Related papers: On the Q-BOR-FDTD method
Schwinger-Dyson equations are used to study the phase diagram of QED in three dimensions. This computation is made with full frequency-dependence in the two-point function gap equations for the first time. We also demonstrate that reliable…
The self-consistent Born approximation quantitatively fails to capture disorder effects in semimetals. We present an alternative, simple-to-use non-perturbative approach to calculate the disorder induced self-energy. It requires a…
In this paper we apply the ideas of New Q-Newton's method directly to a system of equations, utilising the specialties of the cost function $f=||F||^2$, where $F=(f_1,\ldots ,f_m)$. The first algorithm proposed here is a modification of…
First we introduce and analyze a convergent numerical method for a large class of nonlinear nonlocal possibly degenerate convection diffusion equations. Secondly we develop a new Kuznetsov type theory and obtain general and possibly optimal…
In this paper, we investigate the unique solvability of a mixed boundary value problem for a fractional partial differential equation featuring a degenerate coefficient. By introducing a novel operator and applying the method of separation…
For a q-deformed harmonic oscillator, we find explicit coordinate representations of the creation and annihilation operators, eigenfunctions, and coherent states (the last being defined as eigenstates of the annihilation operator). We…
The purpose of this work is to study spectral methods to approximate the eigenvalues of nonlocal integral operators. Indeed, even if the spatial domain is an interval, it is very challenging to obtain closed analytical expressions for the…
We develop a quantum filter diagonalization method (QFD) that lies somewhere between the variational quantum eigensolver (VQE) and the phase estimation algorithm (PEA) in terms of required quantum circuit resources and conceptual…
In this article we are interested for the numerical study of nonlinear eigenvalue problems. We begin with a review of theoretical results obtained by functional analysis methods, especially for the Schrodinger pencils. Some recall are given…
A new symbolic algorithmic implementation of the functional-discrete (FD-) method is developed and justified for the solution of fourth order Sturm--Liouville problem on a finite interval in the Hilbert space. The eigenvalue problem for the…
Main purposes of the paper are followings: 1) To show examples of the calculations in domain of QFT via ``derivative rules'' of an expert system; 2) To consider advantages and disadvantage that technology of the calculations; 3) To reflect…
In application of the complex Langevin method to QCD at high density and low temperature, the singular-drift problem occurs due to the appearance of near-zero eigenvalues of the Dirac operator. In order to avoid this problem, we proposed to…
Degenerate perturbation theory from quantum mechanics is inadequate in density functional theory (DFT) because of nonlinearity in the Kohn-Sham potential. Herein, we develop the fully general perturbation theory for open-shell, degenerate…
It is shown that a model recently proposed for numerical calculations of bound states in QED$_3$ is in fact an improper truncation of the Aharonov-Bohm potential.
Bridging the gap between first principles methods and empirical schemes, the density functional based tight-binding method (DFTB) has become a versatile tool in predictive atomistic simulations over the past years. One of the major…
In this paper, we study several degenerate trigonometric functions, which are degenerate versions of the ordinary trigonometric functions, and derive some identities among such functions by using elementary methods. Especially, we obtain…
This paper is devoted to the asymptotics of eigenvalues for a Schr\"o-dinger operator in the case when the potential V does not tend to infinity at infinity. Such a potential is called degenerate. The point is that the set in the phase…
Friedberg, Lee and Zhao proposed a method for effectively evaluating the eigenenergies and eigen wavefunctions of quantum systems. In this work, we study several special cases to investigate applicability of the method. Concretely, we…
We prove a Kakeya-Nikodym bound on eigenfunctions and quasimodes, which sharpens a result of the authors and extends it to higher dimensions. As in the prior work, the key intermediate step is to prove a microlocal version of these…
The Born-Jordan method for constructing the quantum condition of the Matrix Mechanics is pointed out to be inappropriate in the present work. We modify this method and reconstruct the quantum condition by setting up a new expression for the…