arXiv subjects

Jian-Yang Zhu

Publications and source records attributed to Jian-Yang Zhu.

64 records · Page 4Linked to original sources

arXiv2003

Small-World Network Effect in Competing Glauber- and Kawasaki-type Dynamics

In this article, we investigate the competing Glauber-type and Kawasaki-type dynamics with small-world network (SWN) effect, in the framework of the Gaussian model. The Glauber-type single-spin transition mechanism with probability p simulates the contact of the system with a heat bath and the Kawasaki-type dynamics with probability 1-p simulates an external energy flux. Two different types of SWN effect are studied, one with the total number of links increased and the other with it conserved. The competition of the dynamics leads to an interesting self-organization process that can be characterized by a phase diagram with two identifiable temperatures. By studying the modification of the phase diagrams, the SWN effect on the two dynamics is analyzed. For the Glauber-type dynamics, more important is the altered average coordination number while the Kawasaki-type dynamics is enhanced by the long range spin interaction and redistribution.

cond-mat.stat-mech↗

arXiv2003

The effect of aging on network structure

In network evolution, the effect of aging is universal: in scientific collaboration network, scientists have a finite time span of being active; in movie actors network, once popular stars are retiring from stage; devices on the Internet may become outmoded with techniques developing so rapidly. Here we find in citation networks that this effect can be represented by an exponential decay factor, $e^{-βτ}$, where $τ$ is the node age, while other evolving networks (the Internet for instance) may have different types of aging, for example, a power-law decay factor, which is also studied and compared. It has been found that as soon as such a factor is introduced to the Barabasi-Albert Scale-Free model, the network will be significantly transformed. The network will be clustered even with infinitely large size, and the clustering coefficient varies greatly with the intensity of the aging effect, i.e. it increases linearly with $β$ for small values of $β$ and decays exponentially for large values of $β$. At the same time, the aging effect may also result in a hierarchical structure and a disassortative degree-degree correlation. Generally the aging effect will increase the average distance between nodes, but the result depends on the type of the decay factor. The network appears like a one-dimensional chain when exponential decay is chosen, but with power-law decay, a transformation process is observed, i.e., from a small-world network to a hypercubic lattice, and to a one-dimensional chain finally. The disparities observed for different choices of the decay factor, in clustering, average node distance and probably other aspects not yet identified, are believed to bear significant meaning on empirical data acquisition.

cond-mat.stat-mech↗

arXiv2003

Decay of spin-1/2 field around Reissner-Nordstrom black hole

To find what influence the charge of the black hole $Q$ will bring to the evolution of the quasinormal modes, we calculate the quasinormal frequencies of the neutrino field (charge $e=0$) perturbations and those of the massless Dirac field ($e\neq 0$) perturbations in the RN metric. The influences of $Q$, $e$, the momentum quantum number $l$, and the mode number $n$ are discussed. Among the conclusions, the most important one is that, at the stage of quasinormal ringing, the larger when the black hole and the field have the same kind of charge ($eQ>0$), the quasinormal modes of the massless charged Dirac field decay faster than those of the neutral ones, and when $eQ<0$, the massless charged Dirac field decays slower.

gr-qc↗

arXiv2003

Spin-lattice models: inhomogeneity and diffusion

In spin-lattice models with order parameter conserved, we generalize the idea of spin diffusion incorporating a variety factors as possible driving forces, including the external field and the temperature. The Kawasaki dynamics in the Gaussian model and the one-dimensional Ising model are studied. The Gaussian model is rigorously treated and the critical exponent $γ=1$ is obtained. The competition of the internal and the external inhomogeneities may lead to interesting and rich dynamic behavior. The diffusion induced by the inhomogeneity of the magnetization itself is believed to vanish near the critical point, meanwhile the nonvanishing diffusion induced by the inhomogeneity of the environment may be coupled to the spin configuration and weakened by thermal noise. Several interesting examples are visualized, and the concept of local hysteresis is proposed in this spin-conserved dynamics. A dynamic phase transition is observed in the one-dimensional Ising model subject to an electromagnetic wave.

