Dissipation and fluctuation of the relative momentum in nucleus-nucleus collisions

The dissipation of the relative momentum in nucleus-nucleus collisions is treated in terms of a Langevin equation with a fluctuating force. Equations of motion for first and second moments of the macroscopic variables are derived directly from the Langevin equation. The properties of the fluctuating force which results from random particle exchange are investigated in detail. Drift and diffusion coefficients are calculated microscopically and analytical expressions are given which can be used in any trajectory calculation. An important feature of the model is that the Einstein relation between dissipation and fluctuation turns out to be only a limiting case of a more general expression which includes nonthermal fluctuations. By treating the two nuclei as intrinsically equilibrated but not in thermal equilibrium with respect to each other, several important aspects of the dissipative behaviour, seen in heavy-ion collisions with final energies above the Coulomb barrier, can be understood.     

Relationship between Symmetries andConservation Laws

The fundamental relation between Lie-Bäcklund symmetry generators andconservation laws of an arbitrary differential equation is derived without regardto a Lagrangian formulation of the differential equation. This relation is used inthe construction of conservation laws for partial differential equations irrespectiveof the knowledge or existence of a Lagrangian. The relation enables one toassociate symmetries to a given conservation law of a differential equation.Applications of these results are illustrated for a range of examples.     

非保守力学系统Nielsen方程的形式不变性

研究非保守力学系统Nielsen方程的形式不变性.给出非保守力学系统Nielsen方程的形式不变性的定义和判据,研究形式不变性和Noether对称性的关系,并举例说明结果的应用 关键词： 非保守力学系统 Nielsen方程 形式不变性 Noether对称性     

各向异性颗粒PDF输运方程及其颗粒湍流扩散

根据Minier的模型,获得颗粒所见流体脉动速度的朗之万模型,并推导颗粒所见流体湍流脉动速度自关联函数,该函数具有各向异性的特征,进一步由流体脉动速度朗之万模型和颗粒运动方程获得相应的颗粒PDF输运方程.为描述在网格生成湍流中的颗粒扩散运动,将颗粒PDF输运方程作相应的简化,获得一个具有颗粒湍流各向异性的解析解,将方程的解与Wellsand Stock的颗粒湍流扩散实验结果进行比较,获得了很好的结果.揭示了具有各向异性特征的颗粒PDF输运方程的优越性.     

Self-diffusion in fluids with weak long-range forces

Diffusion of a test particle in a homogeneous classical fluid with weak long-range forces is studied. The dominant mean-field effect (Vlasov's theory) vanishes for symmetry reasons. Dynamical phenomena follow then from fluctuations of the effective potential energy felt by the propagating particle. The kinetic equation corresponding to this mechanism is derived with the use of the multiple-time-scale method. Its structure resembles very much that of the (linearized) Balescu-Lenard equation of hot plasma theory. It is shown that the kinetic equation holds only if no phase transition occurs in the system. The thermalization of the diffusing particle and the high-temperature and Lorentz gas limits are discussed.     

长时相干效应与分形布朗运动

 我们研究了阻尼布朗粒子，在具有幂律长时相干C(t)~t^-β（0<β<1，1<β<2）的无规涨落力作用下的运动情况。我们发现它是作分形布朗运动，而不是作普通的布朗运动，而且，找出了分形布朗运动的有效Fokker-Planck方程，以及相应的精确解。于是第一次把长时相干效应和分形布朗运动建立了定量的联系。     

研究两相流中固粒对流体湍动特性影响的新方法

本文提出了计算两相流中固粒对流体湍动特性影响的一种新方法，得到不同情况下固粒对流体端动特性的影响。将该方法用于槽流湍流场的求解，说明该方法是可行的。     

Transport in a fluctuating potential

We study the overdamped motion of a particle in a fluctuating one-dimensional periodic potential. The potential has no inversion symmetry, and the fluctuations are correlated in time. At finite temperatures, a stationary current is induced. The amplitude and the direction of the current depend on the details of the noise process that is responsible for the potential fluctuations. We discuss several limiting situations for a general case. Furthermore we calculate the current in the case of a piecewise linear potential for different noise processes and parameters. A detailed discussion of the results is given, including a discussion of the mechanism that is responsible for the current reversal. We compare the present results with results for transport in a ratchet-like potential due to a fluctuating force. We also discuss the biological relevance of the present models for molecular motors. We present a model for the motion of molecular motors that explains why similar molecular motors can move in different directions.     

Brownian motion in a classical ideal gas: A microscopic approach to Langevin’s equation

We present an insightful ‘derivation’ of the Langevin equation and the fluctuation dissipation theorem in the specific context of a heavier particle moving through an ideal gas of much lighter particles. The Newton’s law of motion (mx = F) for the heavy particle reduces to a Langevin equation (valid on a coarser time-scale) with the assumption that the lighter gas particles follow a Boltzmann velocity distribution. Starting from the kinematics of the random collisions we show that (1) the average force 〈F〉 ∞ −x and (2) the correlation function of the fluctuating forceη = F — 〈F〉 is related to the strength of the average force. Deceased     

Fluctuation theorem for currents in the Spinning Lorentz Gas

We study the fluctuation theorem formulated in terms of the currents present in a Hamiltonian system with coupled mass and energy transport. To drive the system out of equilibrium, we assume it to be connected to two ideal thermodynamical baths. The fluctuation symmetry is, thus, expressed in terms of the joint probability distribution of energy and particle currents in the system. This relation is verified numerically for the stationary state in the Spinning Lorentz Gas (SLG), driven out of equilibrium by temperature and/or chemical potential differences between the baths, as well as in the presence of an applied field.     

