Augmented Langevin approach to fluctuations in nonlinear irreversible processes

A Fokker-Planck equation derived from statistical mechanics by M. S. Green [J. Chem. Phys. 20:1281 (1952)] has been used by Grabertet al. [Phys. Rev. A 21:2136 (1980)] to study fluctuations in nonlinear irreversible processes. These authors remarked that a phenomenological Langevin approach would not have given the correct reversible part of the Fokker-Planck drift flux, from which they concluded that the Langevin approach is untrustworthy for systems with partly reversible fluxes. Here it is shown that a simple modification of the Langevin approach leads to precisely the same covariant Fokker-Planck equation as that of Grabertet al., including the reversible drift terms. The modification consists of augmenting the usual nonlinear Langevin equation by adding to the deterministic flow a correction term which vanishes in the limit of zero fluctuations, and which is self-consistently determined from the assumed form of the equilibrium distribution by imposing the usual potential conditions. This development provides a simple phenomenological route to the Fokker-Planck equation of Green, which has previously appeared to require a more microscopic treatment. It also extends the applicability of the Langevin approach to fluctuations in a wider class of nonlinear systems.     

Isospin effects of projectile fragmentation in a Boltzmann-Langevin approach

The iso spin effects of projectile fragmentation at intermediate energies are investigated using an iso spindependent Boltzmann-Langevin model.The collisions of mass-symmetric reactions including ~(58)Fe,~(58)Ni+~(58)Fe,and~(58)Ni at intermediate energies,in the 30 to 100 MeV/A range,are studied for different symmetry energies.Yield ratios of the isotopic,isobaric,and isotonic pairs of fragments from the intermediate-mass region using three symmetry energies are extracted as functions of the N/Z ratio of the composite systems in the entrance channel and the incident energies.It is found that the yield ratios are sensitive to symmetry energies,especially for neutron-rich systems,and the calculations using soft symmetry energy are closer to the experimental data.The iso spin effect is stronger for the soft symmetry energy,owing to the competition of the repulsive Coulomb force and the symmetry energy attractive force on the proton.For the first time,the splits are presented,revealing a transition from the iso spin equilibrium at lower energies to translucency at intermediate energies.The results show a degree of transparency in that intermediate mass fragments undergo a transition from dependence on the composite systems in the entrance channel to reliance on the projectile and target nuclei.     

Intrinsic fluctuations in explosive reactions

A reaction is called explosive when the amount of a reactant becomes infinite in a finite time. When the intrinsic stochastic character of the reaction is taken into account, the explosion time is a random quantity. We compute its probability distribution, or at least its average and variance, for various kinds of reactions. If a reaction is unstable, so that a reactant can either explode or disappear, one first has to compute the probability for an explosion to occur at all, and then the average explosion time. Finally, the same ideas are applied to more general Markov processes.     

A comment on chemical Langevin equations

It is noted that the diffusion Langevin stochastic sources in chemical reaction-diffusion theories should really arise from a stochastic source term added to the deterministic form of Fick's law. This gives rise to results for correlation functions which agree with those from stochastic master equations provided parameters are appropriately chosen.Some authors use the term Langevin force. Sinceg _i(x,t) is dimensionally not a force, we shall eschew this dangerous terminology.     

Dynamical consequences of a constraint on the Langevin thermostat in molecular cluster simulation

We investigate some unusual behaviour observed while performing molecular dynamics simulations of small molecular clusters using a constrained Langevin thermostat. Atoms appear to be thermalised to different temperatures that depend on their mass and on the total number of particles in the system. The deviation from the zeroth law of thermodynamics can be considerable for small systems of heavy and light particles. We trace this behaviour to the absence of thermal noise acting on the centre of mass of the system. This is demonstrated by solving the stochastic dynamics for the constrained thermostat and comparing the results with simulation data. By removing the constraint, the Langevin thermostat may be restored to its intended behaviour. We also investigate a Langevin thermostat constrained to have zero total force acting on its centre of mass, and find similar deficiencies.     

