Related papers: Approximate Green's Function for the Conductivity …
Exploiting the generalization of the Weierstrass $\wp$ function to genus $2$ given by Komori, we give the exact connection of the related monodromy problem for genus $2$ and the classical weak $n$-point correlation functions. We also…
The Green's function plays a crucial role when studying the nature of quantum many-body systems, especially strongly-correlated systems. Although the development of quantum computers in the near future may enable us to compute energy…
Superconductivity in the t-J model is studied by extending the recently introduced extremely correlated fermi liquid theory. Exact equations for the Greens functions are obtained by generalizing Gor'kov's equations to include extremely…
The $GW$ approximation is a widely used framework for studying correlated materials, but it struggles with certain limitations, such as its inability to explain pseudogap phenomena. To overcome these problems, we propose a systematic…
In this work we study differential problems in which the reflection operator and the Hilbert transform are involved. We reduce these problems to ODEs in order to solve them. Also, we describe a general method for obtaining the Green's…
In this paper, we first establish a strong approximation version for the first order limit theorem of some additive functionals related to two non-Markovian Gaussian processes: the fractional Brownian motion (fBm) and the Riemann-Liouville…
A value given by a simple mathematical expression is proposed which is close to the fine structure constant given by 1998 CODATA recommended values of the fundamental physical constants up to relative accuracy 10^{-7}. This expression…
A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of…
We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using…
We use finite field-dependent BRS transformations (FFBRS) to connect the Green functions in a set of two otherwise unrelated gauge choices. We choose the Lorentz and the axial gauges as examples. We show how the Green functions in axial…
Green's functions are highly useful in analyzing the dynamical behavior of polynomials in their escaping set. The aim of this paper is to construct an analogue of Green's functions for planar quasiregular mappings of degree two and constant…
The classical Green's function associated to a simply connected domain in the complex plane is easily expressed in terms of a Riemann mapping function. The purpose of this paper is to express the Green's function of a finitely connected…
A first principle theory of charge transport in spatially inhomogeneous quantum systems composed of any finite number of particles and subject to weak electro-magnetic fields is developed. Simple analytical expressions for the linear…
In the present paper, we consider an elliptic divergence form operator in $\mathbb{R}^n\setminus\mathbb{R}^d$ with $d<n-1$ and prove that its Green function is almost affine, in the sense that the normalized difference between the Green…
In this work we develop an algebraic theory of linear recurrence equations and systems with constant coefficients and reflection. We obtain explicit solutions and the Green's functions associated to different problems under general linear…
The aim of this paper consists on the study of the following fourth-order operator: \begin{equation}\label{Ec::T4} T[M]\,u(t)\equiv u^{(4)}(t)+p_1(t)\,u"'(t)+p_2(t)\,u"(t)+M\,u(t)\,,\ t\in I \equiv [a,b]\,, \end{equation} coupled with the…
Let $\Omega $ be an open, smooth, bounded subset of $ \Bbb R ^n$. In connection with the fractional Laplacian $(-\Delta )^a$ ($a>0$), and more generally for a $2a$-order classical pseudodifferential operator ($\psi $do) $P$ with even…
This thesis comprises two parts centered around the functional renormalization-group framework: in the first part, I study the role of symmetries and conservation laws in approximate solutions, while in the second part I analyze Friedel…
We construct an explicit Green's function for the conjugated Laplacian $e^{-\omega \cdot x/h}\Delta e^{-\omega \cdot x/h}$, which let us control our solutions on roughly half of the boundary. We apply the Green's function to solve a partial…
In this paper, we continue to study properties of rational approximations to Euler's constant and values of the Gamma function defined by linear recurrences, which were found recently by A. I. Aptekarev and T. Rivoal. Using multiple…