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We study semi-martingale obliquely reflected Brownian motion with drift in the first quadrant of the plane in the transient case. Our main result determines a general explicit integral expression for the moment generating function of…
A system of equations resulting from an approximation of the equation of motion of Green functions for correlated electron systems is usually solved using Matsubara technique. In this work we propose an alternative method which works…
We present a semi-analytic approach to solving the Boltzmann equation describing the comptonisation of low frequency input photons by a thermal distribution of electrons in the Thomson limit. Our work is based on the formulation of the…
The luminosity of accreting magnetised neutron stars can largely exceed the Eddington value due to appearance of accretion columns. The height of the columns can be comparable to the neutron star radius. The columns produce the X-rays…
Let G(x_r-x_e) be the causal Green function for the wave equation in four spacetime dimensions, representing the signal received at the spacetime point x_r due to an impulse emitted at the spacetime point x_e. Such emission and reception…
Green's functions in Physics have proven to be a valuable tool for understanding fundamental concepts in different branches, such as electrodynamics, solid-state and many -body problems. In quantum mechanics advanced courses, Green's…
A method for the computation of scattering data and of the Green function for the one-dimensional Schr\"{o}dinger operator $H:=-\frac{d^2}{dx^2}+q(x)$ with a decaying potential is presented. It is based on representations for the Jost…
Spectral properties of super-Eddington accretion flows are investigated by means of a parallel line-of-sight calculation. The subjacent model, taken from two-dimensional radiation hydrodynamic simulations by Ohsuga et al. (2005), consists…
We compute a spectrum of parametric X-ray radiation (PXR) inside a crystal from a bunch of electrons, which is periodically modulated in density. We consider that the bunch of electrons is exiting from a XFEL channel. We demonstrate that in…
We use a diagrammatic hopping expansion to calculate finite-temperature Green functions of the Bose-Hubbard model which describes bosons in an optical lattice. This technique allows for a summation of subsets of diagrams, so the divergence…
The functional integral method can be used in quantum mechanics to find the scattering amplitude for particles in the external field. We will obtain the potential scattering amplitude form the complete Green function in the corresponding…
We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with…
This paper proposes, for wave propagating in a globally perturbed half plane with a perfectly conducting step-like surface, a sharp Sommerfeld radiation condition (SRC) for the first time, an analytic formula of the far-field pattern, and a…
Isolating the singularity in the Green's function solution of the inhomogeneous, differential equation for the Stermheimer function of a layered electron gas, permits the construction of an approximate solution of the Stermheimer function…
Two-particle Green's functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at two-particle level often suffer from large…
X-ray spectroscopy offers an opportunity to study the complex mixture of emitting and absorbing components in the circumnuclear regions of active galactic nuclei, and to learn about the accretion process that fuels AGN and the feedback of…
Using the Green function integral representation the Dyson-Schwinger equations are solved directly in Minkowski space. Essential ideas of the spectral techniques are discussed and applied on two renormalizable models: the Yukawa theory with…
A method for solving Schwinger-Dyson equations for the Green function generating functional of non-Abelian gauge theory is proposed. The method is based on an approximation of Schwinger-Dyson equations by exactly soluble equations. For the…
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…
Sub-barrier photo-induced fission in $^{236}$U$(\gamma,f)$ is investigated within the non-equilibrium Green function (NEGF) method. A model space for the fission process is constructed by superposing Skyrme-Hartree-Fock wave functions along…