周期场中非各态历经布朗运动

将自由状态下呈弹道扩散的非各态历经系统置于周期场中,进而将非各态历经布朗运动分为两类.第一类是阻尼核的Laplace变换的低频为零的系统,当温度远大于势垒高度时,系统平均能量的动能部分依赖粒子的初始速度分布;随温度降低,系统的各态历经性得到恢复.然后将第一类系统的稳定速度变量作为一个内部噪声,再去驱动一个自由布朗粒子,则阻尼核的Laplace变换在零频时为无穷大.结果发现,粒子扩散系数随温度的增加而趋于零,显示一种经典局域化特征,系统的渐进分布依赖于初始坐标分布.这是第二类非各态历经性运动,不能通过外加势而恢复. 关键词： 非各态历经 非Markov布朗运动 扩散系数 噪声谱     

对称双势阱玻色-爱因斯坦凝聚系统在周期驱动下的动力学相变及其量子纠缠熵表示

研究了在对称双势阱玻色-爱因斯坦凝聚体系粒子间相互作用项上外加周期调制而引起的系统动力学相变,特别地研究了该系统通向混沌的相变过程.发现在一定驱动参数下,当外加调制频率与系统固有频率达到共振时,相平面会出现不稳定性现象,即混沌.在混沌区域,粒子在各量子态随机分布,平均布居数差在零附近波动.特别地,研究表明,混沌现象的出现可以用量子纠缠熵来表征,混沌现象出现时,两种平均纠缠熵都趋于它们的最大值. 关键词： 玻色-爱因斯坦凝聚 双势阱 混沌 纠缠熵     

两种类粒子间的聚集与完全湮没竞争过程的标度行为

考虑一个由两种类粒子组成的系统,同种类粒子相遇时发生不可逆的聚集反应;不同种类的粒子相遇时,则发生不可逆的完全湮没反应.利用Mont-Carlo模拟各种参数条件下的粒子聚集-完全湮没竞争过程,分析了聚集速率、湮没速率以及初始浓度分布对系统动力学行为的影响.模拟结果表明:1)粒子大小分布总是满足一定的标度律;2)当两种粒子的聚集速率都等于湮没速率的2倍时,粒子大小分布的标度指数与粒子初始浓度分布有关;3)其余情况下,标度指数则取决于反应速率的相对大小.此外,当两种粒子的聚集速率都大于或等于湮没速率的两倍,系统的所有粒子将完全湮没;当且仅当至少一种粒子的聚集速率小于湮没速率的两倍,聚集速率较小的那一种粒子才可能最终保存下来.模拟结果与已报道的理论分析结果符合得较好.     

对称双势阱玻色-爱因斯坦凝聚系统在周期驱动下的动力学相变及其量子纠缠熵表示

研究了在对称双势阱玻色-爱因斯坦凝聚体系粒子间相互作用项上外加周期调制而引起的系统动力学相变，特别地研究了该系统通向混沌的相变过程.发现在一定驱动参数下，当外加调制频率与系统固有频率达到共振时，相平面会出现不稳定性现象，即混沌.在混沌区域，粒子在各量子态随机分布，平均布居数差在零附近波动.特别地，研究表明，混沌现象的出现可以用量子纠缠熵来表征，混沌现象出现时，两种平均纠缠熵都趋于它们的最大值.     

非线性阻尼驱动的莱维飞行动力学性质

基于动力学连续时间无规行走方法,对受非线性阻尼驱动的莱维飞行在自由势场以及周期势场中的扩散行为进行了研究.非线性阻尼取代斯托克斯阻尼,通过动力学连续时间无规行走方法体现在莱维随机行走粒子的每一步跳跃中.结果显示,非线性阻尼的强阻尼耗散作用导致莱维飞行的超扩散行为衰减为正常扩散,粒子速度定态分布呈现双峰与单峰的相互转化.周期势场的束缚作用会导致粒子扩散达到一个稳定态,而莱维粒子自身性质会使粒子存在极小概率跃出周期势阱的跳跃行为,表现为方均位移随时间的演化出现跃迁现象.     

玻色-爱因斯坦凝聚体系中的混沌隧穿行为

研究了双势阱玻色-爱因斯坦凝聚(BEC)系统在外加周期调制下的混沌相变过程,着重讨论了混沌现象对BEC系统隧穿的影响.当外加调制频率与系统固有频率达到共振时,相平面会出现不稳定现象,即混沌现象.在量子情况下,研究了系统的Husimi函数随时间的演化.研究发现：当混沌现象出现时,系统中粒子间相互作用增大,使得混沌区域扩大,进而引起混沌辅助隧穿程度的变化. 关键词： 玻色-爱因斯坦凝聚 混沌 隧穿     

耗散两态系统的动力学特性

利用Born-Oppenheimer近似研究了零温时耗散两态系统的动力学特性.在不同环境谱分布下,给出了两态之间的跃迁几率随时间的变化.数值结果表明:当环境的谱分布为Ohmic形式时,跃迁几率是一个衰减的函数;而当谱分布为随机取值时,跃迁几率具有“量子跳跃”的特性.与之相对比,我们还给出了当把环境等价成无穷多个谱振子的集合时,跃迁几率随时间的变化.     

