We elucidate the intermediate of macroscopic fluid model and microscopic kinetic by studying Poisson algebraic structure one-dimensional Vlasov–Poisson system. The water-bag helps formulating hierarchy sub-algebras, which interpolates gap between models. By analyzing embedding sub-manifold an in a more hierarchy, we characterize effect as symmetry breaking pertinent to invariant.

Abstract We consider stochastic differential equations of the form $dX_t = |f(X_t)|/t^{\gamma} dt+1/t^{\gamma} dB_t$ , where f ( x ) behaves comparably to $|x|^k$ in a neighborhood origin, for $k\in [1,\infty)$ . show that there exists threshold value $ \,{:}\,{\raise-1.5pt{=}}\, \tilde{\gamma}$ $\gamma$ depending on k such if $\gamma \in (1/2, \tilde{\gamma})$ then $\mathbb{P}(X_t\rightarrow 0...

Quantum walks play an important role for developing quantum algorithms and simulations. Here, we introduce a first of its kind one-dimensional lazy walk in the ternary domain show equivalence circuit realization logic. Using appropriate logical mapping position space on which walker evolves onto multiqutrit states, present efficient circuits implementation system. We also address scalability te...