We present a model which displays Griffiths phase i.e. algebraic decay of density with continuously varying exponent in the absorbing phase. In active phase, the memory of initial conditions is lost with continuously varying complex exponent in this model. This is 1-D model where fraction r of sites obey rules leading to directed percolation (DP) class and the rest evolve according to rules leading to compact directed percolation (CDP) class. For infection probability $p < p_c$, the fraction of active sites $ρ(t) = 0$ asymptotically. For $p > p_c$, $ρ(infty) > 0$. At $p = p_c$, $ρ(t)$, the survival probability from single seed and the average number of active sites starting from single seed decay logarithmically. The local persistence $P_l(\infty) > 0$ for $p < p_c$ and $P_l(\infty) = 0$ for $p > p_c$. For $p > p_s$, local persistence $P_l(t)$ decays as a power law with continuously varying exponents. The persistence exponent is clearly complex as $p\rightarrow 1$. The complex exponent implies logarithmic periodic oscillations in persistence. The wavelength and the amplitude of the logarithmic periodic oscillations increases with p. We note that underlying lattice or disorder does not have self-similar structure.
We study the local persistence probability during non-stationary time evolutions in disordered contact processes with long-range interactions by a combination of the strong-disorder renormalization group (SDRG) method, a phenomenological theory of rare regions, and numerical simulations. We find that, for interactions decaying as an inverse power of the distance, the persistence probability tends to a non-zero limit not only in the inactive phase but also in the critical point. Thus, unlike in the contact process with short-range interactions, the persistence in the limit $t\to\infty$ is a dis…
We study the time-dependence of the local persistence probability during a non-stationary time evolution in the disordered contact process in $d=1,2$, and $3$ dimensions. We present a method for calculating the persistence with the strong-disorder renormalization group (SDRG) technique, which we then apply in the critical point analytically for $d=1$ and numerically for $d=2,3$. According to the results, the average persistence decays at late times as an inverse power of the logarithm of time, with a universal, dimension-dependent generalized exponent. For $d=1$, the distribution of sample-dep…
We explore the emergence of nonequilibrium collective motion in disordered non-thermal active matter when persistent motion and crowding effects compete, using simulations of a two-dimensional model of size polydisperse self-propelled particles. In stark contrast with monodisperse systems, we find that polydispersity stabilizes a homogeneous active liquid at arbitrary large persistence times, characterized by remarkable velocity correlations and irregular turbulent flows. For all persistence values, the active fluid undergoes a nonequilibrium glass transition at large density. This is accompan…
Non-markovian global persistence in phase-ordering kinetics
本文分析了处于相序动力学过程中的简单铁磁体在从完全无序态淬火到低于临界温度（T<T_c）后的整体序参量的持续概率P_g（t）。有人认为，在整个低温阶段的持久性概率随时间代数衰减。对于马尔可夫过程，相关的全局持续性指数θ g =（2 λ C -d）/（2 z）与自相关指数λ C有关.在精确求解的一维伊辛模型和d维球模型中，这种关系被证实是相序的。对于二维Glauber-伊辛模型，θ_g=0.063（2），表明整体序参量的动力学过程是一个非马尔可夫过程.
We propose a model for the motion of a single active particle in a heterogeneous environment where the heterogeneity may arise due to the crowding, conformational fluctuations and/or slow rearrangement of the surroundings. Describing the active particle in terms of the Ornstein-Uhlenbeck process (OUP) and incorporating the heterogeneity in the thermal bath using the two separate models, namely "diffusing diffusivity" and "switching diffusion", we explore the essential dynamical properties of the particle for its one-dimensional motion. In addition, we show how the dynamical behavior is control…
Persistence of the Berezinskii-Kosterlitz-Thouless transition with long-range couplings
Technical University of Munich（慕尼黑工业大学）；Max-Planck-Institut für Physik komplexer Systeme（马克斯·普朗克复杂系统物理研究所）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；Imperial College London（帝国理工学院）
Dense assemblies of self propelled particles, also known as active or living glasses are abundantaround us, covering different length and time scales: from the cytoplasm to tissues, from bacterialbio-films to vehicular traffic jams, from Janus colloids to animal herds. Being structurally disorderedas well as strongly out of equilibrium, these systems show fascinating dynamical and mechanicalproperties. Using extensive molecular dynamics simulation and a number of different dynamicaland mechanical order parameters we differentiate three dynamical steady states in a sheared modelactive glassy sy…
Confinement of excitations induces quasilocalized dynamics in disorder-free isolated quantum many-body systems in one spatial dimension. This occurrence is signalled by severe suppression of quantum correlation spreading and of entanglement growth, long-time persistence of spatial inhomogeneities, and long-lived coherent oscillations of local observables. In this work, we present a unified understanding of these dramatic effects. The slow dynamical behavior is shown to be related to the Schwinger effect in quantum electrodynamics. We demonstrate that it is quantitatively captured for long time…
We study the phase transition from the persistence phase to the extinction phase for the SIRS (susceptible/ infected/ refractory/ susceptible) model of diseases spreading on small world network. We show the effects of all the parameters associated with this model on small world network and we create the full phase space. The results we obtained are consistent with those obtained in Ref.[7] in terms of the existence of a phase transition from a fluctuating endemic state to self-sustained oscillations in the size of the infected subpopulation at a finite value of the disorder of the network. And…
