Phase Structure of Systems with Infinite Numbers of Absorbing States

Critical properties of systems exhibiting phase transitions into phases with infinite numbers of absorbing states are studied. We analyze a non-Markovian Langevin equation recently proposed to describe the critical behavior of such systems, and also introduce and study a non-Markovian discrete model, which is argued to present the same critical features. On the basis of mean-field analysis, Monte Carlo simulations, and theoretical arguments, we conclude that the phenomenology of the non-Markovian models closely parallels that of systems with many absorbing states in one and two dimensions. The bulk or static critical properties of these systems fall in the directed percolation (DP) universality class. By contrast, the critical properties associated with the spread of an initially localized seed exhibit a more complex behavior: Depending on parameter values they can, both in one and two dimensions, fall either in the dynamical percolation or DP universality class, or else exhibit apparently nonuniversal exponents. In contrast to previous results, however, the nonuniversal exponents in 2D are found to satisfy a scaling law which implies that a particular linear combination of them is universal and assumes DP values. These results demonstrate the efficacy of the non-Markovian approach for understanding systems with many absorbing states, which are difficult to analyze in their original microscopic formulation.     

Adaptive Regulation for Noise-Aided Weak Signal Detection in Spiking Neurons

Spiking neurons usually change their membrane properties, especially ion channel activity, during adaptation or synaptic modification to improve information processing and transmission. Using simple and biophysically realistic models, our analyses reveal that activity-dependent regulation of membrane properties contributes to sensitivity adaptation that improves the neuron ability of detecting sub-threshold signals in the presence of background noises. The improvement is achieved by regulating the conductance of ion channels on the membrane, dependent on the neuron firing activity.     

FitzHugh-Nagumo神经元网络的联想记忆与分割

以广泛讨论的Fitz Hugh-Nagumo神经元节点组成脉动神经元网络,从神经系统空时模式编码理论研究网络的记忆(或模式)存储与时间分割问题.给定一个输入模式,它是几种模式的叠加,网络能够以一部分神经元同步发放的形式一个接一个地分割出每一种模式.如果输入的模式有缺损,系统能够把它们恢复成原型,即神经网络的联想记忆功能.模拟需要调节耦合强度和噪声强度等参数使得网络在特定的参数值和中等强度噪声达到最优的时间分割,与广泛讨论的随机共振现象一致.     

Quantum Correlations in Infinite XY Spin-1/2 Chains and Quantum Phase Transition

We examine the ability of quantum discord (QD) and entanglements (concurrence, EoF and negativity) to detect the critical points associated to quantum phase transitions (QPTs) for XY models, i.e., the isotropic XY model with three-spin interactions at zero temperature, and the anisotropic XY model in a transverse magnetic field h at finite temperatures. For the case of zero temperature, we found that both entanglements and QD can spotlight the critical points of QPTs for these two models. Moreover, QD versus distance M exhibits the long-range behavior of quantum correlation for the anisotropic XY model, while entanglement is short-ranged. For the case of finite temperatures, we found that negativity has the same behaviors with concurrence at or near transition points. Moreover, QD for the anisotropic XY model can increase with temperature even in the absence of a magnetic field.     

Phenomenological Free-Energy-Function,Fractal Dimension,and Critical Indices for Phase Transition Systems

Considering the relations between interaction terms in microscopic Hamiltonian and φⁿ terms in macroscopic Landau's free-energy-function (FEF) of a phase transition system, we propose a modified Landau's phenomenological FEF to deal with critical phenomena.According to scaling symmetry, it ie indeed true tiat, the dimension of interaction space is fractal at critical points for a phase transition system. Following these analyses, we obtain all the critical indices reasonably classified in the classes denoted by n, whid satisfy all the scaling laws and coincide with experiments. A cogent example ie given.     

Phase Transition in Modified Newtonian Dynamics (MONDian) Self-Gravitating Systems

We study the statistical mechanics of binary systems under the gravitational interaction of the Modified Newtonian Dynamics (MOND) in three-dimensional space. Considering the binary systems in the microcanonical and canonical ensembles, we show that in the microcanonical systems, unlike the Newtonian gravity, there is a sharp phase transition, with a high-temperature homogeneous phase and a low-temperature clumped binary one. Defining an order parameter in the canonical systems, we find a smoother phase transition and identify the corresponding critical temperature in terms of the physical parameters of the binary system.     

Phase Transition in Three-Dimensional Noncollinear Magnetic Systems with Additional Two-Fold Degeneracy

JETP Letters - Using Monte Carlo simulations, we investigate the critical behavior in a three-dimensional frustrated helimagnet with an additional two-fold degeneracy, realized in a...     

Phase Transition in Particle Systems with a Nonnegatively Defined Interaction Potential

We have obtained equations for calculating the parameters of phase transitions in particle systems with a nonnegatively defined interaction potential. The parametrized Gibbs distribution is part of the basis of our derivation. It takes the features of a non-negatively defined interaction potential into account and leads to the corresponding Bogolyubov chain of equations. Using this approach, we obtain a convenient method for finding the free energy of the system. On the basis of this method, we have studied the phase transition in a system of hard spheres and the dependence of the phase-transition temperature on the temperature of argon at high pressures.     

