Related papers: Ergodicity Breaking in a Deterministic Dynamical S…
We investigate the ergodic properties of Brownian motion in heterogeneous media through the statistics of occupation times. Using the Feynman-Kac formalism, we derive analytical expressions for the distributions, moments, and ergodicity…
We examine the consequences of classical ergodicity for the localization properties of individual quantum eigenstates in the classical limit. We note that the well known Schnirelman result is a weaker form of quantum ergodicity than the one…
Canonical characterization techniques that rely upon mean squared displacement ($\mathrm{MSD}$) break down for non-ergodic processes, making it challenging to characterize anomalous diffusion from an individual time-series measurement.…
Ergodic theory provides a rigorous mathematical description of chaos in classical dynamical systems, including a formal definition of the ergodic hierarchy. How ergodic dynamics is reflected in the energy levels and eigenstates of a quantum…
A successful method to describe the asymptotic behavior of various deterministic and stochastic processes such as asymptotically autonomous differential equations or stochastic approximation processes is to relate it to an appropriately…
Multistability, i.e. the coexistence of several attractors for a given set of system parameters is one of the most important phenomena occurring in dynamical systems. We consider it in velocity dynamics of a Brownian particle driven by…
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 demonstrate the non-ergodicity of a simple Markovian stochastic processes with space-dependent diffusion coefficient $D(x)$. For power-law forms $D(x) \simeq|x|^{\alpha}$, this process yield anomalous diffusion of the form $\ < x^2(t)\ >…
We explore the mechanism responsible for the ergodicity breaking in systems with long-range forces. In thermodynamic limit such systems do not evolve to the Boltzmann-Gibbs equilibrium, but become trapped in an out-of-equilibrium…
While the glass transition at non-zero temperature seems to be hard to access for experimental, theoretical, or simulation studies, jamming at zero temperature has been explored in great detail. It is a widely discussed question whether…
We describe classes of ergodic dynamical systems for which some statistical properties are known exactly. These systems have integer dimension, are not globally dissipative, and are defined by a probability density and a two-form. This…
The study of microscopic protein dynamics has historically presented significant challenges to researchers seeking to develop a comprehensive and detailed description of its diverse and intriguing features. Recent experimental and…
A one dimensional classically chaotic spin chain with asymmetric coupling and two different inter-spin interactions, nearest neighbors and all-to-all, has been considered. Depending on the interaction range, dynamical properties, as…
Population dynamics in random ecological networks are investigated by analyzing a simple deterministic equation. It is found that a sequence of abrupt changes of populations punctuating quiescent states characterize the long time behavior.…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
Non-ergodicity impacts statistical inference in a diverse range of disciplines inside and outside of physics. However the concept of ergodicity is used inconsistently, and may refer to several nonequivalent notions. To help address this, we…
Generic quantum many-body systems are expected to thermalize, scrambling initial coherence while local observables relax to equilibrium values. Weak ergodicity breaking, often associated with quantum many-body scarring of homogeneous…
A mechanical system is presented exhibiting a non-deterministic singularity, that is, a point in an otherwise deterministic system where forward time trajectories become non-unique. A Coulomb friction force applies linear and angular forces…
We directly detect the ergodicity breaking in a lattice glass model by a numerical simulation. The obtained results nicely agree with those by the cavity method that the model on a regular random graph exhibits a dynamical transition with…
We study characterizations of ergodicity, weak mixing and strong mixing of W*-dynamical systems in terms of joinings and subsystems of such systems. Ergodic joinings and Ornstein's criterion for strong mixing are also discussed in this…