Related papers: Regularized Green's Function for the Inverse Squar…
In this paper, we utilize the method in Dodson-Murphy [4] to establish the radial scattering result for the focusing nonlinear Schr\"odinger equation with inverse square potential $i\pa_tu-\la u=-|u|^{p-1}u$ in the energy space…
The aim of this study is to investigate a class of generalized boundary value transmission problems (BVTP's) for Sturm-Liouville equation on two separate intervals. We introduce modified inner product in direct sum space $L_{2}[a,c)\oplus…
Inspired by the recent proposed Legendre orthogonal polynomial representation of imaginary-time Green's functions, we develop an alternate representation for the Green's functions of quantum impurity models and combine it with the…
The quantum action for a three-dimensional real sextic model using the background field method is considered. Four-loop renormalization of this model is performed with a cutoff regularization in the coordinate representation. The…
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,…
By employing the Pekeris approximation, the D-dimensional Schr\"odinger equation is solved for the nuclear deformed Woods-Saxon potential plus double ring-shaped potential within the framework of the Asymptotic Iteration Method (AIM). The…
Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two…
Green's function provides an inherent connection between theoretical analysis and numerical methods for elliptic partial differential equations, and general absence of its closed-form expression necessitates surrogate modeling to guide the…
We solve the inverse problems to recover Dirac systems on an interval or semiaxis from their spectral functions (matrix valued functions) for the case of locally square-integrable potentials. Direct problems in terms of spectral functions…
In this paper, the Green function theory of quantum many-particle systems recently presented is reworked within the framework of nonextensive statistical mechanics with a new normalized $q$-expectation values. This reformulation introduces…
Using a recently developed approach for solving the three dimensional Dirac equation with spherical symmetry, we obtain the two-point Green's function of the relativistic Dirac-Morse problem. This is accomplished by setting up the…
We consider the variational problem of maximizing the weighted equilibrium Green's energy of a distribution of charges free to move in a subset of the upper half-plane, under a particular external field. We show that this problem admits a…
Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two…
We consider modified dispersion relations in quantum field theory on curved space-time. Such relations, despite breaking the local Lorentz invariance at high energy, are considered in several phenomenological approaches to quantum gravity.…
We consider two main inverse Sturm-Liouville problems: the problem of recovery of the potential and the boundary conditions from two spectra or from a spectral density function. A simple method for practical solution of such problems is…
The properties of the gauge invariant two-point quark Green's function are studied in the large-Nc limit of two-dimensional QCD. The analysis is done by means of an exact integrodifferential equation. The Green's function is found infrared…
The Galilei-covariant fermionic field theories are quantized by using the path-integral method and five-dimensional Lorentz-like covariant expressions of non-relativistic field equations. Firstly, we review the five-dimensional approach to…
We show that the Green's functions in non-linear gauge in the theory of perturbative quantum gravity is expressed as a series in terms of those in linear gauges. This formulation is also holds for operator Green's functions. We further…
An interesting inverse optimization spectral problem, with important applications in structural health monitoring and damage detection, material design, seismic wave analysis, sonar detection, and related fields, involves reconstructing a…
In this paper we derive the inverse spatial Laplacian for static, spherically symmetric backgrounds by solving Poisson's equation for a point source. This is different from the electrostatic Green function, which is defined on the four…