Lorenz系统的可预报性

定义一个动态窗口，以Lorenz模型为预报方程，通过对落入动态窗口中的粒子数和平均预报X分量随积分时间演化规律的分析，从另一个角度初步研究了Lorenz系统的可预报性问题，并讨论了高斯白噪声对系统可预报性的影响.结果表明，落入动态窗口中的粒子数在一定程度上反映了系统的可预报性，处于不同区域的初值集合预报时限各不相同，且不同区域内的初值对于小扰动的敏感程度不一样；对于不同区域内的初值集合，高斯白噪声对系统的可预报时限的影响各不相同. 关键词： 可预报性 Lorenz 动态窗口     

单晶铜中冲击波阵面结构的数值模拟研究

 用分子动力学方法模拟计算了在初始温度为0 K时单晶铜中的冲击波结构,相互作用势采用铜的嵌入原子势（EAM）,模拟计算结果表明即使是在初始温度为0 K的FCC晶体中,冲击波波阵面后的区域也会向平衡态演化。局域分析表明冲击波阵面后区域的压力、粒子速度、应变和温度随时间逐步变化到稳定态,在所研究的冲击波强度（约262 GPa）下,波后区域的平均压力、粒子速度、应变均在约1 ps内逐渐上升并达到稳定值。动能温度在波阵面处始终为最大值,随着冲击波的传播,波后非零温度区域逐渐扩大,不同时刻的粒子速度分布函数说明波后区域逐渐向热力学平衡态演化,并最终达到热力学平衡,进一步的分析说明局域平衡是系统向平衡态演化的基本过程。     

多粒子W态的绝热制备

通过利用时间依赖的外磁场,提出了绝热制备多粒子W态的新方法.同时给出了驱动n个自旋1/2粒子从未纠缠态到W态的相互作用哈密顿量以及绝热和非绝热演化条件,展示了能量和靶态布据随时间的演化图.     

强迫耗散系统的有序结构和系统的发展(Ⅱ)，广义能量极小值原理和系统的发展

利用大气非线性动力学证明了广义能量极小值原理，进一步从理论上证明它是同大气非平衡 态热力学最小熵产生原理在物理上是一致的.前者表明，强迫耗散动力系统的终态广义能量 达极小值；而最小熵产生原理表明，远离热力学平衡态的开放系其终态时系统内部的不可逆 过程最弱.而且，系统广义能量达极小值和系统熵产生达极小值的终态一般是一个稳定的定 态，它对应着系统的某种有序结构.也就是说它是一个“低耗高效”的有序定态.大气系统作 为自然界一个典型的物理复杂系统，其最小熵产生原理和广义能量极小值原理隐示了自然界 复杂系统的一个一 关键词： 强迫耗散系统 能量极值原理 有序结构 动力系统     

极化激元系统时间演化的量子涨落特性和非经典统计行为

将极化激元系统约化成模型单模光子-TO声子有效相互作用系统， 在此基础上以解析形式讨论了系统的力学量、压缩态、量子涨落特性以及亚泊松分布等非经典效应的动力学演化行为.结果表明，光子场与极化波量子场彼此交换能量过程随时间演化呈振荡性质，光子场和声子场都可以演化成压缩态，其二阶压缩度随时间演化成复杂周期振荡特性，这种非经典特性是非线性相互作用的结果并且以k₁项和k₂项同时存在并相互关联为前提.而此时光子和声子统计分布随时间演化呈现介于超Poison分布和亚Poison分布之间复杂周期振荡的新结果，非线性作用k₁项和k₂项对这种非经典统计行为都有贡献. 关键词： 极化激元系统动力学演化 单模光场-TO声子有效模型哈密顿量 量子涨落与压缩态 亚泊松分布     

高能量粒子再分布模型在CFETR上的应用

在中国聚变工程实验堆(CFETR)设计参数下,利用一种高能量粒子(EP)物理简化模型分析了磁流体动力学(MHD)不稳定中新经典撕裂模(NTM)引起的粒子再分布和损失。相位矢量旋转法利用EP相空间中小间隔区域内跟踪探测粒子对来判定粒子轨道随机与否,即记录连接矢量旋转角的方法标记该区域是否存在KAM面破缺,以此为据修正相空间的粒子分布函数和判断粒子损失。利用相空间探测粒子对相位矢量旋转法标记一定NTM幅度下的随机区域分布并迭代得到稳态分布剖面。对捕获粒子区域的共振岛探测结果表明,低频或零频率扰动不会与高能量α粒子形成有效共振,MHD扰动和有效碰撞效应可能使捕获-通行轨道边界附近形成损失通道。     

