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In loop quantum cosmology nonperturbative modification to a scalar matter field at short scales implies inflation which also means a violation of the strong energy condition. In the framework of effective Hamiltonian we discuss the issue of violation of the strong energy condition in the presence of quantum geometry potential. It shows that the appearance of quantum geometry potential strengthens the violation of the strong energy condition in small volume regions. In the small volume regions superinflation can easily happen. Furthermore, when the evolution of the universe approaches the bounce scale, this trend of violating the strong energy condition can be greatly amplified., Comment: New improved version

Navigation process is studied on a variant of the Watts-Strogatz small world network model embedded on a square lattice. With probability $p$, each vertex sends out a long range link, and the probability of the other end of this link falling on a vertex at lattice distance $r$ away decays as $ r^{-\alpha}$. Vertices on the network have knowledge of only their nearest neighbors. In a navigation process, messages are forwarded to a designated target. For $\alpha <3$ and $\alpha \neq 2$, a scaling relation is found between the average actual path length and $pL$, where $L$ is the average length of the additional long range links. Given $pL>1$, dynamic small world effect is observed, and the behavior of the scaling function at large enough $pL$ is obtained. At $\alpha =2$ and 3, this kind of scaling breaks down, and different functions of the average actual path length are obtained. For $\alpha >3$, the average actual path length is nearly linear with network size., Comment: Accepted for publication in Phys. Rev. E

In this paper, we offer a competing dynamic analysis of the one-dimensional Ising model built on the small-world network (SWN). Adding-type SWNs are investigated in detail using a simplified Hamiltonian of mean-field nature, and the result of rewiring-type is given because of the similarities of these two typical networks. We study the dynamical processes with competing Glauber mechanism and Kawasaki mechanism. 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. By studying the phase diagram obtained in the present work, we can realize some dynamical properties influenced by the small-world effect., Comment: 5 pages, one figure, accepted for publication in Physical Review E

In this paper, the two-dimensional Reissner-Nordstr\"{o}m black hole is considered as a system of the Casimir type. In this background the Casimir effect for the massless Dirac field is discussed. The massless Dirac field is confined between two ``parallel plates'' separated by a distance $L$ and there is no particle current drilling through the boundaries. The vacuum expectation values of the stress tensor of the massless Dirac field at infinity are calculated separately in the Boulware state, the Hartle-Hawking state and the Unruh state., Comment: 10 pages, no figure. Accepted for publication in IJMPD

This paper demonstrates a dynamical evolution model of the black hole (BH) horizon. The result indicates that a kinetic area-cells model of the BH's horizon can model the evolution of BH due to the Hawking radiation, and this area-cell system can be considered as an interacting geometrical particle system. Thus the evolution turns into a problem of statistical physics. In the present work, this problem is treated in the framework of non-equilibrium statistics. It is proposed that each area-cell possesses the energy like a microscopic black hole, and has the gravitational interaction with the other area-cells. We consider both a non-interaction ideal system, and a system with small nearest-neighbor interactions, and obtain an analytic expression of the expected value of the horizon area of a dynamical BH. We find that, after a long enough evolution, a dynamical BH with the Hawking radiation can be in equilibrium with a finite temperature radiation field. However, we also find that, the system has a critical point, and when the temperature of the radiation field surrounding the BH approaches the critical temperature of the BH, a critical slowing down phenomenon occurs., Comment: Accepted for publication in Classical and Quantum Gravity

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., Comment: 18 pages, 1 figure. Accepted for publication in "The European Physical Journal B (EPJB)"

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.

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, $e^{-\beta \tau}$, where $\tau $ 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 $\beta $ for small values of $\beta $ and decays exponentially for large values of $\beta $. 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., Comment: 8 pages, 9 figures,V2, accepted for publication in Phys. Rev. E

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 $\gamma =1$ 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., Comment: 9 pages, 4 figures,V2: Minor changes in Sec.II B

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., Comment: 30 pages, 1 ps figures, REVTEX, accepted for publication in Phys. Rev. E

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., Comment: 4 pages,5 figures

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/\nu $ is found., Comment: 21 pages

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., Comment: 11 pages

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., Comment: 9 pages

In this article, we have given a systematic formulation of the new generalized competing mechanism: the Glauber-type single-spin transition mechanism, with probability p, simulates the contact of the system with the heat bath, and the Kawasaki-type spin-pair redistribution mechanism, with probability 1-p, simulates an external energy flux. These two mechanisms are natural generalizations of Glauber's single-spin flipping mechanism and Kawasaki's spin-pair exchange mechanism respectively. On the one hand, the new mechanism is in principle applicable to arbitrary systems, while on the other hand, our formulation is able to contain a mechanism that just directly combines single-spin flipping and spin-pair exchange in their original form. Compared with the conventional mechanism, the new mechanism does not assume the simplified version and leads to greater influence of temperature. The fact, order for lower temperature and disorder for higher temperature, will be universally true. In order to exemplify this difference, we applied the mechanism to 1D Ising model and obtained analytical results. We also applied this mechanism to kinetic Gaussian model and found that, above the critical point there will be only paramagnetic phase, while below the critical point, the self-organization as a result of the energy flux will lead the system to an interesting heterophase, instead of the initially guessed antiferromagnetic phase. We studied this process in details., Comment: 11 pages,1 figures

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., Comment: accepted for publication in PRE