Related papers: A brief introduction to dispersive methods
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…
Starting with the Green's functions found for normal diffusion, we construct exact time-dependent Green's functions for subdiffusive equation (with fractional time derivatives), with the boundary conditions involving a linear combination of…
We establish a general relation between the statistics of the local Green's function for systems with chaotic wave scattering and a uniform energy loss (absorption) and its two-point correlation function for the same system without…
In these lectures we provide a basic introduction into the topic of dispersion relation and analyticity. The properties of 2-point functions are discussed in some detail from the viewpoint of the K\"all\'en-Lehmann and general dispersion…
We study the one-dimensional diffusion process which takes place between two reflecting boundaries and which is acted upon by a time-dependent and spatially-constant force. The assumed force possesses both the harmonically oscillating and…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
Strings propagating along surfaces with Dirichlet boundaries are studied in this paper. Such strings were originally proposed as a possible candidate for the QCD string. Our approach is different from previous ones and is simple and general…
A linear singularly perturbed convection-diffusion problem with characteristic layers is considered in three dimensions. Sharp bounds for the associated Green's function and its derivatives are established in the $L_1$ norm. The dependence…
These lectures introduce some of the basic methods of perturbative QCD and their applications to phenomenology at high energy. Emphasis is given to techniques that are used to study QCD and related field theories to all orders in…
The two-time Green function method in quantum electrodynamics of high-Z few-electron atoms is described in detail. This method provides a simple procedure for deriving formulas for the energy shift of a single level and for the energies and…
We consider the transmission of massless Dirac fermions through an array of short range scatterers which are modeled as randomly positioned $\delta$- function like potentials along the x-axis. We particularly discuss the interplay between…
Recently, general point interactions in one dimension has been used to model a large number of different phenomena in quantum mechanics. Such potentials, however, requires some sort of regularization to lead to meaningful results. The usual…
We consider the Green's functions associated to a scalar field propagating on a curved, ultra-static background, in the presence of modified dispersion relations. The usual proper-time deWitt-Schwinger procedure to obtain a series…
The study of wave propagation and scattering in time-dependent materials is a rapidly growing field of research. Whereas for 1D applications there is a simple relation between the wave equations for space-dependent and time-dependent…
We use the collective field theory known for the Calogero-Sutherland model to study a variety of low-energy properties. These include the ground state energy in a confining potential upto the two leading orders in the particle number, the…
We give a pedagogical introduction to the founding ideas of dispersion relations in particle physics. Starting from elementary mechanical systems, we show how the physical principle of causality is closely related to the mathematical…
I construct a well-defined expansion in $\epsilon=2-d$ for diffusion processes on small-world networks. The technique permits one to calculate the average over disorder of moments of the Green's function, and is used to calculate the…
Computationally inexpensive approximations describing electron-phonon scattering in molecular-scale conductors are derived from the non-equilibrium Green's function method. The accuracy is demonstrated with a first principles calculation on…
We consider a two-dimensional diffusion process in a two-layered plane, governed by distinct covariance matrices in the upper and lower half-planes and by two drift vectors pointed away from the $x$-axis. We first analyze the case where the…
This paper presents a full-spectrum Green function methodology (which is valid, in particular, at and around Wood-anomaly frequencies) for evaluation of scattering by periodic arrays of cylinders of arbitrary cross section-with application…