Langevin equation with multi-Poissonian noise

A general master equation is shown to be equivalent to a Langevin equation whose noise is expressed as a linear superposition of Poissonian random variables (multi-Poissonian noise). As typical examples, a birth and death process and a Boltzmann-Langevin equation are given.     

The validity of nonlinear Langevin equations

In the presence of internal noise the variables describing a system are intrinsically stochastic. If they constitute a Markov process the expansion enables one to extract a deterministic macroscopic equation and to compute the fluctuations in successive approximations. In the lowest or linear noise approximation the fluctuations can be represented by a Langevin equation, provided it is handled appropriately. Higher orders cannot be described by any white noise Langevin equation. The question whether the equation has to be interpreted according to Itô or Stratonovich concerns these higher orders, for which the equation is not valid anyway.     

The mechanism of complex Langevin simulations

We discuss conditions under which expectation values computed from a complex Langevin processZ will converge to integral averages over a given complex-valued weight function. The difficulties in proving a general result are pointed out. For complex-valued polynomial actions, it is shown that for a process converging to a strongly stationary process one gets the correct answer for averages of polynomials ifc (k) E(e^ikZ()) satisfies certain conditions. If these conditions are not satisfied, then the stochastic process is not necessarily described by a complex Fokker-Planck equation. The result is illustrated with the exactly solvable complex frequency harmonic oscillator.     

Solving Langevin equation with the bicolour rooted tree method

Stochastic differential equations, especially the one called Langevin equation, play an important role in many fields of modern science. In this paper, we use the bicolour rooted tree method, which is based on the stochastic Taylor expansion, to get the systematic pattern of the high order algorithm for Langevin equation. We propose a popular test problem, which is related to the energy relaxation in the double well, to test the validity of our algorithm and compare our algorithm with other usually used algorithms in simulations. And we also consider the time-dependent Langevin equation with the Ornstein-Uhlenbeck noise as our second example to demonstrate the versatility of our method.     

Non-Markovian Diffusion Over a Saddle with a Generalized Langevin Equation

The diffusion over a simple parabolic barrier is exactly solved with a non-Markovian Generalized Langevin Equation. For a short relaxation time, the problem is shown to be similar to a Markovian one, with a smaller effective friction. But for longer relaxation time, the average trajectory starts to oscillate and the system can have a very fast first passage over the barrier. For very long relaxation times, the solution tends to a zero-friction limit. PACS: 02.50.EY, 05.40.−a, 25.70.Jj     

Diffusion described with quantum Langevin equation in tilted periodic potential

In this paper, diffusion behavior of Brownian particles moving in a 1D periodic potential landscape has been theoretically investigated by using the general quantum Langevin equation. At first, in the condition of weak disorder, some anomalous diffusive behaviors have been revealed in the process. Then, two types of mean square displacement, ensemble averaged and time averaged mean square displacement, have been investigated in a long time, and the weak ergodicity breaking phenomenon has been revealed. It is shown that the general quantum Langevin equation can exhibit some novel details of the experimental diffusion process.     

异质二聚体反应中心的电荷转移过程

在低温的状态下,类球红细菌内天然叶绿素的反应中心发生的电荷分离对激发波长有较弱的依赖性,而这种依赖可能来源于分子内电荷转移态。我们采用表现出更多的电荷转移态性质的突变叶绿素为反应中心,对这种电荷分离过程中的激发波长依赖和温度依赖的性质做了进一步的研究。研究发现:突变的异质二聚体存在的两种激发态(定域的激发态与分子内电荷转移态)是相互强耦合的,在突变的分子异质二聚体中形成的电荷转移态并不是电荷分离的有效途径。随着温度的降低,异质二聚体的活性降低,从而电荷分离产率下降。     

Fractional generalized Langevin equation approach to single-file diffusion

Fractional generalized Langevin equation with external force is used to model single-file diffusion. It is found that for external force that varies with power law the solution for such a fractional Langevin equation gives the correct short and long time behavior for the mean square displacement of single-file diffusion when appropriate choice of parameters associated with fractional generalized Langevin equation are used. By considering some special cases of the fractional generalized Langevin equation, a new class of closed analytic expressions for the mean square displacement of single-file diffusion can be obtained. The effective Fokker-Planck equation associated with single-file diffusion is briefly considered.     

巯基丙酸分子对CdSe核壳量子点和 ZnO纳米粒子薄膜之间电荷转移的影响

通过稳态光谱和时间分辨荧光光谱研究了巯基丙酸(MPA)分子对由量子点到ZnO纳米粒子薄膜的电荷转移过程的影响。研究发现,相对于CdSe纳米粒子薄膜样品,没有MPA分子参与作用的CdSe/ZnO薄膜样品和有MPA分子连接的CdSe/MPA/ZnO薄膜样品中都存在从CdSe量子点到ZnO纳米粒子薄膜的有效电荷分离过程,但是相对于CdSe/ZnO样品, CdSe/MPA/ZnO样品中电荷转移速率明显变小。这表明MPA分子本身它并不能促进CdSe到ZnO电荷分离过程,因此可以认为用金属氧化物薄膜直接吸附量子点吸收材料,将能获得高功率转换效率的量子点敏化太阳能电池。     

Temperature dependent fission fragment distribution in the Langevin equation

The temperature dependent width of the fission fragment distributions was simulated in the Langevin equation by taking two-parameter exponential form of the fission fragment mass variance at scission point for each fission event. The result can reproduce experimental data well, and it permits to make reliable estimate for unmeasured product yields near symmetry fission.     

