Related papers: Clustering in particle chains - summation techniqu…
In the present paper, employing properties of the complete elliptic integrals of the first and second kind, we deduce closed-form formulae for the lattice sums and other new formulae. Applications to the effective properties of regular and…
We present a new, highly efficient yet accurate approximation for the Green's functions of dressed particles, using the Holstein polaron as an example. Instead of summing a subclass of diagrams (e.g. the non-crossed ones, in the…
In this work, simple exact results are presented for summations in two-particle potential with long-range interactions. Polygamma function is used to evaluate summations. Results are found when a periodic media is consider. Periodic…
The linked-cluster expansion technique for the high-temperature expansion of spin model is reviewed. A new algorithm for the computation of three-point and higher Green's functions is presented. Series are computed for all components of…
In geophysical fluid dynamics, the screened Poisson equation appears in the shallow-water, quasi geostrophic equations. Recently, many attempts have been made to solve those equations on the sphere using different numerical methods. These…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…
In this work we present a three step procedure for generating a closed form expression of the Green's function on both closed and open finite quantum graphs with general self-adjoint matching conditions. We first generalize and simplify the…
In a previous work (arXiv:2505.05574), a summation formula for harmonic Maass forms of polynomial growth was established. In this note, we use the theory of $L$-series of harmonic Maass forms to state and prove a summation formula for such…
We present linear response theories in the continuum capable of describing continuum spectra and dynamical correlations of finite systems with no spatial symmetry. Our formulation is essentially the same as the continuum random-phase…
This paper, Part I in a two-part series, presents (i) A simple and highly efficient algorithm for evaluation of quasi-periodic Green functions, as well as (ii) An associated boundary-integral equation method for the numerical solution of…
We propose a general method to obtain the scalar worldline Green function on an arbitrary 1D topological space, with which the first-quantized method of evaluating 1-loop Feynman diagrams can be generalized to calculate arbitrary ones. The…
In a recent series of scanning probe experiments, it became possible to visualize local electron flow in a two-dimensional electron gas. In this paper, a Green's function technique is presented that enables efficient calculation of the…
In this paper, we summarize the technique of using Green functions to solve electrostatic problems. We start by deriving the electric potential in terms of a Green function and a charge distribution. We then provide a variety of example…
A first order differential equation of Green's Function, at the origin G(0), for the one- dimensional lattice is derived by simple recurrence relation. Green's Function at site (m)is then calculated in terms of G(0). A simple recurrence…
The evaluation of the interaction between objects arranged on a lattice requires the computation of lattice sums. A scenario frequently encountered are systems governed by the Helmholtz equation in the context of electromagnetic scattering…
We summarize recent developments in the field of higher dimensional bosonization made by the authors and collaborators and propose a general formula for the field operator in terms of currents and densities in one dimension using a new…
The well-known expressions for the Green's functions for the Helmholtz equation in polar coordinates with Dirichlet and Neumann boundary conditions are transformed. The slowly converging double series describing these Green's functions are…
The fast assembling of stiffness and mass matrices is a key issue in isogeometric analysis, particularly if the spline degree is increased. We present two algorithms based on the idea of sum factorization, one for matrix assembling and one…
We present a new method for calculating the Green functions for a lattice scalar field theory in $D$ dimensions with arbitrary potential $V(\phi)$. The method for non-perturbative evaluation of Green functions for $D \! = \! 1$ is…
We show that cluster algorithms for quantum models have a meaning independent of the basis chosen to construct them. Using this idea, we propose a new method for measuring with little effort a whole class of Green's functions, once a…