聚集效应对银纳米粒子的二阶非线性光学特性的影响研究

运用超瑞利散射(HRS)技术,对由KNO3诱导聚集的银纳米粒子的二阶光学非线性特性进行了实验研究.通过粒子尺寸测量和透射电镜观察，表明银纳米粒子的聚集方式为链状聚集.当聚集体平均尺寸为120nm时，银纳米粒子聚集体的HRS信号强度比聚集前增大了约15倍.分析表明，聚集导致银纳米粒子表面电场极化强度的增强和极化分布的改变，并通过表面和体贡献机理对二阶非线性极化过程产生影响. 关键词： 银纳米粒子 超瑞利散射 二阶光学非线性 聚集     

零质量玻色场,自发破缺与Goldstone定理

本文讨论零质量玻色场φ(x)在动量空间的零频部分,它不是动量趋于零时的极限,所以并不代表粒子的产生和湮灭算符。由于正则量子化得到一连续量子数,因此所有物理态都不能归一。真空变成一个无穷宽能带中的任意一个态。当φ(x)是厄米场时,真空并不存在简并,因此没有真空自发破缺;当φ(x)是复数场时,每一真空都是无穷地分立简并,因此也没有连续对称的自发破缺。利用这些态容易验证 Goldstone 定理证明中所插入的零动量零能量中间态并非代表不同数目的 Goldstone 粒子的相干迭加,也不一定与原来的真空态正交。文章亦讨论了φ(x)→φ(x)+η的生成元,它作用在φ(x)上的真空平均值及作用在真空态上的结果。     

具有幂次相互作用的磁性粒子凝聚过程的数值研究

在扩散限制凝聚模型的基础上引入粒子的自旋自由度(包括自旋向上和向下),并假设粒子间存在幂次Ising磁相互作用,采用Monte Carlo方法研究了在不同相互作用力程情况下磁性粒子的分形生长规律.模拟结果表明,当粒子间以反铁磁方式耦合时,凝聚体中的粒子自旋交替凝聚.当粒子间以铁磁方式耦合时,凝聚体中粒子的自旋分布与相互作用力程有关:对于短程作用系统,凝聚体中存在大小不同的自旋畴块,即为铁磁生长;而对于长程相互作用系统,凝聚体中的自旋出现反常分布,即中心区域是近似反铁磁生长的结构,其外围后续生长的粒子却保持 关键词： 幂次相互作用 扩散限制凝聚模型 自旋     

Hydrodynamic Limit of Condensing Two-Species Zero Range Processes with Sub-critical Initial Profiles

Two-species condensing zero range processes (ZRPs) are interacting particle systems with two species of particles and zero range interaction exhibiting phase separation outside a domain of sub-critical densities. We prove the hydrodynamic limit of nearest neighbour mean zero two-species condensing ZRP with bounded local jump rate for sub-critical initial profiles, i.e., for initial profiles whose image is contained in the region of sub-critical densities. The proof is based on H.T. Yau’s relative entropy method, which relies on the existence of sufficiently regular solutions to the hydrodynamic equation. In the particular case of the species-blind ZRP, we prove that the solutions of the hydrodynamic equation exist globally in time and thus the hydrodynamic limit is valid for all times.     

Power laws in zero-range processes on random networks

We study statistical properties of a zero-range process (ZRP) on random networks.We derive an analytic expression for the distribution of particles (also called node occupation distribution)in the steady state of the ZRP in the ensemble of uncorrelated random graphs. We analyze the dependence of this distribution on the node-degree distribution.In particular, we show that when the degree distribution is tuned properly, one can obtainscale-free fluctuations in the distribution of particles.Such fluctuations lead to a power law in the distribution of particles, just like in the ZRP with the hopping rate u(m) = 1+b/mon homogeneous graphs.     

Evolutionary games on scale-free networks with a preferential selection mechanism

Considering the heterogeneity of individuals’ influence in the real world, we introduce a preferential selection mechanism to evolutionary games (the Prisoner’s Dilemma Game and the Snowdrift Game) on scale-free networks and focus on the cooperative behavior of the system. In every step, each agent chooses an individual from all its neighbors with a probability proportional to k^α indicating the influence of the neighbor, where k is the degree. Simulation results show that the cooperation level has a non-trivial dependence on α. To understand the effect of preferential selection mechanism on the evolution of the system, we investigate the time series of the cooperator frequency in detail. It is found that the cooperator frequency is greatly influenced by the initial strategy of hub nodes when α>0. This observation is confirmed by investigating the system behavior when some hub nodes’ strategies are fixed.     