Langevin representation of Coulomb collisions for bi-Maxwellian plasmas

Langevin model corresponding to the Fokker–Planck equation for bi-Maxwellian particle distribution functions is developed. Rosenbluth potentials and their derivatives are derived in the form of triple hypergeometric functions. The Langevin model is tested in the case of relaxation of the proton temperature anisotropy and implemented into the hybrid expanding box model. First results of this code are presented and discussed.     

Stochastic equations of the Langevin type under a weakly dependent perturbation

Asymptotic expansions for the probability density of the solution of a stochastic differential equation under a weakly dependent perturbation are proposed. In particular, linear partial differential equations for the first two terms of the correlation time expansion are derived. It is shown that in these expansions the boundary layer part appears and non-Gaussianity of the perturbation is important for the Fokker-Planck approximation correction.     

耦合系统的朗之万动力学产生法

提出一种朗之万动力学方法获取处于热平衡态耦合系统内部振子坐标,数值模拟了单端固定简谐振子链的时间演化行为,并将其平衡性质与解析解进行了比较.结果表明了朗之万动力学方法的有效性.推广应用于非简谐四次方型耦合系统,模拟得到振子的四次方均坐标,与理论值验证;以模拟结果作为样本点计算哈密顿量,其能量分布与Boltzmann分布相符.     

Temperature dependent fission fragment distribution in the Langevin equation

The temperature dependent width of the fission fragment distributions was simulated in the Langevin equation by taking two-parameter exponential form of the fission fragment mass variance at scission point for each fission event. The result can reproduce experimental data well, and it permits to make reliable estimate for unmeasured product yields near symmetry fission.     

Langevin equation for self-organized morphologies of thin heteroepitaxial films

The self-organization of nanostructures on strained epitaxial films is expressed as a Langevin equation obtained from an atomistic model of the growth kinetics. The transition rules are based on the incorporation of strain effects into environment-dependent detachment barriers. Comparisons are made with a previous approach based on continuum elasticity to provide an atomistic interpretation of the governing equation for the morphological evolution of strained films.     

Probing Electron Transfer in DNA – New Life Science with Muons

Using the method of labelled electrons with muons which was first applied to conducting polymers and recently extended to representative electron-transfer proteins, electron transfer phenomena in DNA were successfully studied, for the first time microscopically. The characteristic dependence of muon spin relaxation on inverse magnetic field between 80 and 4000 G strongly suggests an existence of topological one-dimensional (1D) electron transfer along the DNA strands in both A- and B-forms. The low-field behavior, on the other hand, showed remarkable dependence on the molecular conformations. This revised version was published online in August 2006 with corrections to the Cover Date.     

Novel perturbation expansion for the Langevin equation

We discuss the randomly driven systemdx/dt= -W(x) +f(t), wheref(t) is a Gaussian random function or stirring force withf(t)f(t)=2(t–t), andW(x) is of the formgx ¹⁺². The parameter is a measure of the nonlinearity of the equation. We show how to obtain the correlation functionsx(t)f(t)···x(t( n)) _f as a power series in. We obtain three terms in the expansion and show how to use Padé approximants to analytically continue the answer in the variable. By using scaling relations, we show how to get a uniform approximation to the equal-time correlation functions valid for allg and.     

Temporal breakdown and Borel resummation in the complex Langevin method

We reexamine the Parisi–Klauder conjecture for complex e^iθ/2?⁴$e^{i\theta /2}{?}^4$ measures with a Wick rotation angle 0≤θ/2≤π/2$0\le \theta /2\le \pi /2$ interpolating between Euclidean signature and Lorentzian signature. Our main result is that the asymptotics for short stochastic times t$t$ encapsulates information also about the equilibrium aspects. The moments evaluated with the complex measure and with the real measure defined by the stochastic Langevin equation have the same t→0$t\to 0$ asymptotic expansion which is shown to be Borel summable. The Borel transform correctly reproduces the time dependent moments of the complex measure for all t$t$, including their t→∞$t\to \infty$ equilibrium values. On the other hand the results of a direct numerical simulation of the Langevin moments are found to disagree from the ‘correct’ result for t$t$ larger than a finite t_c$t_c$. The breakdown time t_c$t_c$ increases powerlike for decreasing strength of the noise’s imaginary part but cannot be excluded to be finite for purely real noise. To ascertain the discrepancy we also compute the real equilibrium distribution for complex noise explicitly and verify that its moments differ from those obtained with the complex measure.