Related papers: Insight of the Green's function as a defect state …
The Green function has a complex dependence upon its underlying domain and differential operator. We briefly review Hadamard's formula for the first variation of the Green function due to a perturbation of the domain. We then take a…
The well-known expressions for the Green's functions for the Helmholtz equation in polar coordinates with Dirichlet and Neumann boundary conditions are transformed. The slowly converging double series describing these Green's functions are…
The Green's function method which has been originally proposed for linear systems has several extensions to the case of nonlinear equations. A recent extension has been proposed to deal with certain applications in quantum field theory. The…
An earlier contour expression for the Green function of a free complex scalar field in the presence of a conical singularity with localised magnetic flux is shown to yield expressions for the field correlator and defect block expansions…
In this paper, we define the Green function for the Dirac operator under two local boundary conditions: the condition associated with a chirality operator (also called the chiral bag boundary condition) and the $\MIT$ bag boundary…
We present a calculation of the spectral properties of a single charge doped at a Cu($3d$) site of the Cu-F plane in KCuF$_{3}$. The problem is treated by generating the equations of motion for the Green's function by means of subsequent…
We construct the Hadamard Green's function by using the eigenfunction, which are obtained by solving the wave equation for the massless conformal scalar field on the S^n-1 of a n-dimensional closed, static universe. We also consider the…
It is known that the equation $x'(t)=Ax(t)+f(t)$, where $A$ is a bounded linear operator, has a unique bounded solution $x$ for any bounded continuous free term~$f$ if and only if the spectrum of the coefficient $A$ does not intersect the…
We have studied possible applications of a particular pseudo-differential algebra in singular analysis for the construction of fundamental solutions and Green's functions of a certain class of elliptic partial differential operators. The…
It has been shown that the Schwinger-Dyson equations for non-Hermitian theories implicitly include the Hilbert-space metric. Approximate Green functions for such theories may thus be obtained, without having to evaluate the metric…
In this article we obtain two-sided estimates for the Greens function of fractional boundary value problems on $\mathbb R_+ \times \mathbb R_+ \times \mathbb R^d$ of the form \[(-{}_{t_1}D^\beta_{0+*} - {}_{t_2}D^\gamma_{0+*})u(t_1, t_2, x)…
An end-to-end strategy for hybrid quantum-classical computations of Green's functions in many-body systems is presented and applied to the pairing model. The scheme makes explicit use of the spectral representation of the Green's function,…
We use a lattice Green function approach to study the stationary modes of a linear/nonlinear (Kerr) impurity embedded in a periodic one-dimensional lattice where we replace the standard discrete Laplacian by a fractional one. The energies…
It is shown that the conventional many-body techniques to calculate the Green's functions can be applied to the wide, compressible edge of a quantum Hall bar. The only ansatz we need is the existence of stable density modes that yields a…
Energy-dependent Green's functions for the two and three dimensional $\delta$-function plus harmonic oscillator potential systems are derived by incorporating the renormalization and the self-adjoint extension into the Green's function…
In our previous work (Assier \& Shanin, QJMAM, 2019), we gave a new spectral formulation in two complex variables associated with the problem of plane-wave diffraction by a quarter-plane. In particular, we showed that the unknown spectral…
Numerical resolution of exterior Helmholtz problems requires some approach to domain truncation. As an alternative to approximate nonreflecting boundary conditions and invocation of the Dirichlet-to-Neumann map, we introduce a new, nonlocal…
The Green's function method has applications in several fields in Physics, from classical differential equations to quantum many-body problems. In the quantum context, Green's functions are correlation functions, from which it is possible…
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…
We introduce Neural Green's Function, a neural solution operator for linear partial differential equations (PDEs) whose differential operators admit eigendecompositions. Inspired by Green's functions, the solution operators of linear PDEs…