Radiation-spin interaction, Gilbert damping, and spin torque

Magnetization relaxation processes, which are represented by the Gilbert damping term and the spin torque term in the Landau-Lifshitz-Gilbert (LLG) equation, are described by the radiation-spin interaction (RSI), where the radiation field is produced by magnetization precessional motion itself. It is shown that the LLG equation including the Gilbert damping term and the spin torque term is derived from the spin Hamiltonian containing the RSI. The derivation of the LLG equation is given in a self-consistent method. It is also shown that, according to RSI, the magnitude of the magnetization vector deviates from the magnetization saturation with the order of O(alpha(2)), where alpha is the Gilbert damping parameter.     

Monte Carlo Simulation of Stochastic Differential Equation to Study Information Geometry

Information Geometry is a useful tool to study and compare the solutions of a Stochastic Differential Equations (SDEs) for non-equilibrium systems. As an alternative method to solving the Fokker–Planck equation, we propose a new method to calculate time-dependent probability density functions (PDFs) and to study Information Geometry using Monte Carlo (MC) simulation of SDEs. Specifically, we develop a new MC SDE method to overcome the challenges in calculating a time-dependent PDF and information geometric diagnostics and to speed up simulations by utilizing GPU computing. Using MC SDE simulations, we reproduce Information Geometric scaling relations found from the Fokker–Planck method for the case of a stochastic process with linear and cubic damping terms. We showcase the advantage of MC SDE simulation over FPE solvers by calculating unequal time joint PDFs. For the linear process with a linear damping force, joint PDF is found to be a Gaussian. In contrast, for the cubic process with a cubic damping force, joint PDF exhibits a bimodal structure, even in a stationary state. This suggests a finite memory time induced by a nonlinear force. Furthermore, several power-law scalings in the characteristics of bimodal PDFs are identified and investigated.     

稀磁半导体(Ga,Mn)As薄膜激光诱导超快磁化动力学过程拟合方法探究

本文对稀磁半导体(Ga, Mn)As薄膜中超快激光诱导磁化动力学响应信号的不同拟合方法进行了对比分析. 通过Landau-Lifshitz-Gilbert(LLG)方程的数值拟合发现, 由于薄膜平面内和平面外磁光响应强度不同, 磁矢量三维进动的叠加可以导致多个频率振动模式的假象. 当使用高于(Ga, Mn)As带边的能量激发时, 磁化进动的磁光响应信号中叠加着来自光极化载流子的响应, 此时单纯利用LLG方程对薄膜整体磁化动力学过程拟合应谨慎使用. 本工作为正确分析和理解脉冲激光对(Ga, Mn)As铁磁性的超快调控提供了拟合方法上的指导.     

受驱动光学系统多光子量子统计理论(Ⅰ)——Fokker-Planck方程和良腔情况

我们应用广义Wigner分布的Fokker-Planck方程的系统方法,研究了受驱动光学系统的多光子跃迁过程。得到多光子过程普遍的Fokker-Planck方程、态方程以及良腔情况下透射光谱公式。计算了n光子双稳态的透射光谱并与单光子情况进行比较。还证明了在良腔情况,对于多光子过程,原子-原子关联也可以忽略。 关键词：     

吸收和色散混合受驱动光学系统多光子FPE和稳态方程

应用广义Wigner分布的Fokker-Planck方程的系统方法,研究了混合吸收和色散特征的受驱动光学系统的多光子跃迁过程。得到多光子、混合型Fokker-Plauck方程和稳态方程。并讨论了稳态方程的性质。 关键词：     

Analysis of price fluctuations in futures exchange markets

We show that the fluctuations of the tick-by-tick logarithmic price in a futures market can be described in terms of the Fokker-Planck equation (FPE). We calculate the corresponding drift and diffusion coefficients and argue that these values can contain some information pertaining to the market state. It is particularly showed that the Korean treasury bond (KTB) futures is well described by a FPE and has a similar structure to turbulence.     