相空间中相互垂直的相干态迭加态以及相应的双模纠缠态研究

相干态是最接近经典态的量子态，而广泛研究的相干迭加态——如奇偶相干态、Schleich的镜像迭加相干态等——则显示更多非经典效应。另外，双模及多模迭加态，特别是所谓的纠缠态，在量子信息处理如量子隐形传态和量子密码术中扮演重要角色。我们就相空间中相互垂直的相干态的迭加态进行讨论，研究其非经典特性，如光子数统计分布、正交分量压缩效应、Wigner分布函数的负性以及由此引入的非经典判别子。结果表明，这一类相干迭加态在满足某种条件下具有亚泊松光子统计分布和正交分量的压缩效应，并且参数变量在一定范围内这两种非经典效应同时存在；这些迭加态的Wigner分布中存在不同程度的负值区域．并与奇偶相干态做出了比较．计算相廊的Wigner函数积分判别子可以定最地分析其负性的深度。     

时频分布技术在激光与等离子体相互作用粒子模拟诊断中的应用

在对超短超强激光与等离子体相互作用进行粒子模拟诊断的研究中,输出量普遍为时间或空间上的非平稳信号。将时频分布技术引入粒子模拟结果的诊断,指出用时频分布技术等现代信号处理技术诊断模拟结果中的非平稳信号具有重要意义。作为实例,考察了用线性啁啾激光打靶条件下,包含nc/4(nc为等离子体临界密度）的非均匀等离子体区域中的受激拉曼散射的演化,并用时频分布技术得到了清晰的物理图像。     

周期驱动的二能级系统中的准宇称-时间对称动力学

本文研究了一个周期驱动的非宇称-时间对称二能级量子系统的非厄米动力学.通过经典相空间分析方法,解出了该非厄米系统的Floquet态和准能谱,并解析构造了由该非厄米哈密顿量支配下的量子态的非幺正时间演化算符,给出了不同参数区域的量子态演化.本文数值和分析证明,该非宇称-时间对称二能级Floquet系统,类似于宇称-时间对称系统,存在一个准能谱从实数谱到复数谱的相变.本文还揭示了在量子态的动态演化中存在一种准宇称-时间对称动力学,即,该系统的粒子布居概率演化完全满足时间空间对称(宇称-时间对称),但是由于相位演化违反了宇称-时间对称性的要求,因此包含相位信息的量子态演化不满足时间空间对称(宇称-时间对称).这些结果加深了对非厄米物理的理解,拓展和推广了传统的宇称-时间对称概念.     

氢原子相干态研究的进展与启示

近年来的理论及实验研究都表明，在实空间中，期望用氢原子定态波函数的叠加以得到满足最小测不准关系的同时又不发生扩散的相干态是不可能的但若把三维氢原子体系映射到另外的空间，则可以发现氢原子体系可以存在真正的相干态，可这种相干态都不随物理的时间而是随另一个“虚假的时间”因子而演化。     

Attractor vicinity decay for a cellular automaton

The temporal decay of an attractor's vicinity for a domain-wall dominated cellular automaton (CA) is studied. Using selected initial pattern ensembles, state space structures in this high-dimensional nonlinear spatial system can be identified via the resulting decay to its attractors. Considered over a range of lattice sizes, the decay behavior falls into three main classes, each of which shows a characteristic profile. The first consists of even-size lattices showing a decelerating decay to small nonattracted ensemble fractions. The second class, also for even lattices, is a catastrophic decay to very small or vanishing nonattracted fractions. The third class also shows catastrophic decay and contains all odd-size lattices. Stochastic models are constructed that mimic the behavior of typical lattices throughout their evolution until finite-size effects appear. Weak additive noise causes all states on all lattices to fall into the attractor. In the end we find it overwhelmingly likely that the recently proposed attractor-basin portrait captures the CA's qualitative dynamics.     

Numerical approach for the evolution of spin-boson systems and its application to the Buck–Sukumar model

We study the evolution properties of spin-boson systems by a systematic numerical iteration approach, which performs well in the whole coupling regime. This approach evaluates a set of coefficients in the formal expression of the time-dependent Schr?dinger equation by expanding the initial state in Fock space. This set of coefficients is unique for the spin-boson Hamiltonian studied, allowing one to calculate the time evolution from different initial states. To complement our numerical calculations, we apply the method to the Buck–Sukumar model. We find that when the ground-state energy of the model is unbounded and no ground state exists in a certain parameter space, the time evolution of the physical quantities is naturally unstable.     

