色关联乘性和加性色噪声驱动的多稳态系统的稳态特性

研究了色关联乘性和加性色噪声作用下的三稳态系统的稳态问题.首先利用一致有色噪声近似方法,推导出稳态概率密度函数的表达式,然后分析了乘性噪声和加性噪声的强度以及关联性对稳态概率密度函数的影响,研究结果表明:加性噪声强度、加性噪声和乘性噪声的关联强度和关联时间可以诱导系统的非平衡相变.     

双量子点Aharonov-Bohm干涉系统输运性质的大偏离分析

由于电子的多体关联和量子相干性的联合作用, 双量子点Aharonov-Bohm 干涉系统中的电子输运过程隐含 内在的快、慢两条通道, 且通道之间的有效耦合强度可以通过磁通调控. 但是, 这一非平庸的内在性质, 在通常的稳态输运电流中不能得以反映. 本文利用在研究非平衡动力学相变中所发展的大偏离方法, 对该输运系统中的电子动力学路径做大偏离统计分析. 结果显示, 以上内在性质将诱导出路径空间中清晰的动力学相变行为.     

双色噪声激励下FHN神经元系统的稳态性质

应用统一色噪声理论研究了双色噪声激励下一维FitzHugh-Nagumo (FHN)神经元系统的动力学性质,即稳态概率分布函数和其平均值. 给出了FHN神经元系统的稳态概率密度和平均值的解析表达式. 结果表明: 乘性噪声的自关联时间τ ₁、加性噪声的自关联时间τ ₂、加性噪声强度α 和乘性噪声强度D都能够诱导非平衡相变的产生. α和D的增大有利于系统从激发态向静息态转换. τ₁, τ₂的增大有利于系统从静息态向激发态转换. 噪声强度和其自关联时间的作用完全相反.     

关联高斯与非高斯噪声激励的FHN神经元系统的稳态分析

本文主要研究了关联乘性非高斯噪声和加性高斯白噪声共同激励的FHN(Fitz Hugh-Nagumo)神经元系统.利用路径积分法和统一色噪声近似,推导出该系统的定态概率密度函数表达式.通过研究发现,乘性噪声强度D、加性噪声强度Q、噪声自关联时间τ以及互关联系数λ均可以诱导系统产生非平衡相变现象,而非高斯参数q却不可以诱导系统产生非平衡相变现象.此外,我们还发现参数D和λ的增大有利于神经元系统从激发态向静息态转换,Q和τ的增大有利于神经元系统从静息态向激发态转换,q的增大会使得神经元系统停留在静息态的概率增加.     

色噪声驱动的非对称双稳系统的平均首次穿越时间

研究了由关联乘性色噪声及加性白噪声驱动的非对称双稳系统中势阱的非对称性及噪声对系统两个方向平均首次穿越时间的影响. 首先利用一致有色噪声近似推导了系统的稳态概率密度的表达式，根据最速下降法推导了平均首次穿越时间的表达式. 数值结果表明：势阱的非对称性对两个方向的平均首次穿越时间的影响是不同的；由于噪声的关联性，即使对于关联乘性色噪声及加性白噪声驱动的对称双稳系统，两个方向的平均首次穿越时间也不再相等；在lnT₊-r和lnT_{-关键词： 平均首次穿越时间 非对称双稳系统 乘性色噪声 加性白噪声}     

分形结构对CO催化氧化非线性动力学行为影响的理论研究

在平均场近似下建立了包含分形上反常扩散在内的理论模型，描述了典型单分子－双分子反应：ＣＯ＋Ｏ２的非线性动力学规律，并着重考察了分形结构对振荡行为以及非平衡相变的影响，我们发现：①随分形维数ｄｆ的降低，振荡区向ＣＯ的低分压方向偏移并减小，甚至消失；同时，在相同的反应条件下，对二维规则表面不存在振荡行为的区域，有可能因分形上的受限扩散而诱导振荡。②在较高温度下，分形结构除了控制体系的非线性动力学行为，     

具有Dzyaloshinskii-Moriya相互作用的XY模型的量子相干性

研究了具有Dzyaloshinskii-Moriya(DM)相互作用的一维横场XY自旋链的量子相变和量子相干性.采用约旦-维格纳变换严格求解了哈密顿量,并描绘了体系的关联函数和相图,相图包含反铁磁相、顺磁相和螺旋相.利用相对熵和Jensen-Shannon熵讨论了XY模型的量子相干性.研究发现,相对熵与Jensen-Shannon熵所表现的行为都可以很好地表征该模型的量子相变.非螺旋相中量子相干性不依赖DM相互作用,而在螺旋相DM相互作用对量子相干性有显著影响.此外,指出了在带有DM相互作用的这一类反射对称破缺体系中关联函数计算的常见问题.     

