Related papers: Ergodicity Breaking in a Deterministic Dynamical S…
Coherent structures are spatially varying regions which disperse minimally over time and organise motion in non-autonomous systems. This work develops and implements algorithms providing multilayered descriptions of time-dependent systems…
Consider a chaotic dynamical system generating Brownian motion-like diffusion. Consider a second, non-chaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in…
In ergodic physical systems, time-averaged quantities converge (for large times) to their ensemble-averaged values. Large deviation theory describes rare events where these time averages differ significantly from the corresponding ensemble…
We study the onset of weak ergodicity violations in closed quantum many-body systems and focus on cases in which they occur through a transition that is controlled by a model parameter. Our analysis is based on representing quantum systems…
Quantum systems that violate the eigenstate thermalisation hypothesis thereby falling outside the paradigm of conventional statistical mechanics are of both intellectual and practical interest. We show that such a breaking of ergodicity may…
In single-particle tracking experiments measuring anomalous diffusion dynamics, understanding ergodicity is crucial, as it ensures that the time average of an observable matches the ensemble average, and can thus be fitted with known…
Consider a stochastic nonlinear system controlled over a possibly noisy communication channel. An important problem is to characterize the largest class of channels for which there exist coding and control policies so that the closed-loop…
We study the dynamics of compositions of a sequence of holomorphic mappings in projective space. We define ergodicity and mixing for non-autonomous dynamical systems, and we construct totally invariant measures for which our sequence…
Self-organized criticality (SOC) is widely proposed as a fundamental mechanism for collective behavior, yet its role in objective-driven, heterogeneous adaptive systems underpinning real complex systems remains less understood. We introduce…
One of the major breakthroughs in science of the last (20th) century was building a bridge between the worlds of stochastic (random) systems and deterministic (dynamical) systems. It was started by the celebrated 1958 paper by…
It is a common assumption that quantum systems with time reversal invariance and classically chaotic dynamics have energy spectra distributed according to GOE-type of statistics. Here we present a class of systems which fail to follow this…
We study the limit behaviour of upper and lower bounds on expected time averages in imprecise Markov chains; a generalised type of Markov chain where the local dynamics, traditionally characterised by transition probabilities, are now…
Quasiperiodic systems in one dimension can host non-ergodic states, e.g. localized in position or momentum. Periodic quenches within localized phases yield Floquet eigenstates of the same nature, i.e. spatially localized or ballistic.…
Time-dependently driven stochastic systems form a vast and manifold class of non-equilibrium systems used to model important applications on small length scales such as bit erasure protocols or microscopic heat engines. One property that…
We consider a class of semi-linear differential Volterra equations with memory terms, polynomial nonlinearities and random perturbation. For a broad class of nonlinearities, we study statistically steady states of the system and find that…
We prove that for an arbitrary indexing group, every ergodic infinitely divisible stationary process that is separable in probability is weakly mixing. This shows that, as in the well-known case of Gaussian stationary processes, ergodicity…
Experiments in Rydberg atoms have recently found unusually slow decay from a small number of special initial states. We investigate the robustness of such long-lived states (LLS) by studying an ensemble of locally constrained random systems…
In the physics literature "ergodicity" is taken to mean that a system, including a macroscopic one, visits all microscopic states in a relatively short time. We show that this is an impossibility even if that time is billions of years. We…
The temperature dependence of the non-ergodicity factor of vitreous GeO$_2$, $f_{q}(T)$, as deduced from elastic and quasi-elastic neutron scattering experiments, is analyzed. The data are collected in a wide range of temperatures from the…
We study the dynamics of the `batch' minority game with market-impact correction using generating functional techniques to carry out the quenched disorder average. We find that the assumption of weak long-term memory, which one usually…