Chen's biharmonic conjecture is well-known and stays open: The only biharmonic submanifolds of Euclidean spaces are the minimal ones. In this paper, we consider an advanced version of the conjecture, replacing $Delta$ by its extension, $L_1$-operator ($L_1$-conjecture). The $L_1$-conjecture states that any $L_1$-biharmonic Euclidean hypersurface is 1-minimal. We prove that the $L_1$-conje...

Two measure preserving dynamical systems are weakly disjoint if some pointwise convergence property is satisfied by ergodic averages on their direct product (a precise definition is given below). Disjointness implies weak disjointness. We start studying this new concept, both by stating some general properties and by giving various examples. The content of the article is summarized in the intro...

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 ...