Related papers: Analytic properties of the electromagnetic Green's…
The fundamental problem of optical wave propagation is the determination of the field at an observation point, given a disturbance specified over some finite aperture. In both vacuum and inhomogeneous media, the solution of this problem is…
Radiation by solid or fluid bodies can be characterized by resonance modes. They are complex, as well as resonance frequencies, because of the energy loss due to radiation. For ducts, they can be computed from the knowledge of the radiation…
We have developed a Green's function formalism based on the use of an overcomplete semicoherent basis of vortex states, specially devoted to the study of the Hamiltonian quantum dynamics of electrons at high magnetic fields and in an…
The Green's function of the discrete Sch\"odinger operator on a finite graph is considered. This setting reproduces Laplacian and signless Laplacian by adjusting appropriate potentials. We show two ways of the expression for the Green's…
The Green's function for a hole moving in an antiferromagnet is derived analytically in the long-wavelength limit. We find that the infrared divergence is eliminated in two and higher dimensions so that the quasiparticle weight is finite.…
We predict that spin-waves in an ordered square quantum antiferromagnet in a transverse magnetic field (h) may demonstrate three modes of spin excitations. Starting from the self-consistent rotation-invariant Green's function method, a new…
The Hubbard model, a cornerstone in the field of condensed matter physics, serves as a fundamental framework for investigating the behavior of strongly correlated electron systems. This paper presents a novel perspective on the model,…
Laser-atom interaction can be an efficient mechanism for the production of coherent electrons. We analyze the dynamics of monoenergetic electrons in the presence of uniform, perpendicular magnetic and electric fields. The Green function…
We study wave propagation phenomena modelled in the frequency domain by the Helmholtz equation in heterogeneous media with focus on media with discontinuous, highly oscillating wave speed. We restrict to problems with spherical symmetry and…
A new expression for the Green's function of a finite one-dimensional lattice with nearest neighbor interaction is derived via discrete Fourier transform. Solution of the Heisenberg spin chain with periodic and open boundary conditions is…
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…
The integral expressions served to decompose vector field into irrotational and divergence-free components represent modern version of the Helmholtz decomposition theorem. These expressions are also widely used to decompose the…
Fourier methods well known in signal processing are applied to three-dimensional wave propagation problems. The Fourier transform of the Green function, when written explicitly in terms of a real-valued spatial frequency, consists of…
The 2-parameter Green functions occur as a crucial ingredient in the character formula for Lusztig induction in finite reductive groups. Still, very little is known about these functions, in particular in the case of groups arsing from…
We revisit the Fourier transform of a Hankel function, of considerable importance in the theory of knife edge diffraction. Our approach is based directly upon the underlying Bessel equation, which admits manipulation into an alternate…
Recently, the degenerate gamma functions are introduced as a degenerate version of the usual gamma function by Kim-Kim. In this paper, we investigate several properties of them. Namely, we obtain an analytic continuation as a meromorphic…
Despite recent advances, systematic quantitative treatment of the electron correlation problem in extended systems remains a formidable task. Systematically improvable Green's function methods capable of quantitatively describing weak and…
We consider a transient Brownian motion reflected obliquely in a two-dimensional wedge. A precise asymptotic expansion of Green's functions is found in all directions. To this end, we first determine a kernel functional equation connecting…
The determination of ultra-long-range molecular potential curves has been reformulated using the Coulomb Greens function to give a solution in terms of the roots of an analytical determinantal equation. For a system consisting of one…
Many electrical grid transients can be described by the propagation of electromechanical (EM) waves that couple oscillations of power flows over transmission lines and the inertia of synchronous generators. These EM waves can take several…