Related papers: Ergodicity breaking in area-restricted search of a…

Many natural phenomena are quantified by counts of observable events, from the annihilation of quasiparticles in a lattice to predator-prey encounters on a landscape to spikes in a neural network. These events are triggered at random…

Quantum many-body systems can exhibit distinct regimes where dynamics is either ergodic, dynamically exploring an extensive region of available state-space, or non-ergodic, where the dynamics may be restricted. An example is the many-body…

The concept of weak ergodicity breaking is defined and studied in the context of deterministic dynamics. We show that weak ergodicity breaking describes a weakly chaotic dynamical system: a nonlinear map which generates subdiffusion…

Stochastic processes of interacting particles with varying length are relevant e.g. for several biological applications. We try to explore what kind of new physical effects one can expect in such systems. As an example, we extend the…

Experiments on particles' motion in living cells show that it is often subdiffusive. This subdiffusion may be due to trapping, percolation-like structures, or viscoelatic behavior of the medium. While the models based on trapping (leading…

We study the breaking of ergodicity measured in terms of return probability in the evolution of a quantum state of a spin chain. In the non ergodic phase a quantum state evolves in a much smaller fraction of the Hilbert space than would be…

Time averages extracted from single-particle trajectories in complex media often vary strongly from one trajectory to another, even for long measurement times. Such persistent trajectory-to trajectory scatter is commonly observed in…

We study the phenomenon of weak ergodicity breaking for a class of globally correlated random walk dynamics defined over a finite set of states. The persistence in a given state or the transition to another one depends on the whole previous…

We study a general class of random walks driven by a uniquely ergodic Markovian environment. Under a coupling condition on the environment we obtain strong ergodicity properties for the environment as seen from the position of the walker,…

1. Predicting space use patterns of animals from their interactions with the environment is fundamental for understanding the effect of habitat changes on ecosystem functioning. Recent attempts to address this problem have sought to unify…

Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem…

We study the nature and mechanisms of broken ergodicity (BE) in specific random walk models corresponding to diffusion on random potential surfaces, in both one and high dimension. Using both rigorous results and nonrigorous methods, we…

The goal of animal movement analysis is to understand how organisms explore and exploit the complex and varying environment. Animals usually exhibit varied and complicated movements, from apparently deterministic behaviors to highly random…

Ergodicity, the central tenet of statistical mechanics, requires that an isolated system will explore all of its available phase space permitted by energetic and symmetry constraints. Mechanisms for violating ergodicity are of great…

We discuss conditions for unique ergodicity of a collective random walk on a continuous circle. Individual particles in this collective motion perform independent (and different in general) random walks conditioned by the assumption that…

We study the Ergodic Properties of Random Walks in stationary ergodic environments without uniform ellipticity under a minimal assumption. There are two main components in our work. The first step is to adopt the arguments of Lawler to…

Human mobility is known to be distributed across several orders of magnitude of physical distances , which makes it generally difficult to endogenously find or define typical and meaningful scales. Relevant analyses, from movements to…

The behavior of lattice models in which time reversibility is enforced at the level of trajectories (microscopic reversibility) is studied analytically. Conditions for ergodicity breaking are explored, and a few examples of systems…

Experimental studies of the diffusion of biomolecules in the environment of biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule…

We study ergodicity breaking in the clean Bose-Hubbard chain for small hopping strength. We see the existence of a non-ergodic regime by means of indicators as the half-chain entanglement entropy of the eigenstates, the average level…