Related papers: A differential identity for Green functions
We have developed an approach to calculate the single-particle Green function of a one-dimensional many-body system in the strongly localized limit at zero temperature. Our approach, based on the locator expansion, sums the contributions of…
A formula relating quotients of determinants of elliptic differential operators sharing their principal symbol, with local boundary conditions, to the corresponding Green function is given.
The imaginary-time Green's function is a building block of various numerical methods for correlated electron systems. Recently, it was shown that a model-independent compact orthogonal representation of the Green's function can be…
An analysis shows that the ground state of the inhomogeneous system of interacting electrons in the static external field, which satisfies the thermodynamic limit, can be consistently described only using the Green function theory based on…
We study the many-body physics of different quantum systems using a hierarchy of correlations, which corresponds to a generalization of the $1/\mathcal{Z}$ hierarchy. The decoupling scheme obtained from this hierarchy is adapted to…
This introduction to Green's functions is based on their role as kernels of differential equations. The procedures to construct solutions to a differential equation with an external source or with an inhomogeneity term are put together to…
The Hamiltonian of an isolated quantum mechanical system determines its dynamics and physical behaviour. This study investigates the possibility of learning and utilising a system's Hamiltonian and its variational thermal state estimation…
We get a Pohozaev-type identity for the fractional Green function, which extends to the fractional setting a classical result by Brezis and Peletier. Our result complements with some more recent ones obtained by Djitte and Sueur concerning…
The main aim of this paper is to provide a novel approach to deriving identities for the Bernstein polynomials using functional equations. We derive various functional equations and differential equations using generating functions.…
In this short note we review some facts about elliptic differential operators on Riemannian manifolds.
We derive an identity that relates a class of multiple integrals involving Vandermonde polynomials to divided differences. Alternatively the identity can be viewed as an integral formula for divided differences. As part of the derivation we…
In this paper, a pointwise weighted identity for some stochastic partial differential operators (with complex principal parts) is established. This identity presents a unified approach in studying the controllability, observability and…
We develop a range-separated stochastic resolution of identity approach for the $4$-index electron repulsion integrals, where the larger terms (above a predefined threshold) are treated using a deterministic resolution of identity and the…
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…
We show that a many-body Hamiltonian that corresponds to a system of fermions interacting through a pairing force is an integrable problem, i.e. it has as many constants of the motion as degrees of freedom. At the classical level this…
In this paper we develop a way of obtaining Green's functions for partial differential equations with linear involutions by reducing the equation to a higher-order PDE without involutions. The developed theory is applied to a model of heat…
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 generating function of a Hamiltonian $H$ is defined as $F(t)=\langle e^{-itH}\rangle$, where $t$ is the time and where the expectation value is taken on a given initial quantum state. This function gives access to the different moments…
Discovering hidden partial differential equations (PDEs) and operators from data is an important topic at the frontier between machine learning and numerical analysis. This doctoral thesis introduces theoretical results and deep learning…
We provide explicit representations of Green's functions for general linear fractional differential operators with {\it variable coefficients} and Riemann-Liouvilles derivatives. We assume that all their coefficients are continuous in $[0,…