As a paradigm of weak ergodicity breaking in disorder-free nonintegrable models, quantum many-body scars (QMBS) can offer deep insights into the thermalization dynamics gauge theories. Having been first discovered spin-$1/2$ link formulation Schwinger model, it is fundamental question as to whether QMBS persist for $S>1/2$ since such theories converge lattice model large-$S$ limit, which approp...

We study the quantum dynamics of Josephson-junction arrays. find isolated groups low-entanglement eigenstates that persist even when Josephson interaction is strong enough to destroy overall organization spectrum in multiplets, and a perturbative description no longer possible. These lie inner part spectrum, far from spectral edge, provide weak ergodicity breaking, reminiscent scars. Due presen...

We are interested in prey-predator communities where the predator population evolves much faster than the prey’s (e.g. insect-tree communities). We introduce a piecewise deterministic model for these prey-predator communities that arises as a limit of a microscopic model when the number of predators goes to infinity. We prove that the process has a unique invariant probability measure and that ...

The weak ergodic theorems of mathematical demography state that the age distribution of a closed population is asymptotically independent of the initial distribution. In this paper, we provide a new proof of the weak ergodic theorem of the multistate population model with continuous time. The main tool to attain this purpose is a theory of multiplicative processes, which was mainly developed by...

A nonsingular transformation is said to be doubly ergodic if for all sets A and B of positive measure there exists an integer n > 0 such that (T n(A) \ A) > 0 and (T n(A) \ B) > 0. While double ergodicity is equivalent to weak mixing for nite measure-preserving transformations, we show that this is not the case for in nite measure preserving transformations. We show that all measure-preserving ...