基于小关联时间两相湍流色噪声的近似模型及数值模拟

从一般高斯型色噪声模型出发,通过泛函导数,应用小关联时间,近似计算多维色噪声,得到有效Fokker-Planck方程.将其应用到两相湍流中得到颗粒相的概率密度函数输运方程,从而得到颗粒相的二阶矩模型.将颗粒应力方程简化成代数方程,建立代数应力模型.将对流扩散方程的有限分析法运用到求解两相流模型中,对壁面两相射流进行数值模拟,并将求解结果与实验结果进行对比分析.     

Relationship between a non-Markovian process and Fokker–Planck equation

We demonstrate the equivalence of a non-Markovian evolution equation with a linear memory-coupling and a Fokker–Planck equation (FPE). In case the feedback term offers a direct and permanent coupling of the current probability density to an initial distribution, the corresponding FPE offers a non-trivial drift term depending itself on the diffusion parameter. As the consequence the deterministic part of the underlying Langevin equation is likewise determined by the noise strength of the stochastic part. This memory induced stochastic behavior is discussed for different, but representative initial distributions. The analytical calculations are supported by numerical results.     

System Driven by Correlated Gaussian Noises Related with Disorder

A system driven by correlated Gaussian noises related with disorder is investigated. The Fokker-Planck equation （FPE） for the system is derived. Using the FPE derived, some systems driven by correlated Gaussian noises related with disorder can be investigated for Brownian motors, nonequilibrium transition, resonant activation, stochastic resonance, and so on. We only give one example： i.e., using the FPE derived, we study the resonant activation for a single motor protein model with correlated noises related to disorder. Since the correlated noise related to disorder usually exists with the friction, for the temperature, and so on, our results have generic physical meanings for physics, chemistry, biology and other sciences.     

Fick's law and Fokker-Planck equation in inhomogeneous environments

In inhomogeneous environments, the correct expression of the diffusive flux is not always given by the Fick's law Γ=−D∇n. The most general hydrodynamic equation modelling diffusion is indeed the Fokker-Planck equation (FPE). The microscopic dynamics of each specific system may affect the form of the FPE, either establishing connections between the diffusion and the convection term, as well as providing supplementary terms. In particular, the Fick's form for the diffusion equation may arise only in consequence of a specific kind of microscopic dynamics. It is also shown how, in the presence of sharp inhomogeneities, even the hydrodynamic FPE limit may becomes inaccurate and mask some features of the true solution, as computed from the Master equation.     

Out-of-Plane Torque Influence on Magnetization Switching and Susceptibility in Magnetic Multilayers

Based on both the spin diffusion equation and the Landau-LlTshitz-Gilbert （LLG） equation, we demonstrate the influence of out-of-plane spin torque on magnetization switching and susceptibility in a magnetic multilayer system. The variation of spin accumulation and local magnetization with respect to time are studied in the magnetization reversal induced by spin torque. We also research the susceptibility subject to a microwave magnetic field, which is compared with the results obtained without out-of-plane torque.     

关于状态分立系统的改进的Metropolis方法

对状态分立系统的平衡态统计问题给出了一个改进的Metropolis方法,并在伊辛模型上与传统方法进行了对比,得到了一致的结果,效率提高了约25%.针对伊辛模型的抽样过程给出了其马尔科夫过程所对应的Master方程.将所提出的方法应用于伊辛模型,相当于对其Master方程进行了模拟.作为推广,一大类临界动力学模型的Master方程都可以用本方法进行模拟,以用于其暂态过程的研究.     

THE OPERATOR METHOD FOR SOLVING THE MOMENT EQUATION OF FOKKER-PLANCK EQUATION

In this paper we study the moment equation of Fokker-Planck equation (FPE) , by using the translation operator and the technique of the exponential operator decomposition. Some results of the relaxation process described by FPE are obtained.     

