晶格原子间非简谐相互作用对离子注入的影响

本文用经典力学中推广的朗之万方程研究了离子注入中入射离子与固体的相互作用。在计入晶格原子间的非简谐力相互作用的情况下,得到了入射离子与靶原子之间的能量交换,靶原子对入射离子的核阻止本领和入射离子在靶中的投影射程分布,同时还讨论了入射离子激发的固体声子谱对核阻止的影响。将以上所得结果在低能范围与TRIM88的计算结果进行了比较,二者符合较好。 关键词：     

通过48Ca+249Bk 合成Z=117的可能性研究

利用两步模型对可能合成 Z=117 的核反应48Ca+249Bk 进行了研究。模型将熔合过程分为弹靶接触前的粘连过程和从弹靶接触到形成复合核的形成过程。结合统计蒸发模型,计算了297117 蒸发数个中子的剩余截面。结果表明,在激发能 E* = 31 MeV且复合核蒸发3中子时的剩余截面最大为 0.34 pb ,已经可以用实验方法进行探测。     

光抽运双光子激光朗之万量子理论

本文采用朗之万量子理论获得光抽运双光子激光具有双光子损耗时的朗之万方程,进一步获得稳态平均光子数、频率牵引、线宽和动态斯塔克效应,对激光增益来源的分析表明,非相干抽运仅有单双光子两步过程有贡献,而相干抽运,除上述过程外还有单双光子一步过程有贡献,而且,上述两个过程都受到负反馈和饱和因子的制约,线宽与稳态平均光子数无关。 关键词：     

密立根油滴实验中的布朗运动

在进行密立根油滴实验时,如果选择的油滴过小,油滴会有明显的布朗运动,造成测得的下落时间与理想下落时间存在偏差.本文对密立根油滴实验中油滴的下落问题进行了实验观察和理论研究,并基于朗之万理论,求解了描述油滴运动的随机微分方程.通过引入单次下落时间偏差和多次下落时间偏差分别考察了油滴布朗运动的剧烈程度以及布朗运动对油滴下落时间的影响.结果表明,实验中由于实验次数有限,当油滴比较小时油滴的布朗运动对于实验的影响仍然需要考虑.     

朗之万方程模拟核裂变碎片的同位旋标度

使用结合朗之万方程和统计分支的组合模型模拟¹¹²Sn+¹¹²Sn和¹¹⁶Sn+¹¹⁶Sn两个同位旋相关的反应系统, 通过高斯分布采样的方式得到了核裂变的碎片分布, 将两系统碎片的同位素和同中子异位素的分布相比, 发现存在同位旋标度律现象. 同时提取了同位旋标度系数, 发现同位旋标度系数是和碎片分布宽度相关的, 并且同能量、单位质量的粘滞系数也有很强的依赖关系.     

互联网流量控制的朗之万模型及相变分析

为互联网中的流量控制协议构建恰当模型,从而阐明具体协议算法与网络宏观性能间的关系,一直是互联网研究者面临的重大挑战.本文通过逻辑演绎,建立了互联网传输控制协议下流量的朗之万方程.在此基础上,细致分析了主动队列管理算法的有效性,在理论上证明了此类算法存在从畅通态到拥塞态到瘫痪态的相变过程,并给出了相变临界点与系统参数的显式关系.本建模与分析方法虽以具体的主动队列管理算法为例,但其方法可以应用于一般的网络流量控制问题. 关键词： 互联网 流量控制 朗之万方程 相变     

多色噪声的数值模拟和动力学效应

阐述了一个产生从红噪声到绿噪声的多色噪声源的途径,给出了这种噪声的关联函数和谱密度。提出用积分闭合方法模拟多色噪声,用龙格-库塔方法求解朗之万方程的整体。研究了在锯齿型周期势场中运动的布朗粒子的平均输运行为。结果表明:绿噪声所趋动的粒子的稳定速流与通常的红噪声的结果相反,存在一个使粒子运动方向反转的某种颜色噪声。     

双光腔耦合下机械振子的基态冷却

机械振子的基态冷却是腔量子光力学中的基本问题之一.所谓的基态冷却就是让机械振子的稳态声子数小于1.本文通过光压涨落谱和稳态声子数研究双光腔光力系统(标准单光腔光力系统中引入第二个光腔,并与第一个光腔直接耦合)的基态冷却.首先得到系统的有效哈密顿量,然后给出朗之万方程和速率方程,最后分别给出空腔和原子腔的光压涨落谱、冷却率和稳态声子数.通过光压涨落谱、冷却率和稳态声子数表达式,重点讨论空腔时机械振子的基态冷却,发现当满足最佳参数条件(机械振子的冷却跃迁速率对应光压涨落谱的最大值,而加热跃迁速率对应光压涨落谱的最小值)时,机械振子可以被冷却到稳态声子数足够少.此外分析:当辅助腔内注入原子系综时,若参数选择恰当可能更利于基态冷却.     

