Related papers: Fourier methods for the perturbed harmonic oscilla…
In his monograph Chebyshev and Fourier Spectral Methods, John Boyd claimed that, regarding Fourier spectral methods for solving differential equations, ``[t]he virtues of the Fast Fourier Transform will continue to improve as the relentless…
Rational solutions of partial differential equations (PDEs) are notoriously difficult to approximate via spectral Fourier methods due to their algebraically slow decay rate. In this work we discuss approximating rational PDE solutions in a…
We develop a new method of implementing the Hartree-Fock calculations. A class of Gaussian bases is assumed, which includes the Kamimura-Gauss basis-set as well as the set equivalent to the harmonic-oscillator basis-set. By using the…
We present $\mathcal{O}(N^2)$ estimators for the small-scale power spectrum and bispectrum in cosmological simulations. In combination with traditional methods, these allow spectra to be efficiently computed across a vast range of scales,…
The numerical evaluation of integrals of the form \begin{align*} \int_a^b f(x) e^{ikg(x)}\,dx \end{align*} is an important problem in scientific computing with significant applications in many branches of applied mathematics, science and…
For quantum systems with competing potentials, the conventional perturbation theory often yields an asymptotic series and the subsequent numerical outcome becomes uncertain. To tackle such kind of problems, we develop a general solution…
In this paper we propose a method to solve the Kadomtsev--Petviashvili equation based on splitting the linear part of the equation from the nonlinear part. The linear part is treated using FFTs, while the nonlinear part is approximated…
The harmonic oscillator with a time-dependent frequency has a family of linear quantum invariants for the time-dependent Schr\"{o}dinger equation, which are determined by any two independent solutions to the classical equation of motion.…
The adaptive perturbation method decomposes a Hamiltonian by the diagonal elements and non-diagonal elements of the Fock state. The diagonal elements of the Fock state are solvable but can contain the information about coupling constants.…
A typical procedure to integrate numerically the time dependent Schr\"o\-din\-ger equation involves two stages. In the first one carries out a space discretization of the continuous problem. This results in the linear system of differential…
We introduce a general purpose algorithm for rapidly computing certain types of oscillatory integrals which frequently arise in problems connected to wave propagation and general hyperbolic equations. The problem is to evaluate numerically…
This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and…
Cooling methods and particle slowers as well as accelerators are basic tools for fundamental research and applications in different fields and systems. We put forward a generic mechanism to scale the momentum of a particle, regardless of…
This paper presents a comprehensive investigation of the problem of a harmonic oscillator with time-depending frequencies in the framework of the Vlasov theory and the Wigner function apparatus for quantum systems in the phase space. A new…
Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…
In this work, we present a new diagrammatic method for computing the effective Hamiltonian of driven nonlinear oscillators. At the heart of our method is a self-consistent perturbation expansion developed in phase space, which establishes a…
Some properties of the fractional Fourier transform, which is used in information processing, are presented in connection with the tomography transform of optical signals. Relation of the Green function of the quantum harmonic oscillator to…
The scattering of electromagnetic pulses is described using a non-singular boundary integral method to solve directly for the field components in the frequency domain, and Fourier transform is then used to obtain the complete space-time…
In many time-harmonic electromagnetic wave problems, the considered geometry exhibits an axial symmetry. In this case, by exploiting a Fourier expansion along the azimuthal direction, fully three-dimensional (3D) calculations can be carried…
We present several methods, which utilize symplectic integration techniques based on two and three part operator splitting, for numerically solving the equations of motion of the disordered, discrete nonlinear Schr\"odinger (DDNLS)…