Related papers: An Efficient Method for the Solution of Schwinger-…
In the Euclidean-space formulation of integral equations for the structure of quantum chromodynamics (QCD) bound states, the quark propagators with complex-valued momentum are densely sampled. We therefore propose an accurate and efficient…
The solution to the Schwinger-Dyson equation that describes the summation over Pomeron loop diagrams is derived. The solution is a closed expression which splits into two parts. The first leads directly to the renormalization of the BFKL…
This paper discusses a fast direct solver using boundary integral equations for Helmholtz transmission problems involving multiple inclusions in two dimensions. Efficiently addressing scattering problems in the presence of numerous…
The Schwinger-Dyson Equations (SDEs) of matrix models are known to form (half) a Virasoro algebra and have become a standard tool to solve matrix models. The algebra generated by SDEs in tensor models (for random tensors in a suitable…
A simple method has been introduced to derive the all order quantum corrected Bose-Einstein distribution as the solution of the Wigner equation. The process is a perturbative one where the Bose-Einstein distribution has been taken as the…
The analytic structure of the quark propagator in Minkowski space is more complex than in Euclidean space due to the possible existence of poles and branch cuts at timelike momenta. These singularities impose enormous complications on the…
Effective mass and energy are investigated using the Schwinger-Dyson equation (SDE) in the complex plane. As simple examples, we solve the SDE for the (1+1)-dimensional model and the strongly coupled quantum electrodynamics (QED). We also…
We derive dispersion estimates for solutions of the one-dimensional discrete perturbed Schr\"odinger and wave equations. In particular, we improve upon previous works and weaken the conditions on the potentials. To this end we also provide…
For lambda phi^4 problems, convergent perturbative series can be obtained by cutting off the large field configurations. The modified series converge to values exponentially close to the exact ones. For lambda larger than some critical…
This report discusses two new ideas for using perturbation methods to solve the time-independent Schr\"odinger equation. The first concept begins with rewriting the perturbation equations in a form that is closely related to matrix…
Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an…
We illustrate the stochastic method for solving the Schwinger-Dyson equations in large-N quantum field theories described in ArXiv:1009.4033 on the example of the Gross-Witten unitary matrix model. In the strong-coupling limit, this method…
A new deterministic, numerical method to solve fermion field theories is presented. This approach is based on finding solutions $Z[J]$ to the lattice functional equations for field theories in the presence of an external source $J$. Using…
We demonstrate the power of a first principle-based and practicable method that allows for the perturbative computation of reduced density matrix elements of an open quantum system without making use of any master equations. The approach is…
Novel solutions of Minkowski QED2+1 and large $N_f$ QCD Schwinger-Dyson equations will be presented and discussed. The resultant propagators of confined degrees of freedom will be shown.
The periodic s-d(f) exchange model is characterized by a wide variety of interesting applications, a simple mathematical structure and a limited number of reliable approximations which take care of the quantum nature of the participating…
In this paper, we propose a fast distributed solver for linear equations given by symmetric diagonally dominant M-Matrices. Our approach is based on a distributed implementation of the parallel solver of Spielman and Peng by considering a…
Many properties of current \emph{ab initio} approaches to the quantum many-body problem, both perturbational or otherwise, are related to the singularity structure of Rayleigh--Schr\"odinger perturbation theory. A numerical procedure is…
We present a perturbation approach to calculate the short-time propagator, or transition density, of the one-dimensional Fokker-Planck equation, to in principle arbitrary order in the time increment. Our approach preserves probability…
We use the perturbation method to approximately solve subdiffusion-reaction equations. Within this method we obtain the solutions of the zeroth and the first order. The comparison our analytical solutions with the numerical results shown…