Related papers: Unitary equivalence between the Green's function a…
Starting from linear equations for the complex scalar field, the two- and three-point Green's functions are obtained in the infrared approximation. We show that the infrared singularity factorizes in the vertex function as in spinorial QED,…
We combine the recently developed many-body Green's function theory for electrons and nuclei with the exact factorization of the wave function. The existing Born-Oppenheimer Green's functions are shown to be special cases of our exact…
In this paper we study the time dependent Schr\"odinger equation with all possible self-adjoint singular interactions located at the origin, which include the $\delta$ and $\delta'$-potentials as well as boundary conditions of Dirichlet,…
This article presents a novel and succinct algorithmic framework via alternating quantum walks, unifying quantum spatial search, state transfer and uniform sampling on a large class of graphs. Using the framework, we can achieve exact…
A careful functional treatment of quantum scattering is given using Schwinger's dynamical principle which involves a functional differentiation operation applied to a generating functional written in closed form. For long range…
We present a simple combinatorial framework for establishing approximate tensorization of variance and entropy in the setting of spin systems (a.k.a. undirected graphical models) based on balanced separators of the underlying graph. Such…
The negative-AND (NAND) gate is universal for classical computation making it an important target for development. A seminal quantum computing algorithm by Farhi, Goldstone and Gutmann has demonstrated its realization by means of quantum…
Consider a random regular graph of fixed degree $d$ with $n$ vertices. We study spectral properties of the adjacency matrix and of random Schr\"odinger operators on such a graph as $n$ tends to infinity. We prove that the integrated density…
The graph isomorphism problem asks whether two graphs are identical up to vertex relabeling. While the exact problem admits quasi-polynomial-time classical algorithms, many applications in molecular comparison, noisy network analysis, and…
We propose an approach to quantize discrete networks (graphs with discrete edges). We introduce a new exact solution of discrete Schrodinger equation that is used to write the solution for quantum graphs. Formulation of the problem and…
The classical Green's function associated to a simply connected domain in the complex plane is easily expressed in terms of a Riemann mapping function. The purpose of this paper is to express the Green's function of a finitely connected…
Graph embedding, representing local and global neighborhood information by numerical vectors, is a crucial part of the mathematical modeling of a wide range of real-world systems. Among the embedding algorithms, random walk-based algorithms…
The non-equilibrium quantum field dynamics is usually described in the closed-time-path formalism. The initial state correlations are introduced into the generating functional by non-local source terms. We propose a functional approach to…
A quantum walk model which reflects the $2$-cell embedding on the orientable closed surface of a graph in the dynamics is introduced. We show that the scattering matrix is obtained by finding the faces on the underlying surface which have…
Graph similarity learning, crucial for tasks such as graph classification and similarity search, focuses on measuring the similarity between two graph-structured entities. The core challenge in this field is effectively managing the…
In quantum field theory, the Green function is usually calculated as the expectation value of the time-ordered product of fields over the vacuum. In some cases, especially in degenerate systems, expectation values over general states are…
We revisit the volume Green's function integral equation for modelling light scattering with discretization strategies as well as numerical integration recipes borrowed from finite element method. The merits of introducing finite element…
Quantum networks are often modelled using Schroedinger operators on metric graphs. To give meaning to such models one has to know how to interpret the boundary conditions which match the wave functions at the graph vertices. In this article…
For the massless N=1supersymmetric electrodynamics, regularized by higher derivatives, the Feynman diagrams, which define the divergent part of the two-point Green function and can not be found from Schwinger-Dyson equations and Ward…
Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an efficient site-centered, electronic-structure technique for addressing an assembly of $N$ scatterers. Wave-functions are expanded in a spherical-wave basis on…