Related papers: Explicit Computation of Certain Arakelov-Green Fun…
The aim of this paper is to show certain properties of the Green's functions related to the Hill's equation coupled with different two point boundary value conditions. We will obtain the expression of the Green's function of Neumann,…
In a previous work [Andrade \textit{et al.}, Phys. Rep. \textbf{647}, 1 (2016)], it was shown that the exact Green's function (GF) for an arbitrarily large (although finite) quantum graph is given as a sum over scattering paths, where local…
The complexity of a graph is the number of its labeled spanning trees. In this work complexity is studied in settings that admit regular graphs. An exact formula is established linking complexity of the complement of a regular graph to…
In this article we use linear algebra to improve the computational time for the obtaining of Green's functions of linear differential equations with reflection (DER). This is achieved by decomposing both the `reduced' equation (the ODE…
In this work we calculate the exact Green's function for arbitrary rectangular potentials. Specifically we focus on Green's function for rectangular quantum wells enlarging the knowledge of exact solutions for Green's functions and also…
Graphical functions are positive functions on the punctured complex plane $\mathbb{C}\setminus\{0,1\}$ which arise in quantum field theory. We generalize a parametric integral representation for graphical functions due to Lam, Lebrun and…
This work presents a novel approach to describe spectral properties of graphene layers with well defined edges. We microscopically analyze the boundary problem for the continuous Bogoliubov-de Gennes-Dirac (BdGD) equations and derive the…
In this paper, we build on the work of [T. Hughes, G. Sangalli, VARIATIONAL MULTISCALE ANALYSIS: THE FINE-SCALE GREENS' FUNCTION, PROJECTION, OPTIMIZATION, LOCALIZATION, AND STABILIZED METHODS, SIAM Journal of Numerical Analysis, 45(2),…
The electromagnetic Green's function is a crucial ingredient for the theoretical study of modern photonic quantum devices, but is often difficult or even impossible to calculate directly. We present a numerically efficient framework for…
Gross and Zagier defined certain `higher Green's functions' on products of modular curves and conjectured that the value of these functions at complex multiplication points should be logarithms of algebraic numbers. This is now a theorem of…
We develop a new algebraic setting for treating piecewise functions and distributions together with suitable differential and Rota-Baxter structures. Our treatment aims to provide the algebraic underpinning for symbolic computation systems…
Given a number field $K$ with a Hecke character $\chi$, for each place $\nu$ we study the free scalar field theory whose kinetic term is given by the regularized Vladimirov derivative associated to the local component of $\chi$. These…
Higher Green functions are real-valued functions of two variables on the upper half plane which are bi-invariant under the action of a congruence subgroup, have logarithmic singularity along the diagonal, but instead of the usual equation…
In this paper we develop computational tools to study the higher algebraic $K$-theory of Green functors. We construct a spectral sequence converging to the algebraic $\mathbb{G}$-theory of any $G$-Green functor, for $G$ a cyclic $p$-group.…
By introducing multipe-site correlation functions, we propose a hierarchical Green function approach, and apply it to study the characteristic properties of a 2D square lattice Hubbard model by solving the equation of motions of a…
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
We introduce the partition function of edge-colored graph homomorphisms, of which the usual partition function of graph homomorphisms is a specialization, and present an efficient algorithm to approximate it in a certain domain. Corollaries…
Many numerical methods for evaluating matrix functions can be naturally viewed as computational graphs. Rephrasing these methods as directed acyclic graphs (DAGs) is a particularly effective approach to study existing techniques, improve…
We formulate the dynamical mean field theory directly in the continuum. For a given definition of the local Green's function, we show the existence of a unique functional, whose stationary point gives the physical local Green's function of…
For meromorphic maps of complex manifolds, ergodic theory and pluripotential theory are closely related. In nice enough situations, dynamically defined Green's functions give rise to invariant currents which intersect to yield measures of…