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This introduction to Green's functions is based on their role as kernels of differential equations. The procedures to construct solutions to a differential equation with an external source or with an inhomogeneity term are put together to…
A novel scheme to solve the quantum eigenvalue problem through the imaginary-time Green function Monte Carlo method is presented. This method is applicable to the excited states as well as to the ground state of a generic system. We…
A domain integral method employing a specific Green's function (i.e., incorporating some features of the global problem of wave propagation in an inhomogeneous medium) is developed for solving direct and inverse scattering problems relative…
The solution of some equations involving functional derivatives is given as a series indexed by planar binary trees. The terms of the series are given by an explicit recursive formula. Some algebraic properties of these series are…
In a previous paper, "Generalized Green functions and unipotent classes for finite reductive groups, I", we have determined certain unknown scalars involved in the algorithm of computing generalized Green functions in the case of SL_n. In…
We present a brief pedagogical review of theoretical Green's function methods applicable to open quantum systems out of equilibrium in general, and single molecule junctions in particular. We briefly describe experimental advances in…
Semiclassical techniques have proven to be a very powerful method to extract physical effects from different quantum theories. Therefore, it is expected that in the near future they will play a very prominent role in the context of quantum…
It is known that the equation $x'(t)=Ax(t)+f(t)$, where $A$ is a bounded linear operator, has a unique bounded solution $x$ for any bounded continuous free term~$f$ if and only if the spectrum of the coefficient $A$ does not intersect the…
The main aspects of a gauge-invariant approach to the description of quark dynamics in the nonperturbative regime of QCD are first reviewed. In particular, the role of the parallel transport operation in constructing gauge-invariant Green's…
Building on the many existing algorithms for calculating the DC transport properties of quantum tight-binding models, we develop a systematic approach that expresses finite frequency observables in terms of the stationary Green's function…
We consider the Grover walk on the infinite graph in which an internal finite subgraph receives the inflow from the outside with some frequency and also radiates the outflow to the outside. To characterize the stationary state of this…
Let $\Gamma$ be geometric tree graph with $m$ edges and consider the second order Sturm-Liouville operator $\L[u]=(-pu')'+qu$ acting on functions that are continuous on all of $\Gamma$, and twice continuously differentiable in the interior…
In the paper we give consecutive description of functional methods of quantum field theory for systems of interacting q-particles. These particles obey exotic statistics and appear in many problems of condensed matter physics, magnetism and…
An analytical Green's function is developed to study the acoustic scattering by a flat plate with a serrated edge. The scattered pressure is solved using the Wiener-Hopf technique in conjunction with the adjoint technique. It is shown that…
The delta interaction at a vertex generalizes the Robin (generalized Neumann) boundary condition on an interval. Study of a single vertex with N infinite leads suffices to determine the localized effects of such a vertex on densities of…
In order to account for competition and interplay of localized and itinerant magnetic behaviour in correlated many body systems with complex spectra the various types of spin-fermion models have been considered in the context of the…
Motivated by recent experimental refinements of stellar reaction rates, we establish a non-perturbative Green's function formalism based on the exact solution of the Dyson equation for sub-barrier proton-nucleus resonant scattering. By…
We consider a general 1D matrix Schr\"odinger equation within a transfer matrix approach. For a quadratic kinetic term we discuss expressions for the local Green function in terms of solutions of equations of the Riccati type, and an…
Utilization of electron transfer methods for description of quantum transport is popular due to simplicity of the formulation and its ability to account for basic physics of electron exchange between system and baths. At the same time,…
We review some recent techniques for dealing with non-hermitian random matrix models based on generalized Green's functions. We introduce the diagrammatic methods in the hermitian case and generalize them to the non-hermitian case. The…