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-dependent local persistences is shown to be characterized by a universal limit distribution of effective persistence exponents. By a phenomenological approach of rare-region effects in the active phase, we obtain a non-universal algebraic decay of the average persistence for $d=1$, and enhanced power laws for $d>1$. As an exception, for randomly diluted lattices, the algebraic decay holds to be valid for $d>1$, which is explained by the contribution of dangling ends. Results on the time-dependence of average persistence are confirmed by Monte Carlo simulations. We also prove the equivalence of the persistence with a return probability, a valuable tool for the argumentations.
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…
The question of universality class of pair contact process with diffusion (PCPD) is revisited with an alternative approach. We study persistence in Generalized Pair-Contact Process with diffusion (GPCPD) introduced by Noh and Park, (Phys. Rev. E 69,016122(2004)). This model allows us to interpolate between directed percolation (DP) and PCPD universality classes. We find that transition to nonzero persistence is at same parameter value as transition to zero number density. We obtain finite size scaling and off-critical scaling collapse for persistence and find critical exponents by fitting phen…
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…
We investigate the nonequilibrium phase transition of the disordered contact process in five space dimensions by means of optimal fluctuation theory and Monte Carlo simulations. We find that the critical behavior is of mean-field type, i.e., identical to that of the clean five-dimensional contact process. It is accompanied by off-critical power-law Griffiths singularities whose dynamical exponent $z'$ saturates at a finite value as the transition is approached. These findings resolve the apparent contradiction between the Harris criterion which implies that weak disorder is renormalization-gro…
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 sur…
We derive exact probability distributions for the strain ($ε$) at which the first stress drop event occurs in uniformly strained disordered crystals, with quenched disorder introduced through polydispersity in particle sizes. We characterize these first stress drop events numerically as well as theoretically, and identify them with the first contact breaking event in the system. Our theoretical results are corroborated with numerical simulations of quasistatic volumetric strain applied to disordered near-crystalline configurations of athermal soft particles. We develop a general technique to d…
The packing of hard-core particles in contact with their neighbors is considered as the simplest model of disordered particulate media. We formulate the statically determinate problem which allows analytical investigation of the statistical distribution of contact force magnitude. The toy-model of the Boltzmann type equation for the probability of contact force distribution is formulated and studied. An experimentally observed exponential distribution is derived.
Experiments measuring contact formation between a probe and quencher in disordered chains provide information on the fundamental dynamical timescales relevant to protein folding, but their interpretation usually relies on simplified one-dimensional (1D) diffusion models. Here, we use all-atom molecular simulations to capture both the time-scales of contact formation, as well as the scaling with the length of the peptide for tryptophan triplet quenching experiments. Capturing the experimental quenching times depends on the water viscosity, but more importantly on the configurational space explo…
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.
Distribution of dynamical quantities in the contact process, random walks, and quantum spin chains in random environments
我们研究了各种一维无序模型中动力学量的分布，这些模型的临界行为由无限随机不动点描述。在{ \it无序接触过程}中，在固定随机环境中定义的猝灭生存概率$\mathcal{P}(t)$在临界点处表现出多标度性，这意味着当$t\to\infty$时，$\mathcal{P}(t)=t^{-δ}$，其中（环境和时间相关的）指数$δ$具有普适极限分布.利用强无序重整化群方法，在半无限格点的端点处解析地确定了极限分布，发现极限分布是指数分布，而在无限格点处，则基于数值结果，给出了小、大$δ$的极限行为的表达式.用同样的方法，我们还证明了随机环境中的随机游动问题{ \it random walks in random environments}中的猝灭生存概率也是指数极限分布的多尺度问题.此外，还发现{ \it随机横场伊辛链}的自旋-自旋自相关函数在重正化水平上具有与接触过程的生存概率相似的形式.因此，可以建立两个问题中相应的极限分布之间的关系。最后讨论了该模型中自发磁化强度的分布。
In this paper, thermal transport in bond-disordered harmonic chains is revisited in detail using a nonequilibrium Green's function formalism. For strong bond disorder, thermal conductivity is independent of the system size. However, kinetic temperatures described by the local number of states coupling to external heat reservoirs are anomalous since they form a nonlinear profile in the interior of the system. Both results are accounted for in a unified manner in terms of the frequency-dependent localization length. From this argument, we derive a generic formula describing the asymptotic profil…
We consider and analyze a dynamic model of random hyperbolic graphs with link persistence. In the model, both connections and disconnections can be propagated from the current to the next snapshot with probability $ω\in [0, 1)$. Otherwise, with probability $1-ω$, connections are reestablished according to the random hyperbolic graphs model. We show that while the persistence probability $ω$ affects the averages of the contact and intercontact distributions, it does not affect the tails of these distributions, which decay as power laws with exponents that do not depend on $ω$. We also consider …
We study the absorbing state phase transition in the contact process on the Weighted Planar Stochastic (WPS) Lattice. The WPS lattice is multifractal. Its dual network has a power-law degree distribution function and is also embedded in a bidimensional space. Moreover, it represents a novel way to introduce coordination disorder in lattice models. We investigated the critical behavior of the disordered system using extensive simulations. Our results show the critical behavior is distinct from that on a regular lattice, suggesting it belongs to a different universality class. We evaluate the ex…