Return to thermal equilibrium by the solution of a quantum Langevin equation

A quantum-mechanical treatment of the evolution of an anharmonic oscillator coupled to a heat bath is given. It is shown that for a certain class of anharmonic potentials the heat bath drives the oscillator to an equilibrium state, close to the quantum Gibbs state associated to the potential. Thus a partial proof is provided for a conjecture of R. Benguria and M. Kac.This paper contains part of the author's Ph.D. work, done at the Institute for Theoretical Physics of Groningen State University, Groningen, the Netherlands.     

双喷注事件中单个喷注内部动力学起伏的蒙特卡洛研究

用蒙特卡洛方法研究了91.2GeV e⁺e^－碰撞产生的双喷注事件中单个喷注内部的动力学起伏.结果表明,喷注内部的动力学起伏的各向异性随着截断参数y_cut的变化而明显地改变.存在一个转变点,在该点处动力学起伏在纵横平面是各向异性的,而在横平面是各向同性的.由此得到了产生喷注的一个标度.     

Langevin dynamics of an interface near a wall

We study dynamical contact angles and precursor films using Langevin dynamics for SOS type models, near a wall which favors spreading. We first solve exactly the Gaussian model and discuss various asymptotic regimes. This is only appropriate to partial wetting. We then consider more general models. Using local equilibrium and scaling arguments, we derive the shape of the dynamical profile and the speed of the precursor film which exists when the spreading coefficient is strictly positive. Long-range potentials lead to a layered structure of the precursor film. We also consider the case of a meniscus in a capillary.     

Vacuum lightcone fluctuations in a dielectric

A model for observable effects of time modulated electromagnetic vacuum fluctuations is presented. The model involves a probe pulse which traverses a slab of nonlinear optical material with a nonzero second order polarizability. We argue that the pulse interacts with the ambient vacuum fluctuations of other modes of the quantized electric field, and these vacuum fluctuations cause variations in the flight time of the pulse through the material. The geometry of the slab of material defines a sampling function for the quantized electric field, which in turn determines that vacuum modes whose wavelengths are of the order of the thickness of the slab give the dominant contribution. Some numerical estimates are made, which indicate that fractional fluctuations in flight time of the order of 10⁻⁸$10^{-8}$ are possible in realistic situations. The model presented here is both an illustration of a physical effect of vacuum fluctuations occurring in a finite interval of time, and an analog model for the lightcone fluctuations predicted by quantum gravity.     

Derivation of a Fokker–Planck equation for generalized Langevin dynamics

A Fokker–Planck equation describing the statistical properties of Brownian particles acted upon by long-range stochastic forces with power-law correlations is derived. In contrast with previous approaches (Wang, Phys. Rev. A 45 (1992) 2), it is shown that the distribution of Brownian particles after release from a point source is broader than Gaussian and described by a Fox function. Transport is shown to be ballistic at short times and either sub-diffusive or super-diffusive at large times. The imposition of occasional trapping events onto the Brownian dynamics can result in confined diffusion (d/dtx²→0) at long times when the mean trapping time is divergent. It is suggested that such dynamics describe protein motions in cell membranes.     

A population-level model from the microscopic dynamics in Escherichia coli chemotaxis via Langevin approximation

Recent extensive studies of Escherichia coli (E. coli) chemotaxis have achieved a deep understanding of its mi- croscopic control dynamics. As a result, various quantitatively predictive models have been developed to describe the chemotactic behavior of E. coli motion. However, a population-level partial differential equation (PDE) that rationally incorporates such microscopic dynamics is still insufficient. Apart from the traditional Keller-Segel (K-S) equation, many existing population-level models developed from the microscopic dynamics are integro-PDEs. The difficulty comes mainly from cell tumbles which yield a velocity jumping process. Here, we propose a Langevin approximation method that avoids such a difficulty without appreciable loss of precision. The resulting model not only quantitatively repro- duces the results of pathway-based single-cell simulators, but also provides new inside information on the mechanism of E. coli chemotaxis. Our study demonstrates a possible alternative in establishing a simple population-level model that allows for the complex microscopic mechanisms in bacterial chemotaxis.     

