Kinetics of Brownian particle trapping by randomly distributed traps of various sizes

Diffusion of a particle in a medium in the presence of absorbing traps of various size is considered. A theory describing the kinetics of particle trapping in the entire interval of time is suggested. Analytical relations for the probability of a particle survival in situations when many-body effects are weak and when they dominate are obtained. It is shown that polydispersity of traps leads to the slowdown of particle trapping and to attenuation of many-body effects inherent in the problem.     

Escape by diffusion from a square well across a square barrier

The problem of escape of a particle by diffusion from a square potential well across a square barrier is studied on the basis of the one-dimensional Smoluchowski equation for the space- and time-dependent probability distribution. For the model potential the Smoluchowski equation is solved exactly by a Laplace transform with respect to time. In the limit of a high barrier the rate of escape is given by an asymptotic result similar to that derived by Kramers for a curved well and a curved barrier. An approximate analytic formula is derived for the outward time-dependent probability current in terms of the width and depth of the well and the width and height of the barrier. A similar expression holds for the complete probability distribution.     

多体关联动力学中的自洽平均场

本文仔细地讨论了量子多体关联动力学中的广义自洽平均场,证明无论动态还是定态自洽平均场都是存在的。多体关联通过两体关联c₂及其相应的碰撞项I进入平均场。I的作用是双重的:对单粒子运动量子态的动力学效应和对单粒子态填充数的影响。多体关联还在多体系统的能量表达式中表现出来,使得该表达式不同于通常的HF-Brueckner理论中的表达式。 关键词：     

Memory function approach to the dynamics of interacting Brownian particles

We investigate some of the dynamic properties of diffusing particles described by a many-body Smoluchowski equation. The dynamic structure factor is expressed in terms of a memory function which is evaluated in the cases of i) weak interaction and ii) low particle density, but arbitrary interaction. A one-dimensional system with a hard-core pair potential is treated explicitly. Furthermore, by including a periodic single-particle potential, a model is obtained which has relevance to superionic conductors. For this case we discuss how the frequency-dependent conductivity is affected by the correlated motion of particles.     

Diffusion in a bistable potential

The problem of diffusion of a particle in a bistable potential is studied on the basis of the one-dimensional Smoluchowski equation for the space- and time-dependent probability distribution. The potential is modeled as two parabolic wells separated by a parabolic barrier. For the model potential the Smoluchowski equation is solved exactly by a Laplace transform with respect to time for the initial condition that at time zero the probability distribution is given by a thermal equilibrium distribution in one of the wells. In the limit of a high barrier the rate of transition to the other well is given by an asymptotic result due to Kramers. For a potential barrier of moderate height there are significant corrections to the asymptotic result.     

Dissipative effects on quantum sticking

Using variational mean-field theory, many-body dissipative effects on the threshold law for quantum sticking and reflection of neutral and charged particles are examined. For the case of an Ohmic bosonic bath, we study the effects of the infrared divergence on the probability of sticking and obtain a nonperturbative expression for the sticking rate. We find that for weak dissipative coupling α, the low-energy threshold laws for quantum sticking are modified by an infrared singularity in the bath. The sticking probability for a neutral particle with incident energy E→0 behaves asymptotically as s~E((1+α)/2(1-α)); for a charged particle, we obtain s~E(α/2(1-α)). Thus, "quantum mirrors"-surfaces that become perfectly reflective to particles with incident energies asymptotically approaching zero-can also exist for charged particles. We provide a numerical example of the effects for electrons sticking to porous silicon via the emission of a Rayleigh phonon.     

Joint probability distribution beyond the Smoluchowski limit for brownian motion in position space

We obtain a time convolutionless partial differential equation for the joint probability distribution in position space of a non-markovian brownian particle under the influence of some potential. We discuss the corrections to the Smoluchowski limit in this context.     

Diffusion coefficient for a Brownian particle in a periodic field of force: I. Large friction limit

The diffusion tensor for a Brownian particle in a periodic field of force is studied in the strong damping limit, in which the Smoluchowski equation is valid.A general relation between the diffusion tensor and the Smoluchowski “relaxation operator” is derived; the effect of the periodic force, at least in the simplest situation of diagonal and uniform friction, appears as a dressing of the bare particle mass to an effective tensor mass.From this the explicit form of the diffusion coefficient as a functional of the potential energy in the one-dimensional case is obtained, showing a temperature dependence which deviates at high temperatures from a simple Arrhenius behaviour.Finally, the expression for the mobility of the Brownian particle is derived, and by comparison with the expression for the diffusion coefficient the Einstein relation between diffusion and mobility is proved to be satisfied.     

Stochastic diffusion in a periodic potential

This paper deals with two equations for classical stochastic diffusion in a potential. First, the full Fokker-Planck equation in phase-space for a Brownian particle in a periodic potential and linearly coupled to an external field is considered. The solution discussed previously by the author and co-worker is improved upon. An alternative approximation is introduced. Then, the simpler Smoluchowski equation, which is derivable from the Fokker-Planck equation under suitable conditions, is solved using Hill's determinant method. Finally a WKB-type method is proposed to solve the Smoluchowski equation for a general class of potentials.     

THE RATE OF ESCAPE OF BROWNIAN PARTICLE OVER DOUBLY PEAKED POTENTIAL BARRIERS

The rate of escape of Brownian particle over doubly peaked potential barriers is calculated by the exact solution of the Smoluchowski equation. It is found that the rate depends strongly on the form of the potential barriers.     