Multiple branches of ordered states of polymer ensembles with the Onsager excluded volume potential

We study the branches of equilibrium states of rigid polymer rods with the Onsager excluded volume potential in two-dimensional space. Since the probability density and the potential are related by the Boltzmann relation at equilibrium, we represent an equilibrium state using the Fourier coefficients of the Onsager potential. We derive a non-linear system for the Fourier coefficients of the equilibrium state. We describe a procedure for solving the non-linear system. The procedure yields multiple branches of ordered states. This suggests that the phase diagram of rigid polymer rods with the Onsager potential has a more complex structure than that with the Maier-Saupe potential. A study of free energy indicates that the first branch of ordered states is stable while the subsequent branches are unstable. However, the instability of the subsequent branches does not mean they are not interesting. Each of these unstable branches, under certain external potential, can be made metastable, and thus may be observed.     

Quantum mechanical state preparation II-The statistical ensemble as a thermostat

In this sequel to an earlier paper on quantal state preparation (Park & Band, 1972), the simple model used before is adapted and somewhat generalised to enable an exact treatment of the causal evolution of a system immersed in a statistical ensemble constituted of replicas of the system itself. The ensemble is initially in a state of statistical equilibrium, but the initial state of the system is arbitrary. It is established as a purely dynamical theorem that the system is eventually coerced into the same equilibrium state as that of the replicas in the ensemble. From this general result we obtain as a special case mechanical justification for the common assumption in statistical thermodynamics that an ensemble can function as a thermostat.     

Dicke模型的量子混沌和单粒子相干动力学特性

量子化的Dicke模型在非旋波近似条件下表现为量子混沌动力学特征.利用单粒子一阶时间关联函数,通过数值计算详细考察了Dicke模型中单粒子相干动力学特性.结果表明:当初始相干态处在混沌区域时,一阶时间关联函数曲线衰减较快,而当初始相干态处在规则区域时,一阶时间关联函数曲线衰减较慢,单粒子相干动力学对初态具有较强的敏感性,经典混沌抑制量子相干.考察单粒子相干动力学在相空间的平均演化性质,得到一种较好的量子经典对应关系.最后研究了相空间单粒子相干的整体动力学性质,更好地揭示了相空间的混沌和规则结构.     

Free energy in a Markovian model of a lattice spin system

A Markov process which may be thought of as a classical lattice spin system is considered. States of the system are probability measures on the configuration space, and we study the evolution of the free energy of these states with time. It is proved that for all initial states the free energy is nonincreasing and that it strictly decreases from any initial state which is shift invariant but not an equilibrium state. Finally we show that the state of the system converges weakly to the set of Gibbsian Distributions for the given interaction, and that all shift invariant equilibrium states are Gibbsian Distributions.This work was done while the author was a postdoctoral fellow in the Adolph C. and Mary Sprague Miller Institute for Basic Research in Science.     

声子库的量子态对介观电路量子特性影响的研究

考虑电子与声子间相互作用,研究了两种声子库纯初始态(正则系综与粒子数态)下耗散介观电路的动力学特性.长时间极限下(t→∞)：当环境处于热平衡态时,电路系统中的电流和电荷的平均值只与电路所处初始量子态中的平均值有关,与环境无关;环境初态为粒子数态时,电荷与电流平均值随时间的演化特性与环境初始处于热平衡态下时完全一样,表明介观电路中的电荷与电流的平均值与环境量子态的某组占有数无关.电路中电流和电荷的量子涨落不仅与系统的初态有关,还与系统所处环境的量子态及温度有关.一般地说,电路系统与环境的纠缠会 关键词： 介观耗散电路 声子库 量子初态 量子态纯度     

波包的空时演化与能级免交叉

采用二维谐振子相干态为初始态,在形变原子核系统分别为规则和混沌两种情况下,对其在相空间中的时间行为进行了傅里叶分析,特别比较了混沌系统中波包宽度在整个时间段与达到饱和后两个阶段的傅里叶分析结果.指出系统的混沌运动是由于大量能级免交叉的出现在波包运动的初始阶段就破坏了波包内部的规则结构,波包各成分间的协同性被破坏,波包的运动成为混沌.此后,波包内各成分对波包运动的贡献开始相同,能级之间的免交叉对波包运动的影响也不再明显.     

Stabilizing unstable steady states using extended time-delay autosynchronization

We describe a method for stabilizing unstable steady states in nonlinear dynamical systems using a form of extended time-delay autosynchronization. Specifically, stabilization is achieved by applying a feedback signal generated by high-pass-filtering in real time the dynamical state of the system to an accessible system parameter or variables. Our technique is easy to implement, does not require knowledge of the unstable steady state coordinates in phase space, automatically tracks changes in the system parameters, and is more robust to broadband noise than previous schemes. We demonstrate the controller's efficacy by stabilizing unstable steady states in an electronic circuit exhibiting low-dimensional temporal chaos. The simplicity and robustness of the scheme suggests that it is ideally suited for stabilizing unstable steady states in ultra-high-speed systems. (c) 1998 American Institute of Physics.