Related papers: Sharp estimates of Green function of hyperbolic Br…
Accurate modeling of the electronic structure of warm dense matter is a challenging problem whose solution would allow a better understanding of material properties like equation of state, opacity, and conductivity, with resulting…
A method to calculate exact Green's functions on lattices in various dimensions is presented. Expressions in terms of generalized hypergeometric functions in one or more variables are obtained for various examples by relating the resolvent…
Brownian motion in the three dimensional Lobachevsky space or hyperbolic space is considered in the paper written by F.I.Karpelevich, V.N.Tutubalin and M.G.Shur. A solution for radial symmetric diffusion equation in the three dimensional…
We prove sharp near-diagonal pointwise bounds for the Green function $G_\Omega(x,y)$ for nonlocal operators of fractional order $\alpha \in (0,2)$. The novelty of our results is two-fold: the estimates are robust as $\alpha \to 2-$ and we…
Inspired by a result of Colding, the present paper studies the Green function $G$ on a non-parabolic $\mathrm{RCD}(0,N)$ space $(X, \mathsf{d}, \mathfrak{m})$ for some finite $N>2$. Defining $\mathsf{b}_x=G(x, \cdot)^{\frac{1}{2-N}}$ for a…
In this paper, we establish sharp two-sided estimates for the transition densities of relativistic stable processes [i.e., for the heat kernels of the operators $m-(m^{2/\alpha}-\Delta)^{\alpha/2}$] in $C^{1,1}$ open sets. Here $m>0$ and…
The Green's function, serving as a kernel function that delineates the interaction relationships of physical quantities within a field, holds significant research implications across various disciplines. It forms the foundational basis for…
Considering the kernel of an integral operator intertwining two realizations of the group of motions of the pseudo-Euclidian space, we derive two formulas for series containing Whittaker's functions or Weber's parabolic cylinder functions.…
New exact and asymptotical results for the one particle Green's function of 2D electrons with combined Rashba - Dresselhaus spin - orbit interaction in the presence of in-plane uniform magnetic field are presented. A special case that…
Starting from the Dyson-Beliaev and generalized Gross-Pitaevskii equations with an extra nonlocal potential, we derive an exact expression of the two-particle Green's function K for an interacting Bose-Einstein condensate in terms of…
We present an efficient implementation of a surface Green's-function method for atomistic modeling of surfaces within the framework of density functional theory using a pseudopotential localized basis set approach. In this method, the…
We establish quantitative Green's function estimates for a class of quasi-periodic (QP) operators on $\mathbb{Z}^d$ with certain slowly decaying long-range hopping and analytic cosine type potentials. As applications, we prove the…
The purpose of the paper is to provide a general method for computing hitting distributions of some regular subsets D for Ornstein-Uhlenbeck type operators of the form 1/2\Delta + F\cdot\nabla, with F bounded and orthogonal to the boundary…
We consider a large class of symmetric pure jump Markov processes dominated by isotropic unimodal L\'evy processes with weak scaling conditions. First, we establish sharp two-sided heat kernel estimates for these processes in $C^{1,1}$ open…
This paper provides a new analytical method to obtain Green's functions of linear dispersive partial differential equations. The Euler-Bernoulli beam equation and the one-dimensional heat conduction equation (dissipation equation) under…
Homogeneous and inhomogeneous biharmonic equation are considered on the $n$-dimensional unit sphere. The Green function is given as a series of Gegenbauer polynomials. In the paper, explicit representations of the Green function are found…
A subordinate Brownian motion $X$ is a L\'evy process which can be obtained by replacing the time of the Brownian motion by an independent subordinator. In this paper, when the Laplace exponent $\phi$ of the corresponding subordinator…
In this paper, we employ probabilistic techniques to derive sharp, explicit two-sided estimates for the heat kernel of the nonlocal kinetic operator $$ \Delta^{\alpha/2}_v + v \cdot \nabla_x, \quad \alpha \in (0, 2),\ (x,v)\in {\mathbb…
Green-hyperbolic operators - partial differential operators on globally hyperbolic spacetimes that (together with their formal duals) possess advanced and retarded Green operators - play an important role in many areas of mathematical…
Two-particle Green's functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at two-particle level often suffer from large…