Hybrid MC/RISM technique for simulation of polymer solutions: Monte Carlo+ RISM integral equations

A new (hybrid) method is reported for modelling complex macromolecular systems. The approach combines the traditional atomistic Monte Carlo (MC) computer simulation of flexible polymer chains with the numerical solution of the site-site Ornstein-Zernike-like (RISM) integral equations. The method is used for calculating properties of a linear polymer in dilute solution. Since the condensed-phase environment of a flexible macromolecule affects the equilibrium configuration probability distribution of the macromolecule, the site-site intramolecular correlation function and the intramolecular potential field are treated in a self-consistent manner. Briefly, the MC method is applied to generate the configurations of a single chain molecule. Using the coordinates of chain beads, the averaged intrapolymer correlation function is obtained. Then, solving the coupled RISM equations for a given density of solvent particles, we find the polymer-solvent correlation functions. This yields the medium-induced intrapolymer potential and the corresponding effective intramolecular energies, which are used in the standard Metropolis MC procedure. The structural properties of the polymer chain are computed by averaging over the statistically representative set of configurations. As a result of many such iterations, the intramolecular structure is determined self-consistently. Using the hybrid MC/RISM method, extensive studies have been made of static properties of flexible polymer chains surrounded by LJ particles with purely repulsive interactions between the particles and chain beads. Also, direct molecular dynamics simulations have been carried out and have demonstrated that the hybrid MC/RISM approach gives a quite accurate prediction for condensed-phase effects.     

Accurate and efficient Monte Carlo solutions to the radiative transport equation in the spatial frequency domain

We present an approach to solving the radiative transport equation (RTE) for layered media in the spatial frequency domain (SFD) using Monte Carlo (MC) simulations. This is done by obtaining a complex photon weight from analysis of the Fourier transform of the RTE. We also develop a modified shortcut method that enables a single MC simulation to efficiently provide RTE solutions in the SFD for any number of spatial frequencies. We provide comparisons between the modified shortcut method and conventional discrete transform methods for SFD reflectance. Further results for oblique illumination illustrate the potential diagnostic utility of the SFD phase-shifts for analysis of layered media.     

Exactly solvable Fokker-Planck equation with time-dependent nonlinear drift and diffusion coefficients – the Lie-algebraic approach

In this paper we have analytically solved the Fokker-Planck equation (FPE) associated with a fairly large class of multiplicative stochastic processes with time-varying nonliner drift and diffusion coefficients, which has wide applicability in various areas of physics, e.g. nonlinear optics and chemical reaction dynamics. By exploiting the dynamical symmetry of the FPE, we apply the Lie-algebraic approach to derive the time-dependent analytical closed-form solutions. The derived solutions fall into two different categories, namely (i) one with a moving absorbing boundary, and (ii) one with a fixed absorbing boundary at the origin, depending upon the model parameters. The corresponding escape (or survival) probabilities are also evaluated analytically. We believe that not only our analytically exact results can serve as standard models upon which the discussion of more complicated problems can be based, but they can also be useful as a benchmark to test approximate numerical or analytical procedures.     

Stationary and dynamical properties of finite N-unit Langevin models subjected to multiplicative noises

We have studied the finite N-unit Langevin model subjected to multiplicative noises, by using the augmented moment method (AMM), as a continuation of our previous paper [H. Hasegawa, J. Phys. Soc. Japan 75 (2006) 033001]. Effects of couplings on stationary and dynamical properties of the model have been investigated. The difference and similarity between the results of diffusive and sigmoid couplings are studied in details. Time dependences of average and fluctuations in local and global variables calculated by the AMM are in good agreement with those of direct simulations (DSs). We also discuss stationary distributions of local and global variables with the use of the Fokker–Planck equation (FPE) method and DSs. It is demonstrated that stationary distributions show much variety when multiplicative noise and external inputs are taken into account.     

海气随机气候模式及其应用

基于能量平衡气候模式,考虑了随机力对海-气相互作用的影响和不同时空尺度耦合的作用,将描写海温和气温交互作遥随机动力模式化为一个Fokker-Planck方程,然后用矩阵连分法进行求解,并对CO     

High-temperature expansion for nonequilibrium steady states in driven lattice gases

We develop a controlled high-temperature expansion for nonequilibrium steady states of the driven lattice gas, the "Ising model" for nonequilibrium physics. We represent the steady state as P(eta) alpha e(-betaH(eta)-psi(eta)) and evaluate the lowest order contribution to the nonequilibrium effective interaction psi(eta). We see that, in dimensions d > or = 2, all models with nonsingular transition rates yield the same summable psi(eta), suggesting the possibility of describing the state as a Gibbs state similar to equilibrium. The models with the Metropolis rule show exceptional behavior.