cond-mat.stat-mech↗

arXiv2002

Introducing Small-World Network Effect to Critical Dynamics

We analytically investigate the kinetic Gaussian model and the one-dimensional kinetic Ising model on two typical small-world networks (SWN), the adding-type and the rewiring-type. The general approaches and some basic equations are systematically formulated. The rigorous investigation of the Glauber-type kinetic Gaussian model shows the mean-field-like global influence on the dynamic evolution of the individual spins. Accordingly a simplified method is presented and tested, and believed to be a good choice for the mean-field transition widely (in fact, without exception so far) observed on SWN. It yields the evolving equation of the Kawasaki-type Gaussian model. In the one-dimensional Ising model, the p-dependence of the critical point is analytically obtained and the inexistence of such a threshold p_c, for a finite temperature transition, is confirmed. The static critical exponents, gamma and beta are in accordance with the results of the recent Monte Carlo simulations, and also with the mean-field critical behavior of the system. We also prove that the SWN effect does not change the dynamic critical exponent, z=2, for this model. The observed influence of the long-range randomness on the critical point indicates two obviously different hidden mechanisms.

cond-mat.dis-nn↗

arXiv2002

Driven Dynamics: A Probable Photodriven Frenkel-Kontorova Model

In this study, we examine the dynamics of a one-dimensional Frenkel-Kontorova chain consisting of nanosize clusters (the ''particles'') and photochromic molecules (the ''bonds''), and being subjected to a periodic substrate potential. Whether the whole chain should be running or be locked depends on both the frequency and the wavelength of the light (keeping the other parameters fixed), as observed through numerical simulation. In the locked state, the particles are bound at the bottom of the external potential and vibrate backwards and forwards at a constant amplitude. In the running state, the initially fed energy is transformed into directed motion as a whole. It is of interest to note that the driving energy is introduced to the system by the irradiation of light, and the driven mechanism is based on the dynamical competition between the inherent lengths of the moving object (the chain) and the supporting carrier (the isotropic surface). However, the most important is that the light-induced conformational changes of the chromophore lead to the time-and-space dependence of the rest lengths of the bonds.

cond-mat.mtrl-sci↗

arXiv2002

Glauber Critical Dynamics: Exact Solution of the Kinetic Gaussian Model

In this paper, we have exactly solved Glauber critical dynamics of the Gaussian model on three dimensions. Of course, it is much easy to apply to low dimensional case. The key steps are that we generalize the spin change mechanism from Glauber's single-spin flipping to single-spin transition and give a normalized version of the transition probability . We have also investigated the dynamical critical exponent and found surprisingly that the dynamical critical exponent is highly universal which refer to that for one- two- and three-dimensions they have same value independent of spatial dimensionality in contrast to static (equilibrium) critical exponents.

cond-mat.dis-nn↗

arXiv2002

Solvable Kinetic Gaussian Model in External Field

In this paper, the single-spin transition dynamics is used to investigate the kinetic Gaussian model in a periodic external field. We first derive the fundamental dynamic equations, and then treat an isotropic d-dimensional hypercubic lattice Gaussian spin system with Fourier's transformation method. We obtain exactly the local magnetization and the equal-time pair correlation function. The critical characteristics of the dynamical, the complex susceptibility, and the dynamical response are discussed. The results show that the time evolution of the dynamical quantities and the dynamical responses of the system strongly depend on the frequency and the wave vector of the external field.

cond-mat.dis-nn↗

arXiv2002

Dynamical Decimation Renormalization-Group Technique: Kinetic Gaussian Model on Non-Branching, Braching and Multi-branching Koch Curve

A generalizing formulation of dynamical real-space renormalization that suits for arbitrary spin systems is suggested. The new version replaces the single-spin flipping Glauber dynamics with the single-spin transition dynamics. As an application, in this paper we mainly investigate the critical slowing down of the Gaussian spin model on three fractal lattices, including nonbranching, branching and multibranching Koch Curve. The dynamical critical exponent $z$ is calculated for these lattices using an exact decimation renormalization transformation in the assumption of the magnetic-like perturbation, and a universal result $z=1/ν$ is found.

cond-mat.dis-nn↗

arXiv2002

Kawasaki-type Dynamics: Diffusion in the kinetic Gaussian model

In this article, we retain the basic idea and at the same time generalize Kawasaki's dynamics, spin-pair exchange mechanism, to spin-pair redistribution mechanism, and present a normalized redistribution probability. This serves to unite various order-parameter-conserved processes in microscopic, place them under the control of a universal mechanism and provide the basis for further treatment. As an example of the applications, we treated the kinetic Gaussian model and obtained exact diffusion equation. We observed critical slowing down near the critical point and found that, the critical dynamic exponent z=1/nu=2 is independent of space dimensionality and the assumed mechanism, whether Glauber-type or Kawasaki-type.

cond-mat.dis-nn↗