Fuzzy Reasoning Numerical Spiking Neural P Systems for Induction Motor Fault Diagnosis

The fuzzy reasoning numerical spiking neural P systems (FRNSN P systems) are proposed by introducing the interval-valued triangular fuzzy numbers into the numerical spiking neural P systems (NSN P systems). The NSN P systems were applied to the SAT problem and the FRNSN P systems were applied to induction motor fault diagnosis. The FRNSN P system can easily model fuzzy production rules for motor faults and perform fuzzy reasoning. To perform the inference process, a FRNSN P reasoning algorithm was designed. During inference, the interval-valued triangular fuzzy numbers were used to characterize the incomplete and uncertain motor fault information. The relative preference relationship was used to estimate the severity of various faults, so as to warn and repair the motors in time when minor faults occur. The results of the case studies showed that the FRNSN P reasoning algorithm can successfully diagnose single and multiple induction motor faults and has certain advantages over other existing methods.     

Activity Phase Transition for Constrained Dynamics

We consider two cases of kinetically constrained models, namely East and FA-1f models. The object of interest of our work is the activity A(t){\mathcal {A}(t)} defined as the total number of configuration changes in the interval [0, t] for the dynamics on a finite domain. It has been shown in Garrahan et al. (J Phys A 42:075007, 2009; Phys Rev Lett 98:195702, 2007) that the large deviations of the activity exhibit a non-equilibrium phase transition in the thermodynamic limit and that reducing the activity is more likely than increasing it due to a blocking mechanism induced by the constraints. In this paper, we study the finite size effects around this first order phase transition and analyze the phase coexistence between the active and inactive dynamical phases in dimension 1. In higher dimensions, we show that the finite size effects are determined by the dimension and the choice of the boundary conditions.     

On Entanglement Breaking Channels for Infinite Dimensional Quantum Systems

The topic of entanglement breaking channels plays an important role in quantum information. Horodecki et al. (Rev. Math. Phys. 15:629–641, 2003) gave a complete characterization of entanglement breaking channels for finite dimensional quantum systems. In the note, we will generalize the results in Horodecki et al. (Rev. Math. Phys. 15:629–641, 2003) to the infinite dimensional case. We first generalized the positive map criterion of the entanglement breaking channel from the finite dimensional case to the infinite dimensional case. As a generalization of entanglement breaking channels for finite dimensional quantum systems, the topic of the strong entanglement breaking channel for arbitrary (finite or infinite) dimensional systems is putted forward. We obtain the operator sum representation of the strong entanglement breaking quantum channel. Applying this operator sum representation, we characterize a category of extreme points of the convex set of all strong entanglement breaking channels, which generalizes corresponding results in the finite dimensional case from Horodecki et al. (Rev. Math. Phys. 15:629–641, 2003).     

Research into the Surface Phase Transition of Semibounded Antiferromagnetic Systems via Computer Simulation

Monte-Carlo computer simulation is employed to investigate the surface phase transition (PT) in the 3D semibounded antiferromagnetic Ising model. Simulation is performed at different ratios of exchange integrals on the system surface and in its bulk. The dependence between the PT temperature and the distance to the surface is studied. When the ratio of exchange integrals is less than 1.38, the PT temperature is found to increase with distance from the surface. A comparison with the results of a real experiment is carried out. The simulation results are demonstrated to be in qualitative and quantitative agreement with experimental data.     

Non-Equilibrium Dynamics of Three-Dimensional Infinite Particle Systems

We show existence and uniqueness for the solutions to the Newton equations relative to a system of infinitely many particles in the space, interacting by means of a positive and short-range potential. The initial conditions are chosen in a set sufficiently large to be the support of any reasonable non-equilibrium state. We extend previous results in one and two dimensions, obtained by Lanford and by Fritz and Dobrushin respectively, many years ago. Received: 7 December 1999 / Accepted: 9 May 2000     

Classical Properties of Infinite Quantum Open Systems

Long time asymptotic properties of a class of environmentally induced dynamical semigroups on arbitrary von Neumann algebras are discussed. Such a semigroup selects observables, called effective observables, which are immune to the process of decoherence and so evolve in a reversible automorphic way. In particular, it is shown that effective observables of the quantum system in the thermodynamic limit, subjected to a specific interaction with another quantum system, obey classical dynamics.This work was supported by the KBN research grant no 5P03B 081 21     

利用慢度曲面研究立方晶系晶体的铁弹相变

讨论了慢度曲面与声学模软化之间的关系.立方晶系晶体声学模的软化即对应其在某一方向上的最大慢度,软模的本征矢的方向即为与最大慢度相对应的声学模的偏振化方向.通过求解Christoffel方程可找到某些方向上的最大慢度和与它们对应的声学模的偏振化方向.从而晶体在本征铁弹相变前后结构对称性的变化可以通过分析Christoffel方程的解及利用居里原理来确定.