Coarsely grained stochastic Boltzmann equation and its moment equations

The stochastic Boltzmann equation is coarsely grained. The coarsely grained stochastic (CGS) Boltzmann equation has fluctuating terms in its collision term. On the basis of the CGS Boltzmann equation, reduced Grad’s 26 moment equations are derived. Coarsely grained moment equations obtained from the CGS Boltzmann equation show that fluctuating terms remain as nonvanishing terms owing to the nonlinearity in the collision term of the CGS Boltzmann equation. The Navier-Stokes-Fourier law obtained using the CGS Boltzmann equation indicates that the pressure deviator and heat flux include fluctuations of their one-order higher moments.     

Pseudoscalar Cornell potential for a spin- 1/2 particle under spin and pseudospin symmetries in 1 ＋ 1 dimension

The Cornell potential that consists of Coulomb and linear potentials has received a great deal of attention in particle physics. In this paper, we present the exact solutions of the Dirac equation with the pseudoscalar Cornell potential under spin and pseudospin symmetry limits. The energy eigenvalues and corresponding eigenfunctions are given in closed form.     

Memory effects on the quantum diffusion of a particle in a fluctuating medium

We introduce a phenomenological Hamiltonian for a particle in a medium with sitediagonal and off-diagonal disorder. Without assuming the usual white noise expression for the correlation between fluctuating variables, we arrive at a master equation using second order perturbation theory. This expression is expanded in powers of the correlation time. The mean square displacement and velocity are discussed and corrections to the diffusion coefficient are given.Partially supported by the grant of the Ministry of Education of the Japanese Government and by Sakkokai Foundation     

Influence of coloured noise on the diffusion of a quantum particle. Part I: General results

A general stochastic model for the diffusion of a quantum particle on a fluctuating lattice is considered and several exact results useful in the calculation of transport properties are given. First, we derive a new type of integral equation for the density operator using a time-dependent projection operator and disentangling the stochastic, not the deterministic part of the motion in contrast to previous treatments. The mean square displacement is then expressed by the kernel of this equation in the case of diagonal fluctuations. We obtain an equation of motion for this kernel similar in structure to equations known from Green's function theory and containing a self-energy like quantity. Finally, two general statements concerning the exact solution of correlated models are given.     

Group properties of linear equations

A method of determining the symmetry algebra of a linear homogeneous equation is proposed. The Schrödinger equation that describes the steady state of a particle in a potential field is used as an example. The symmetry operators of this equation, which are second-order differential operators, are studied.     

Brownian Motion of a Charged Particle in Electromagnetic Fluctuations at Finite Temperature

The fluctuation-dissipation theorem is a central theorem in nonequilibrium statistical mechanics by which the evolution of velocity fluctuations of the Brownian particle under a fluctuating environment is intimately related to its dissipative behavior. This can be illuminated in particular by an example of Brownian motion in an ohmic environment where the dissipative effect can be accounted for by the first-order time derivative of the position. Here we explore the dynamics of the Brownian particle coupled to a supraohmic environment by considering the motion of a charged particle interacting with the electromagnetic fluctuations at finite temperature. We also derive particle’s equation of motion, the Langevin equation, by minimizing the corresponding stochastic effective action, which is obtained with the method of Feynman-Vernon influence functional. The fluctuation-dissipation theorem is established from first principles. The backreaction on the charge is known in terms of electromagnetic self-force given by a third-order time derivative of the position, leading to the supraohmic dynamics. This self-force can be argued to be insignificant throughout the evolution when the charge barely moves. The stochastic force arising from the supraohmic environment is found to have both positive and negative correlations, and it drives the charge into a fluctuating motion. Although positive force correlations give rise to the growth of the velocity dispersion initially, its growth slows down when correlation turns negative, and finally halts, thus leading to the saturation of the velocity dispersion. The saturation mechanism in a supraohmic environment is found to be distinctly different from that in an ohmic environment. The comparison is discussed.     

Symmetries of the Free Schrödinger Equation

An algorithm is proposed for studying the symmetry properties of equations used in theoretical and mathematical physics. The application of this algorithm to the free Schrödinger equation permits one to establish that, in addition to the known Galilei symmetry, the free Schrödinger equation possesses also relativistic symmetry in some generalized sense. This property of the free Schrödinger equation provides an extension of the equation into the relativistic domain of the free particle motion under study.     

CONFORMAL INVARIANCE AND PARTICLE ASPECTS IN GENERAL RELATIVITY

We study the breakdown of conformal symmetry in a conformally invariant gravitational model. The symmetry breaking is introduced by defining a preferred conformal frame in terms of the large scale characteristics of the universe. In this context we show that a local change of the preferred conformal frame results in a Hamilton-Jacobi equation describing a particle with adjustable mass. In this equation the dynamical characteristics of the particle substantially depends on the applied conformal factor and local geometry. Relevant interpretations of the results are also discussed.