高能多粒子末态的多重分形维数与动力学起伏强度

研究了多重分形维数与动力学起伏强度的关系,给出了一个能直接描述高能多粒子末态动力学起伏强度的特征参量,并指出了这一参量的适用范围以及在实际高能实验中的应用.     

蛋白质构型变化的二维广义郎之万方程描述

采用二维广义郎之万方程描述蛋白质构型的随机变化,并与电子输运过程的原子密度填充模型相协调. 假设通过键和通过空间的两类电子输运路径分别受到高斯分数噪声和高斯白噪声的影响. 推导了电子转移给体-受体距离涨落和荧光寿命涨落自相关函数的一般表达式. 采用数值拉普拉斯反变换计算了蛋白质构型涨落动力学,并详尽讨论了长时间和短时间行为的渐近解析. 最后,明确了基于二维广义郎之万方程的蛋白质构型描述与一维描述之间的关系.     

Coexistence and fluctuations phenomena with Davidson-like potentials in quadrupole-octupole deformed nuclei

The energy spectra of three types of two-dimensional potentials(we will call them‘Davidson-like potentials’(DLPs)),characterized by four minima separated by barriers,are investigated.The predictions for spectra and wave functions are obtained by using the nine-point finite-difference method.For these potentials,with the existence of a single configuration,a transition of spectra,as a function of barrier height,is covered from tunneling splitting modes to fluctuations phenomena,with equal peaks wave functions,crossing to the spectra of purely anharmonic oscillator potentials(AOPs).A different type of phase transition occurs when two(or more)configurations coexist.With the change of the parameters,a transition of spectra is covered from coexistence phenomena of two distinct quantum tunneling modes to fluctuations phenomena,with unequal peaks wave functions,crossing to the spectra of purely AOPs.Using DLPs,a particular application of the coherent quadropole-octupole model to describe energy bands with alternating parity of the nuclei¹⁰⁰Mo,^146,148Nd,^148,150Sm,²²⁰Ra,^220,222Rn,and^220,222Th is presented.The global parametrization of the model for the selected nuclei is achieved.     

Dynamical effects of spin-dependent interactions in low- and intermediate-energy heavy-ion reactions

It is well known that noncentral nuclear forces, such as the spin–orbital coupling and the tensor force, play important roles in understanding many interesting features of nuclear structures. However, their dynamical effects in nuclear reactions are poorly known because only the spin-averaged observables are normally studied both experimentally and theoretically. Realizing that spin-sensitive observables in nuclear reactions may convey useful information about the in-medium properties of noncentral nuclear interactions, besides earlier studies using the time-dependent Hartree–Fock approach to understand the effects of spin–orbital coupling on the threshold energy and spin polarization in fusion reactions, some efforts have been made recently to explore the dynamical effects of noncentral nuclear forces in intermediate-energy heavy-ion collisions using transport models. The focus of these studies has been on investigating signatures of the density and isospin dependence of the form factor in the spin-dependent single-nucleon potential. Interestingly, some useful probes were identified in the model studies but so far there are still no data to compare with. In this brief review, we summarize the main physics motivations as well as the recent progress in understanding the spin dynamics and identifying spin-sensitive observables in heavy-ion reactions at intermediate energies. We hope the interesting, important, and new physics potentials identified in the spin dynamics of heavy-ion collisions will stimulate more experimental work in this direction.     

用李代数方法解析研究线性三原子分子振动的动力学纠缠

采用李代数方法研究了线性三原子分子非线性伸缩振动的动力学纠缠,给出了描述纠缠行为的线性熵和冯诺伊曼熵的解析表达式,并分别讨论了初态为Fock态和相干态下的HCN和DCN分子伸缩振动纠缠的动力学性质.