Related papers: Resolving the spurious-state problem in Dirac equa…
Out of the four bound-state solutions presented in loc. cit., only one (viz., the spin-symmetric one, in the low-mass regime) is shown compatible with the physical boundary conditions. We clarify the problem, correct the method and offer…
In this paper we apply the stochastic variance reduced gradient (SVRG) method, which is a popular variance reduction method in optimization for accelerating the stochastic gradient method, to solve large scale linear ill-posed systems in…
Dirac algorithm allows to construct Hamiltonian systems for singular systems, and so contributing to its successful quantization. A drawback of this method is that the resulting quantized theory does not have manifest Lorentz invariance.…
The variational method is used widely for determining eigenstates of the QCD hamiltonian for actions with a conventional transfer matrix, e.g., actions with improved Wilson fermions. An alternative lattice fermion formalism, staggered…
In this paper we propose a new high order accurate space-time DG finite element scheme for the solution of the linear elastic wave equations in first order velocity-stress formulation in two and three-space dimensions on staggered…
In this paper, we study loaded modified diffusion equation (the Hallaire equation with the fractional derivative with respect to time). The compact finite difference scheme of Crank-Nicholson type of higher order is developed for…
We present a numerical method which accurately computes the discrete spectrum and associated bound states of Hamiltonians which model electronic "edge" states localized at boundaries of one and two-dimensional crystalline materials. The…
We present a new generic approach to the condensed-matter ground-state problem which is complementary to variational techniques and works directly in the thermodynamic limit. Relaxing the ground-state problem, we obtain semidefinite…
In this paper, we consider the one-dimensional semirelativistic Schr\"{o}dinger equation for a particle interacting with $N$ Dirac delta potentials. Using the heat kernel techniques, we establish a resolvent formula in terms of an $N \times…
The combinatorial integral approximation (CIA) is a solution technique for integer optimal control problems. In order to regularize the solutions produced by CIA, one can minimize switching costs in one of its algorithmic steps. This leads…
The goal of this paper is to provide an intuitive and useful tool for analyzing the impurity bound state problem. We develop a semiclassical approach and apply it to an impurity in two dimensional systems with parabolic or Dirac like bands.…
A Galerkin method is developed to solve the time-dependent Dirac equation in prolate spheroidal coordinates for an electron-molecular two-center system. The initial state is evaluated from a variational principle using a kinetic/atomic…
The Szymanzik improvement program for gauge theories is most commonly implemented using forward finite difference corrections to the Wilson action. Central symmetric schemes naively applied, suffer from a doubling of degrees of freedom,…
Electromagnetic particle-in-cell (PIC) codes are widely used to perform computer simulations of a variety of physical systems, including fusion plasmas, astrophysical plasmas, plasma wakefield particle accelerators, and secondary photon…
We analyse two principal approaches to the quantization of physical models worked out to date. There are the Faddeev-Popov "heuristic" approach, based on fixing a gauge in the FP path integrals formalism, and the "fundamental" approach by…
In this article, we derive \textit{a posteriori} error estimates for the Dirichlet boundary control problem governed by Stokes equation. An energy-based method has been deployed to solve the Dirichlet boundary control problem. We employ an…
A method to compute the scattering solutions of a spinless Salpeter equation (or a Schrodinger equation) with a central interaction is presented. This method relies on the 3-dimensional Fourier grid Hamiltonian method used to compute bound…
We present a pseudoclassical mechanics model which exhibits gauge symmetry and time-reparametrization invariance. As such, first- and second-class constraints restrict the phase space, and the Hamiltonian weakly vanishes. We show that the…
In the present work, we introduce a discrete formulation of the nonlinear Dirac equation in the form of a discretization of the Gross-Neveu model. The motivation for this discrete model proposal is both computational (near the continuum…
The principle of indirect elimination states that an algorithm for solving discretized differential equations can be used to identify its own bad-converging modes. When the number of bad-converging modes of the algorithm is not too large,…