Time-dependent escape rate from a potential well

Time-dependent desorption from an interface is studied by obtaining the Green function for the Smoluchowski equation for a one-dimensional model potential barrier and calculating the time-dependence of the number density, particle current, and escape rate. The asymptotic behavior of the system for long times can be described by equations with independent rate constants. For high potential barriers (relative to k_BT) the Kramers expression for the escape rate is recovered, but for low barriers the escape rate can go through a maximum. The steady state Onsager model is related to the transient solution and numerical results are presented for different potential shapes and sizes.     

ENHANCED NEUTRON EM1SSION IN HEAVY ION REACTIONS BY DIFFUSION MODEL

An extensive Smoluchowski equation with neutron emission is suggested in this paper and is analytically solved by means of van Kampen technique.The average fission rate,fission probability,the ratio of neutron emission to fission are calculated for composite nucleus ²⁴⁰PU. The time evolution of these quantities is analysed and their essential dependence on fission potential height and nuclear temperature are discussed.A fair1y substantial particle evaporation prior to fission in heavy-ion reactions can be well understood in our diffusion model.     

Asymptotics of harmonic microwave mixing in a sinusoidal potential

Analytic asymtotic results are derived for the harmonic microwave mixing voltage due to a stochastic charged particle trapped in the potential thoughs of a sinusoidal pinning potential. The time averaged probability distribution of the corresponding Smoluchowski equation is evaluated from a matrix continued fraction. The problem can be solved by Bessel functions with a field strength matrix appearing in the order index. It is found that the harmonic mixing voltage saturates at a finite value depending only on the microwave field strengths when the potential troughs become very deep compared to thermal energy.     

Transient properties of a bistable kinetic model with quantum corrections

The transient properties of a Brownian particle moving in a bistable system with quantum corrections are investigated. The Quantum Smoluchowski Equation (QSE) is fully valid for high temperatures; for low temperatures it is valid only in a restricted domain of the state space. The quantum effects in a bistable system stand out for low temperatures. Explicit expressions of the mean first-passage time (MFPT) are obtained by using a steepest-descent approximation. The quantum effects are against the particle moving towards the destination from its original position.     

Brownian motion of a classical particle in quantum environment

The Klein–Kramers equation, governing the Brownian motion of a classical particle in a quantum environment under the action of an arbitrary external potential, is derived. Quantum temperature and friction operators are introduced and at large friction the corresponding Smoluchowski equation is obtained. Introducing the Bohm quantum potential, this Smoluchowski equation is extended to describe the Brownian motion of a quantum particle in quantum environment.     

角动量对断前粒子发射壳效应的影响

用Smoluchowski方程研究了角动量对一个轻的闭壳核¹³²Sn裂变前粒子蒸发壳效应的影响,发现壳对断前粒子发射的影响敏感地依赖于这个裂变系统的角动量.对可能的原因进行了讨论     

Exact solution of a coagulation equation with a product kernel in the multicomponent case

In this paper, we obtain the general solution for the continuous Smoluchowski equation in the multicomponent case with a product kernel as a series expansion. The solution of the problem involves the Laplace transform in several dimensions. We obtain a nonlinear partial differential equation (PDE) of the advective kind generalizing the one previously given by other authors for the mono-component case.As in its relative mono-component case, gelation is produced at some point, the conditions for its occurrence being the same as those for the mono-component case, though substituting a sum of derivatives by a derivative in the Laplace transform field. We demonstrate that for a multicomponent particle size distribution (PSD) of multiplicative form, it is sufficient for one of the marginal PSDs to generate instantaneous gelation for the occurrence of instantaneous gelation in the multicomponent PSD.The general solution is applied to several specific cases, a discrete case that recovers a previously known solution, and another two continuous cases which can be used to check numerical methods designed to directly solve the Smoluchowski equation in more general cases.We have compared the solutions for the multicomponent PSD for constant, additive and product kernels and we conjecture about the relation existing between the functional forms for the solutions both in the mono-component and the multicomponent case.Finally, we have analysed the shape of the solutions for multicomponent PSD for constant, additive and product kernels for very small masses of components, obtaining a qualitatively different behaviour for the product kernel. This has effects in the mixing state of the sol phase as time passes.     

Influence of Angular Momentum on Shell Effects of Pre-scission Particle Emission of a Light Closed Shell Nucleus 132Sn

Based on the Smoluchowski equations, we study the influence of angular momentum on the shell effects of pre-scission particle emission for a light closed shell nucleus ¹³²Sn. It has been found that the shell effects of pre-scission particle multiplicity depends on the angular momentum in a complicated way. Possible reasons are discussed.     

The influence of the drift shift of electrons undergoing thermalization on the kinetic characteristics of geminate conductivity and recombination

A program for numerically solving the Smoluchowski equation with a modified initial condition taking into account the drift shift of electrons that experience thermalization in an external electric field was developed. The probability of survival and the polarization current of isolated ion pairs were calculated. Shift effects were shown to be especially strong in the region of medium electric fields on the order of 10⁷ V/m and noticeably weaker in both low and high fields. This was related to the proportional relation between the drift shift and electric field applied. The program was used to critically analyze the available experimental data on pulsed photoconductivity of polyacenes.     

Analytical Solution of Smoluchowski Equation in Harmonic Oscillator Potential

Non-equilibrium fission has been described by diffusion model. In order to describe the diffusion process analytically, the analytical solution of Smoluchowski equation in harmonic oscillator potential is obtained. This analytical solution is able to describe the probability distribution and the diffusive current with the variable x and t. The results indicate that the probability distribution and the diffusive current are relevant to the initial distribution shape, initial position, and the nuclear temperature T; the time to reach the quasi-stationary state is proportional to friction coefficient β, but is independent of the initial distribution status and the nuclear temperature T. The prerequisites of negative diffusive current are justified. This method provides an approach to describe the diffusion process for fissile process in complicated potentials analytically.