Combining extensive single particle tracking microscopy data of endogenous lipid granules in living fission yeast cells with analytical results we show evidence for anomalous diffusion and weak ergodicity breaking. Namely we demonstrate that at short times the granules perform subdiffusion according to the laws of continuous time random walk theory. The associated violation of ergodicity leads ...

Recent discovery of persistent revivals in quantum simulators based on Rydberg atoms have pointed to the existence a new type dynamical behavior that challenged conventional paradigms integrability and thermalization. This novel collective effect has been named many-body scars by analogy with weak ergodicity breaking single particle inside stadium billiard. In this overview, we provide pedagogi...

It is known (see [16]) that there are several notions of mixing (i.e. weak mixing, mixing, completely mixing e.c.t.) of measure preserving transformation on a measure space in the ergodic theory. It is important to know how these notions are related with each other. A lot of papers are devoted to this topic. In [1] a rather thorough study of the mentioned concepts of mixing for Markov operators...

We develop in finite case sufficient conditions for weak ergodicity of a nonstationary Markov chain r-states having transition matrices (Pn) n≥1 with Pn → P, where P has 2 irreducible and aperiodic closed classes and,possibly, transient states.