Related papers: Solving the Klein-Gordon equation using Fourier sp…
The sine-Gordon equation is a nonlinear partial differential equation. It is known that the sine-Gordon has soliton solutions in the 1D and 2D cases, but such solutions are not known to exist in the 3D case. Several numerical solutions to…
We consider the Klein-Gordon equation in FRW-like spacetimes, with compact space sections (not necessarily isotropic neither homogeneous). The bi-scalar kernel allowing to select the positive-frequency part of any solution is developed on…
The Fast Fourier Transform is extended to functions on finite graphs whose edges are identified with intervals of finite length. Spectral and pseudospectral methods are developed to solve a wide variety of time dependent partial…
Whenever we consider any relativistic quantum wave equation we are confronted with the Klein paradox, which asserts that incident particles will suffer a surplus of reflection when dispersed by a discontinuous potential. Following recent…
For the solution of partial differential equations (PDEs), we show that the quantum Fourier transform (QFT) can enable the design of quantum circuits that are particularly simple, both conceptually and with regard to hardware requirements.…
Within this article one finds the statement of the Klein-Gordon problem within the real Hilbert space formalism ($\mathbbm R$HS) in terms of complex wave functions, and in terms of quaternionic wave functions as well. The complex…
In this article we construct the fundamental solutions for the Klein-Gordon equation in de Sitter spacetime. We use these fundamental solutions to represent solutions of the Cauchy problem and to prove $L^p-L^q$ estimates for the solutions…
Despite the fact that it is not integrable, the 1 + 2-dimensional Sine-Gordon equation has N-soliton solutions, whose velocities are lower than the speed of light (c = 1), for all N greater than or equal to 1. Based on these solutions, a…
The Quantum Fourier Transformation (QFT) is a well-known subroutine for algorithms on qubit-based universal quantum computers. In this work, the known QFT circuit is used to derive an efficient circuit for the multidimensional QFT. The…
This paper is devoted to the efficient numerical solution of the Helmholtz equation in a two- or three-dimensional rectangular domain with an absorbing boundary condition (ABC). The Helmholtz problem is discretized by standard bilinear and…
In this work we consider the problem of global existence of small regular solutions to a type nonlinear wave-Klein-Gordon system with semi-linear interactions in two spatial dimension. We develop some new techniques on both wave equations…
The special unitary group SU(2) plays a fundamental role in the description of symmetries in quantum mechanics, theoretical physics, and spherical signal processing. In this paper, we address the computational challenges of performing…
We study in $\mathbb{R}^{3+1}$ a system of nonlinearly coupled Klein-Gordon equations under null condition, with (possibly vanishing) mass varying in the interval $[0, 1]$. Our goal is three folds: 1) we want to establish the global…
We present four quantum algorithms for solving a multidimensional drift-diffusion equation. They rely on a quantum linear system solver, a quantum Hamiltonian simulation, a quantum random walk, and the quantum Fourier transform. We compare…
Nonperturbative calculation of QED processes participated by a strong electromagnetic field, especially provided by strong laser facilities at present and in the near future, generally resorts to the Furry picture with the usage of…
Quantum computing holds the promise of solving computational mechanics problems in polylogarithmic time, meaning computational time scales as $\mathscr{O}((\log N)^c)$, where $N$ is the problem size and $c$ a constant. We propose a quantum…
This analysis proposes an analytical-numerical approach for providing solutions of a class of nonlinear fractional Klein-Gordon equation subjected to appropriate initial conditions in Caputo sense by using the Fractional Reduced…
Quantum computers can be used to address molecular structure, materials science and condensed matter physics problems, which currently stretch the limits of existing high-performance computing resources. Finding exact numerical solutions to…
We derive the Klein--Gordon equation for a single scalar field coupled to gravity at second order in perturbation theory and leading order in slow-roll. This is done in two ways: we derive the Klein--Gordon equation first using the Einstein…
We describe a procedure naturally associating relativistic Klein-Gordon equations in static curved spacetimes to non-relativistic quantum motion on curved spaces in the presence of a potential. Our procedure is particularly attractive in…