Corrections to the density-functional theory electronic spectrum: copper phthalocyanine

A method for improving the electronic spectrum of standard Density-Functional Theory (DFT) calculations (i.e., LDA or GGA approximations) is presented, and its application is discussed for the case of the copper phthalocyanine (CuPc) molecule. The method is based on a treatment of exchange and correlation in a many-body Hamiltonian, and it leads to easy-to-evaluate corrections to the DFT eigenvalues. Self-interaction is largely corrected, so that the modified energy levels do not suffer from spurious crossings, as often encountered for CuPc in DFT, and they remedy the standard underestimation of the gap. As a specific example we study the sequence and position of the CuPc molecular orbitals, which are wrongly calculated by standard DFT, and show that they are correctly reproduced after our corrections are included. The suggested method is fast and simple and, while not as accurate as hybrid or semiempirical functionals for molecular levels, it can be easily applied to any local-orbital DFT approach, improving on several important limitations of standard DFT methods.     

On the derivation of quantum kinetic equations. II. Nonlocal Uehling-Uhlenbeck equation

The binary and triple collision terms of the quantum kinetic equation derived previously are analyzed in the weak coupling approximation. In this approximation the equation appears to be a nonlocal Markovian extension of the kinetic equation due to Uehling and Uhlenbeck. After linearization, its relationship with non-Markovian formulations found in the literature is studied.This investigation is part of the research program of the Stichting voor Fundamenteel Onderzoek der Materie (FOM), which is financially supported by the Nederlandse Organisatie voor Zuiver Wetenschappelijk Onderzoek (ZWO).     

Sine-Gordon Theory for the Equation of State of Classical Hard-Core Coulomb Systems. II. High-Temperature Expansion

We perform a high-temperature expansion of the grand potential of the restrictive primitive model of electrolytes in the frame of the extended sine-Gordon theory exposed in the companion paper. We recover a result already obtained by Stell an Lebowitz (J. Chem. Phys. 49, 3706 (1968)) by means of diagrammatic expansions.     

Asymptotic properties of coupled nonlinear langevin equations in the limit of weak noise. II: Transition to a limit cycle

We apply the singular perturbation technique, developed in the companion paper, to the study of the fluctuations at the onset of a limit cycle, both for the cases of a soft and a hard transition. The technique and results are illustrated on the Poincaré model (soft transition) and on the Van der Pol oscillator (hard transition).     

Anderson impurity model: Double occupancy contribution to the magnetic susceptibility

After solving the single Anderson impurity model (SIAM) within the non-crossing approximation with a finite Coulomb repulsion, U, and vertex corrections (NCAf²v), we focus on the magnetic susceptibility. Using the same diagrammatic expansion the susceptibility can be dressed with two factors, namely, the double state occupancy and the vertex corrections. In this work we analyse the effect of double occupancy on the dynamic and static susceptibility as a function of U and on the degeneracy of the total impurity angular moment, S.     

Calculation of optical properties within the Local Density Approximation to Density Functional Theory: application to palladium

We calculate the optical functions of Pd using the ab initio, all-electron Full Potential Linear Muffin Tin Orbital method within the framework of the Density Functional Theory in the Local Density approximation. We test, in the case of Pd, the convergence of the dielectric function and energy loss function in different energy ranges vs. the completeness of the basis and give a quantitative estimate of the accuracy. The present approach opens the possibility of extending the energy range where the optical functions can be calculated with good accuracy without increasing the computational effort. Received 4 September 2001     

Minimum-Integer Computation Finite Alphabet Message Passing Decoder: From Theory to Decoder Implementations towards 1 Tb/s

In Message Passing (MP) decoding of Low-Density Parity Check (LDPC) codes, extrinsic information is exchanged between Check Nodes (CNs) and Variable Nodes (VNs). In a practical implementation, this information exchange is limited by quantization using only a small number of bits. In recent investigations, a novel class of Finite Alphabet Message Passing (FA-MP) decoders are designed to maximize the Mutual Information (MI) using only a small number of bits per message (e.g., 3 or 4 bits) with a communication performance close to high-precision Belief Propagation (BP) decoding. In contrast to the conventional BP decoder, operations are given as discrete-input discrete-output mappings which can be described by multidimensional LUTs (mLUTs). A common approach to avoid exponential increases in the size of mLUTs with the node degree is given by the sequential LUT (sLUT) design approach, i.e., by using a sequence of two-dimensional Lookup-Tables (LUTs) for the design, leading to a slight performance degradation. Recently, approaches such as Reconstruction-Computation-Quantization (RCQ) and Mutual Information-Maximizing Quantized Belief Propagation (MIM-QBP) have been proposed to avoid the complexity drawback of using mLUTs by using pre-designed functions that require calculations over a computational domain. It has been shown that these calculations are able to represent the mLUT mapping exactly by executing computations with infinite precision over real numbers. Based on the framework of MIM-QBP and RCQ, the Minimum-Integer Computation (MIC) decoder design generates low-bit integer computations that are derived from the Log-Likelihood Ratio (LLR) separation property of the information maximizing quantizer to replace the mLUT mappings either exactly or approximately. We derive a novel criterion for the bit resolution that is required to represent the mLUT mappings exactly. Furthermore, we show that our MIC decoder has exactly the communication performance of the corresponding mLUT decoder, but with much lower implementation complexity. We also perform an objective comparison between the state-of-the-art Min-Sum (MS) and the FA-MP decoder implementations for throughput towards 1 Tb/s in a state-of-the-art 28 nm Fully-Depleted Silicon-on-Insulator (FD-SOI) technology. Furthermore, we demonstrate that our new MIC decoder implementation outperforms previous FA-MP decoders and MS decoders in terms of reduced routing complexity, area efficiency and energy efficiency.