双修饰的Ising-Heisenberg平面模型几何量子关联

双修饰的Ising-Heisenberg平面模型是凝聚态物理领域一个受到比较广泛重视的模型。由于量子关联对于研究低温情况下物质的相变具有十分重要的意义,所以本文里我们考查了这个模型中同一个键里两个海森堡自旋量子关联的几何特性。另一方面,由于任何体系不可避免地要受到外界环境的影响,我们同样也求解了三种不同的局域通道作用下量子关联的几何测量,以期该文的研究结果对于研究噪声存在情况下体系的相变具有一定的借鉴意义。     

Ising自旋体系的非平衡动态相变

在平均场理论架构下, 以含时金兹堡-朗道和Glauber动力学这两类动态模型为基础，研究 了受外场和温度共同驱动的Ising自旋体系的非平衡动态相变.确定了界定动态无序(动态顺 磁相P)和动态有序(动态铁磁相F)转变的动态相界.并根据动态序参量Q和Binder参数U随系统 温度t(r₀)、驱动外场频率ω和振幅h₀的变化规律，就上述两类模 型的动态相界上是否存在区分连续动态转变和非连续动态转变的三临界点这一引发争议的问 题做出了进一步分析说明. 关键词： Ising自旋体系 非平衡动态相变 含时金兹堡-朗道模型 Glauber 动力学模型     

反应扩散系统中的涨落问题

本文用Master方程导出的带有扩散涨落项的福克-普朗克方程讨论了三个化学模型在不同情况下的涨落问题,文章指出:平衡态附近的无空间关联的涨落,偏离平衡时涨落的关联性,Schlogl三分子模型县有非经典的临界指数,而Schligl双分子模型具有经典的临界指数等多样的情况是由系统的本身性质决定的,用本文的方法能统一地处理这些问题,并且因而澄清了文献[6]中提出的关于临界指数的疑点。 关键词：     

The origins of multifractality in financial time series and the effect of extreme events

In this paper, we study the impacts of noise and time delay in the monomer-dimer (MD) surface reaction model by using theoretical analysis. The MD models for various dimer adsorption mechanisms (namely, local and random adsorption models), which exhibit the first- and second-order phase transitions (PTs), are analyzed. By comparison with two various dimer adsorption, it is found that the qualitative predictions of the well-known first- and second-order PTs are better for the random adsorption model than that for the local adsorption model. The validity of approximate analytic results is checked by numerical simulations.     

Delayed stochastic systems

Noise and time delay are two elements that are associated with many natural systems, and often they are sources of complex behaviors. Understanding of this complexity is yet to be explored, particularly when both elements are present. As a step to gain insight into such complexity for a system with both noise and delay, we investigate such delayed stochastic systems both in dynamical and probabilistic perspectives. A Langevin equation with delay and a random-walk model whose transition probability depends on a fixed time-interval past (delayed random walk model) are the subjects of in depth focus. As well as considering relations between these two types of models, we derive an approximate Fokker-Planck equation for delayed stochastic systems and compare its solution with numerical results.     

Measurement-noise maximum as a signature of a phase transition

We propose that a maximum in measurement noise can be used as a signature of a phase transition. As an example, we study the energy and magnetization noise spectra associated with first- and second-order phase transitions by using Monte Carlo simulations of the Ising model and 5-state Potts model in two dimensions. For a finite size system, the total noise power and the low frequency white noise S(f0 and the total noise power vanishes. f(-1)(knee) is approximately the equilibration time.     