Modeling online social networks based on preferential linking

We study the phenomena of preferential linking in a large-scale evolving online social network and find that the linear preference holds for preferential creation,preferential acceptance,and preferential attachment.Based on the linear preference,we propose an analyzable model,which illustrates the mechanism of network growth and reproduces the process of network evolution.Our simulations demonstrate that the degree distribution of the network produced by the model is in good agreement with that of the real network.This work provides a possible bridge between the micro-mechanisms of network growth and the macrostructures of online social networks.     

Influence of zero range process interaction on diffusion

We study the aspects of diffusion for the case of zero range process interaction on scale-free networks, through statistical quantities such as the mean first passage time, coverage, mean square displacement etc., and pay attention to how the interaction, especially the resulted condensation, influences the diffusion. By mean-field theory we show that the statistical quantities of diffusion can be significantly reduced by the condensation and can be figured out by the waiting time of a particle staying at a node. Numerical simulations have confirmed the theoretical predictions.     

Topological Fermi liquids from Coulomb interactions in the doped honeycomb lattice

We propose a simple method for obtaining time reversal symmetry (T) broken phases in simple lattice models based on enlarging the unit cell. As an example we study the honeycomb lattice with nearest neighbor hopping and a local nearest neighbor Coulomb interaction V. We show that when the unit cell is enlarged to host six atoms that permits Kekulé distortions, self-consistent currents spontaneously form creating nontrivial magnetic configurations with total zero flux at high electron densities. A very rich phase diagram is obtained within a variational mean field approach that includes metallic phases with broken time reversal symmetry (T). The predominant (T) breaking configuration is an anomalous Hall phase, a realization of a topological Fermi liquid.     

Complete condensation in a zero range process on scale-free networks

We study a zero range process on scale-free networks in order to investigate how network structure influences particle dynamics. The zero range process is defined with the rate p(n) = n(delta) at which particles hop out of nodes with n particles. We show analytically that a complete condensation occurs when delta < or = delta(c) triple bond 1/(gamma-1) where gamma is the degree distribution exponent of the underlying networks. In the complete condensation, those nodes whose degree is higher than a threshold are occupied by macroscopic numbers of particles, while the other nodes are occupied by negligible numbers of particles. We also show numerically that the relaxation time follows a power-law scaling tau approximately L(z) with the network size L and a dynamic exponent z in the condensed phase.     

Transitions to the Fulde-Ferrell-Larkin-Ovchinnikov phases at low temperature in two dimensions

We explore the nature of the transition to the Fulde-Ferrell-Larkin- Ovchinnikov superfluid phases in the low temperature range in two dimensions, for the simplest isotropic BCS model. This is done by applying the Larkin-Ovchinnikov approach to this second order transition. We show that there is a succession of transitions toward ever more complex order parameters when the temperature goes to zero. This gives rise to a cascade with, in principle, an infinite number of transitions. Except for one case, the order parameter at the transition is a real superposition of cosines with equal weights. The directions of these wavevectors are equally spaced angularly, with a spacing which goes to zero when the temperature goes to zero. This singular behaviour in this T = 0 limit is deeply linked to the two-dimensional nature of the problem.     

A note on the Lie symmetries of complex partial differential equations and their split real systems

Folklore suggests that the split Lie-like operators of a complex partial differential equation are symmetries of the split system of real partial differential equations. However, this is not the case generally. We illustrate this by using the complex heat equation, wave equation with dissipation, the nonlinear Burgers equation and nonlinear KdV equations. We split the Lie symmetries of a complex partial differential equation in the real domain and obtain real Lie-like operators. Further, the complex partial differential equation is split into two coupled or uncoupled real partial differential equations which constitute a system of two equations for two real functions of two real variables. The Lie symmetries of this system are constructed by the classical Lie approach. We compare these Lie symmetries with the split Lie-like operators of the given complex partial differential equation for the examples considered. We conclude that the split Lie-like operators of complex partial differential equations are not in general symmetries of the split system of real partial differential equations. We prove a proposition that gives the criteria when the Lie-like operators are symmetries of the split system.     

蒸汽喷入过冷液面接触冷凝实验研究

对饱和蒸汽垂直喷入过冷液面直接接触冷凝进行了可视化实验,观察到近液面层汽液两相作用区的凝结现象,研究了系统压力响应特性,提出将蒸汽凝结过程分为"压力平衡"和"压力稳定"两个阶段,根据实验结果回归了不同凝结模式下平均凝结换热系数的实验关联式.通过对温度场的分析、得到了热水层的分布规律.