分子尺度不对称体系中热噪声引发的单向输运

不对称体系中的单向输运现象广泛存在于自然界中,宏观理论认为,体系的空间反演不对称性和有一定自相关时间的外加振动是引发单向运动的两个必要条件,因而一般认为,在分子尺度的不对称体系中,仅有热噪声也还是不会引发单向运动的。随着实验技术和计算手段的发展,有迹象表明,在分子尺度的不对称体系中,即使没有外加振动也会有单向运动产生。文章介绍在分子尺度由体系热噪声引发的不对称体系中,单向输运的理论进展,以及产生这种单向输运的条件。     

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.     

具有固有频率涨落的记忆阻尼线性系统的随机共振

研究了在内噪声、外噪声(固有频率涨落噪声)及周期激励信号共同作用下具有指数型记忆阻尼的广义Langevin方程的共振行为.首先将其转化为等价的三维马尔可夫线性系统,再利用Shapiro-Loginov公式和Laplace变换导出系统响应一阶矩和稳态响应振幅的解析表达式.研究发现,当系统参数满足Routh-Hurwitz稳定条件时,稳态响应振幅随周期激励信号频率、记忆阻尼及外噪声参数的变化存在"真正"随机共振、传统随机共振和广义随机共振,且随机共振随着系统记忆时间的增加而减弱.数值模拟计算结果表明系统响应功率谱与理论结果相符.     

基于分数阶环境热浴的非各态历经判据研究

本文从分数阶谱形式的气固耦合模型出发, 理论推导出具有幂律记忆核的广义朗之万方程. 研究气体分子在自由场和简谐势场中的动力学演化和长时渐进行为, 着重分析三种各态历经判据: Khinchin判据、Lee判据以及内在判据和外在表现的适用性. 研究结果表明: Khinchin判据适用于广义朗之万方程描述的所有扩散和输运过程; Lee判据并不适用于布朗运动, 只能用来区分不同类型的扩散过程; 而内在判据和外在表现不仅能够把非各态历经分为两类, 同时可以揭示非各态历经的物理内在根源.     

Microdynamics and nonlinear stochastic processes of gross variables

Starting from classical Hamiltonian mechanics, we derive for the dynamics of gross variables in nonequilibrium systems exact nonlinear generalized Fokker-Planck and Langevin equations in which the effect of the initial preparation is taken into account explicitly. This latter concept allows for the construction of a uniquely determined projection operator. The memory functions occurring in the Langevin equations are related to the random forces by a fluctuation-dissipation theorem of the second kind. We discuss the connection with the generalized Fokker-Planck equation. The known results for equilibrium fluctuations are recovered as a special case.Supported in part by the National Science Foundation, Grant CHE78-21460.     

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.     

Fluctuating hydrodynamic equations of mixed and of chemically reacting gases

The method of the nonlinear Langevin equation is generalized to ordinary mixed and to chemically reacting gases. The stochastic Boltzmann equations of these gases, the fluctuating hydrodynamic equations of mixed gases, and the Langevin equations for the number density of each component of a reaction-diffusion system are obtained.This work was supported financially by the Alexander von Humboldt Foundation. The main part of the paper was written during the author's stay at the Max-Planck Institut für Festkörperforschung (Stuttgart) as a Humboldt fellow.     

Random integral equation formulation of a generalized Langevin equation

In this paper, the generalized Langevin equation introduced by Kubo and Mori is formulated as a random integral equation. We consider (1) the existence and uniqueness of the solution, (2) moments of the solution process, (3) a comparison theorem for solution processes, and (4) the Cauchy polygonal approximation to the solution.     

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.     

过阻尼分数阶Langevin方程及其随机共振

通过对广义Langevin方程阻尼核函数的适当选取,在过阻尼的情形下, 推导出分数阶Langevin方程.给合反常扩散理论和分数阶导数的记忆性, 讨论了分数阶Langevin方程的物理意义,进而得出分数阶Langevin方程产生随机共振的内在机理.数值模拟表明,在一定的阶数范围内,分数阶Langevin方程可以产生随机共振, 并且分数阶下的信噪比增益好于整数阶情形.