Phase Diagram of 2 × 2 Adsorbates at Surfaces with Hexagonal Symmetry

The phase diagram of a lattice-gas model for 2 2 2 adsorbates at surfaces with hexagonal symmetry has been investigated by Monte Carlo simulations. The model relies on repulsive interactions between the particles for distances up to second nearest neighbor sites. It is shown that first- or second-order phase transitions take place depending on the strength of the interactions. Strong first- or second-neighbor interactions are responsible for a first-order transition while for intermediate interaction strength a second-order transition is possible. The critical exponent for the susceptibility shows the expected value of the four-states Potts model in case of a second-order transition. The value of the critical exponent is reduced when the transition changes from first to second order.     

The effect of oxygen–oxygen repulsion in the production of water from hydrogen–oxygen reaction on the surface: A computer simulation study

The formation of water from hydrogen–oxygen reaction on a metal surface is of immense importance due to the technological reasons. This reaction has been studied via a thermal mechanism on a Pt single crystal surface where the two molecules, H₂ and O₂, have been adsorbed dissociatively in atomic form. The reaction takes place between the adsorbed atoms through an intermediate OH radical. We have studied this reaction via a thermal (Langmuir–Hinshelwood mechanism) as well as a non-thermal mechanism (precursor mechanism) by the Monte Carlo computer simulations. In this study, we have applied a novel approach based upon the experimental observations that the dissociated oxygen atoms do not sit next to one another on a catalytic surface. Some interesting results like the shifting of the phase transition points, the broadening of the reaction window width and the elimination of the second-order phase transition in the non-thermal reaction mechanism are obtained by considering various possibilities of the reaction scheme. The phase diagrams as well as the snapshots of the surface covered with the reacting species are presented.     

Effects of the Quenched Random Crystal Field on the Dynamic Spin-1 Blume-Capel Model

In this study, we have analyzed the dynamical phase transitions of spin-1 Blume-Capel model with quenched random crystal field under the effect of a time dependent oscillating magnetic field. We have obtained the magnetic field, temperature (h,T) cross sections of the global phase diagram for constant values of the concentration and the amplitude of the single-ion anisotropy within mean field approximation. There are regions of the phase space where both ordered and disordered phases coexist. In addition, the dynamic phase transition from one regime to the other can be a first- or a second-order depending on the region in the phase diagram. Hence, the system exhibits a number of interesting phenomena and a rich variety of phase diagrams with type being according to the concentration p of active local crystal fields.     

Non-equilibrium dynamical phases of the two-atom Dicke model

In this paper, we investigate the non-equilibrium dynamical phases of the two-atom Dicke model, which can be realized in a two species Bose–Einstein condensate interacting with a single light mode in an optical cavity. Apart from the usual non-equilibrium normal and inverted phases, a non-equilibrium mixed phase is possible which is a combination of normal and inverted phase. A new kind of dynamical phase transition is predicted from non-superradiant mixed phase to the superradiant phase which can be achieved by tuning the two different atom–photon couplings. We also show that a dynamical phase transition from the non-superradiant mixed phase to the superradiant phase is forbidden for certain values of the two atom–photon coupling strengths.     

Partial dynamical symmetry at critical points of quantum phase transitions

We show that partial dynamical symmetries can occur at critical points of quantum phase transitions, in which case underlying competing symmetries are conserved exactly by a subset of states, and mix strongly in other states. Several types of partial dynamical symmetries are demonstrated with the example of critical-point Hamiltonians for first- and second-order transitions in the framework of the interacting boson model, whose dynamical symmetries correspond to different shape phases in nuclei.     

Quantum–classical crossover of the escape rate in the two-parameter doubly periodic potential

The transition from the quantum tunneling to classical hopping for a two-parameter doubly periodic potential is investigated. According to the Chudnovsky's criterion for the first-order transition, it is shown that there is the first- or second-order transition depending on different parameters regions. The phase boundary lines between first- and second-order transitions are calculated, and a complete phase diagram is presented.     

Second order phase transition in neural rate coding: binary encoding is optimal for rapid signal transmission

Here, we derive optimal tuning functions for minimum mean square reconstruction from neural rate responses subjected to Poisson noise. The shape of these tuning functions strongly depends on the length T of the time window within which action potentials (spikes) are counted in order to estimate the underlying firing rate. A phase transition towards pure binary encoding occurs if the maximum mean spike count becomes smaller than approximately three. For a particular function class, we prove the existence of a second-order phase transition. The analytically derived critical decoding time window length is in precise agreement with numerical results. Our analysis reveals that binary rate encoding should dominate in the brain wherever time is the critical constraint.