Related papers: Heat kernel and Green function estimates on affine…
We derive equations of motion for higher order density response functions using the theory of thermodynamic Green's functions. We also derive expressions for the higher order generalized dielectric functions and polarization functions.…
In this paper, we consider a symmetric pure jump Markov process $X$ on a metric measure space with volume doubling conditions. Our focus is on estimating the transition density $p(t,x,y)$ of $X$ and studying its stability when the jumping…
A common tool in Casimir physics (and many other areas) is the asymptotic (high-frequency) expansion of eigenvalue densities, employed as either input or output of calculations of the asymptotic behavior of various Green functions. Here we…
A local-orbital based ab initio approach to obtain the Green function for large heterogeneous systems is developed. First a Green function formalism is introduced based on exact diagonalization. Then the self energy is constructed from an…
We consider an asymptotically stable multidimensional random walk $S(n)=(S_1(n),\ldots, S_d(n) )$. Let $\tau_x:=\min\{n>0: x_{1}+S_1(n)\le 0\}$ be the first time the random walk $S(n)$ leaves the upper half-space. We obtain the asymptotics…
We exploit the many-body self-consistent Green's function method to analyze finite-temperature properties of infinite nuclear matter and to explore the behavior of the thermal index used to simulate thermal effects in equations of state for…
A rational expansion of the Fermi density operator is proposed. This approach allows to calculate efficiently physical properties of fermionic systems at finite temperatures without solving an eigenvalue problem. Using N evaluations of the…
The paper is devoted to a local heat kernel, which is a special part of the standard heat kernel. Locality means that all considerations are produced in an open convex set of a smooth Riemannian manifold. We study such properties and…
The total energy and electron addition and removal spectra can in principle be obtained exactly from the one-body Green's function. In practice, the Green's function is obtained from an approximate self-energy. In the framework of many-body…
We obtain asymptotic expansions of the spatially discrete 2D heat kernels, or Green's functions on lattices, with respect to powers of time variable up to an arbitrary order and estimate the remainders uniformly on the whole lattice. Unlike…
We introduce a spectral density functional theory which can be used to compute energetics and spectra of real strongly--correlated materials using methods, algorithms and computer programs of the electronic structure theory of solids. The…
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 many-body Green's function provides access to electronic properties beyond density functional theory level in ab inito calculations. In this manuscript, we propose a deep learning framework for predicting the finite-temperature Green's…
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…
We extend the use of random evolving sets to time-varying conductance models and utilize it to provide tight heat kernel upper bounds. It yields the transience of any uniformly lazy random walk, on Z^d, d>=3, equipped with uniformly bounded…
A two-dimensional model is proposed for energy efficiency assessment through the simulation of heat transfer in building envelopes, considering the influence of the surrounding environment. The model is based on the \DF ~approach that…
In this paper we describe a spatial decomposition of the thermal conductivity, what we name "site-projected thermal conductivity", a gauge of the thermal conduction activity at each site. The method is based on the Green-Kubo formula and…
In this paper, we establish sharp two-sided estimates for transition densities of a large class of subordinate Markov processes. As applications, we show that the parabolic Harnack inequality and H\"older regularity hold for parabolic…
In this note we prove convergence of Green functions with Neumann boundary conditions for the random walk to their continuous counterparts. Also a few Beurling type hitting estimates are obtained for the random walk on discretizations of…
Developing a reliable kinetic energy density functional within orbital-free density functional theory remains a long-standing challenge, particularly for atomic and molecular systems. A major difficulty lies in the absence of a systematic…