Related papers: Analytic properties of the electromagnetic Green's…
A recently proposed analytical solution for the equations of motion of the one-body Green function of the double quantum dot is extended to the out-of-equilibrium situation. By solving a linear system for the density correlators, not only…
Using the description in terms of the Hubbard operators hole and spin Green's functions of the two-dimensional t-J model are calculated in an approximation which retains the rotation symmetry of the spin susceptibility in the paramagnetic…
Fundamental properties of warm dense matter are described by the dielectric function, which gives access to the frequency-dependent electrical conductivity, absorption, emission and scattering of radiation, charged particles stopping and…
Any elliptic operator defines an automorphism on the orthogonal subspace to the eigenfunctions associated with the lowest eigenvalue, whose inverse is the orthogonal Green operator. In this study, we show that elliptic Schr\"{o}dinger…
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 give two-sided, global (in all variables) estimates of the heat kernel and the Green function of the fractional Schr\"odinger operator with a non-negative and locally bounded potential $V$ such that $V(x) \to \infty$ as $|x| \to \infty$.…
We present a real-time second-order Green's function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of $O(N_{\rm e}^3$), where $N_{\rm e}$ is the number of electrons. The cubic scaling…
Dyadic Green's function is an important tool of computational photonics, giving deeper insights into light-matter interaction. We present an operator approach to the derivation of the dyadic Green's function of a generic anisotropic…
We introduce an $O(M)$ algorithm for evaluating the azimuthal Fourier modes $G_{k,m}$, $m = 0, 1, ..., M$, of the three-dimensional Helmholtz Green's function with real wavenumber $k$, together with all their first- and second-order…
We consider and provide an accurate study for the fractional Zernike functions on the punctured unit disc, generalizing the classical Zernike polynomials and their associated $\beta$-restricted Zernike functions. Mainly, we give the…
The macroscopic electric permittivity of a given medium may depend on frequency, but this frequency dependence cannot be arbitrary, its real and imaginary parts are related by the well-known Kramers-Kronig relations. Here, we show that an…
Natural modes of helical structures are treated by using the periodic dyadic Green's functions in cylindrical coordinates. The formulation leads to an infinite system of one-dimensional integral equations in reciprocal (Fourier) space. Due…
We develop a polymer expansion with large/small field conditions for the mean resolvent of a weakly disordered system. Then we show that we can apply our result to a two-dimensional model, for energies outside the unperturbed spectrum or in…
The fermion Green function and spectral characteristics for the 2D Frohlich model of superconductivity at static fluctuations in the phase of the order parameter are calculated. The results demonstrate strongly non-Fermi-liquid properties…
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…
This paper is being replaced by another of the author's that contains a brief summary of the problem of positivity of Green's functions, heat kernels, and principal eigenvalues of higher-order elliptic differential operators.
By using the generating function formula for the product of two q-Hermite polynomials q-deformation of the Feynman Green function for the harmonic oscillator is obtained.
Marchenko methods are based on integral representations which express Green's functions for virtual sources and/or receivers in the subsurface in terms of the reflection response at the surface. An underlying assumption is that inside the…
We present a robust algorithm for the computation of electromagnetic fields radiated by point sources (Hertzian dipoles) in cylindrically stratified media where each layer may exhibit material properties (permittivity, permeability, and…
Commuting integral and differential operators connect the topics of Signal Processing, Random Matrix Theory, and Integrable Systems. Previously, the construction of such pairs was based on direct calculation and concerned concrete special…