Range-separated (screened) hybrid functionals provide a powerful strategy for incorporating nonlocal exact (Hartree-Fock-type) exchange into density functional theory. Existing implementations of range separation use a fixed system-independent screening parameter. Here, we propose a novel method that uses a position-dependent screening function. These locally range-separated hybrids add substan...

In this article, we consider a combination of local and nonlocal Laplace equation with singular nonlinearities. For such mixed problems, establish the existence at least one weak solution for parameter-dependent nonlinearity multiple solutions perturbed nonlinearity. Our argument is based on variational approximation approach.

We revisit the derivation of nonlocal collision term in Boltzmann equation for spin-1/2 particles, using both Wigner-function approach by de Groot, van Leeuwen, and Weert, Kadanoff-Baym $T$-matrix approximation. Contrary to previous calculations, our results maintain full Lorentz covariance term.

An analysis of the semiclassical regime of the quantum-classical transition is given for open, bounded, one-dimensional chaotic dynamical systems. Environmental fluctuations-characteristic of all realistic dynamical systems-suppress the development of a fine structure in classical phase space and damp nonlocal contributions to the semiclassical Wigner function, which would otherwise invalidate ...

We consider a particle system in continuous time, discrete population, with spatial motion and nonlocal branching. The offspring’s weights and their number may depend on the mother’s weight. Our setting captures, for instance, the processes indexed by a Galton-Watson tree. Using a size-biased auxiliary process for the empirical measure, we determine this asymptotic behaviour. We also obtain a l...

We theoretically study the dynamic screening properties of bilayer graphene within the random-phase approximation assuming quadratic band dispersion and zero gap for the single-particle spectrum. We calculate the frequency-dependent dielectric function of the system and obtain the low-energy plasmon dispersion and broadening of the plasmon modes from the dielectric function. We also calculate t...

As a sequent study following a previous paper, this paper is dedicated to constructing a theory to determine the nonlocal region of quantum field by geometrical method. The study shows that the theory may also be the candidate of the nonperturbative one. Many symmetric laws are not strictly respected in this theory. Concerning QED and QCD, it is found that while the strength of field ~ B and ~ ...

This paper aims at building a unified framework to deal with a wide class of local and nonlocal translation-invariant geometric flows. We introduce a class of nonlocal generalized mean curvatures and prove the existence and uniqueness for the level set formulation of the corresponding geometric flows. We then introduce a class of generalized perimeters, whose first variation is an admissible ge...

The optical response of plasmonic nanogaps is challenging to address when the separation between the two nanoparticles forming the gap is reduced to a few nanometers or even subnanometer distances. We have compared results of the plasmon response within different levels of approximation, and identified a classical local regime, a nonlocal regime and a quantum regime of interaction. For separati...

We study the conditions under which species interaction, as described by continuous versions of the competitive Lotka-Volterra model (namely the nonlocal Kolmogorov-Fisher model, and its differential approximation), can support the existence of localized states, i.e., patches of species with enhanced population surrounded in niche space by species at smaller densities. These states would arise ...