Related papers: Numerical Methods for Handlebody Phases
Approximate bound state solutions of the spinless Salpeter equation for the Hellmann potential are studied for heavy particles. By using functional analysis method, an analytical expression for the energy levels, and the corresponding…
This article proposes a new discrete framework for approximating solutions to shape optimization problems under convexity constraints. The numerical method, based on the support function or the gauge function, is guaranteed to generate…
An improved hyperspherical harmonic method for the quantum three-body problem is presented to separate three rotational degrees of freedom completely from the internal ones. In this method, the Schr\"{o}dinger equation of three-body problem…
A method is introduced for solving Einstein's equations using two distinct coordinate systems. The coordinate basis vectors associated with one system are used to project out components of the metric and other fields, in analogy with the…
Statistical solutions are time-parameterized probability measures on spaces of integrable functions, that have been proposed recently as a framework for global solutions and uncertainty quantification for multi-dimensional hyperbolic system…
We consider solutions of the 2x2 matrix Hamiltonians of the physical systems within the context of the su(2) and su(1,1) Lie algebra. Our technique is relatively simple when compared with the others and treats those Hamiltonians which can…
We derive, in 2+1 dimensions, classical solutions for metric and motion of two or more spinning particles, in the conformal Coulomb gauge introduced previously. The solutions are exact in the $N$-body static case, and are perturbative in…
Finite difference method and pseudo-spectral method have been widely used in the numerical relativity to solve the Einstein equations. As the third major category method to solve partial differential equations, finite element method is much…
We obtain the Einstein-Maxwell equations for (2+1)-dimensional static space-time, which are invariant under the transformation $q_0=i\,q_2,q_2=i\,q_0,\alpha \rightleftharpoons \gamma$. It is shown that the magnetic solution obtained with…
A code for the numerical evaluation of hyperelliptic theta-functions is presented. Characteristic quantities of the underlying Riemann surface such as its periods are determined with the help of spectral methods. The code is optimized for…
In a multidimensional infinite layer bounded by two hyperplanes, the inhomogeneous Helmholtz equation with a polynomial right-hand side is considered. It is shown that the Dirichlet and Dirichlet-Neumann boundary-value problems with…
We construct solutions with prescribed asymptotics to the Einstein constraint equations using a cut-off technique. Moreover, we give various examples of vacuum asymptotically flat manifolds whose center of mass and angular momentum are…
This paper discusses the theory and numerical method of two-scale analysis for the multiscale Landau-Lifshitz-Gilbert equation in composite ferromagnetic materials. The novelty of this work can be summarized in three aspects: Firstly, the…
A generic procedure is proposed to construct many-body quantum Hamiltonians with partial dynamical symmetry. It is based on a tensor decomposition of the Hamiltonian and allows the construction of a hierarchy of interactions that have…
In the theory and practice of inverse problems for partial differential equations (PDEs) much attention is paid to the problem of the identification of coefficients from some additional information. This work deals with the problem of…
What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd et al. (quant-ph/0106064) provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired…
We formulate the 2-body problem of electrodynamics using functional differential equations, and explain the peculiar features of these equations which indicate a paradigm shift in physics. We examine the possible empirical existence of…
The four-body bound state with two-body forces is formulated by the Three-Dimensional approach, which greatly simplifies the numerical calculations of few-body systems without performing the Partial Wave components. We have obtained the…
A method of fundamental solutions has been used to show its effectiveness in solving some well known problems of 1D quantum mechanics (barrier penetrations, over-barrier reflections, resonance states), i.e. those in which we look for…
In this article, we extend Anderson's higher-dimensional Dehn filling construction to a large class of infinite-volume hyperbolic manifolds. This gives an infinite family of topologically distinct asymptotically hyperbolic Einstein…