Related papers: Fourier transformation and response functions
A number of elegant approaches have been developed for the identification of quantum circuits which can be efficiently simulated on a classical computer. Recently, these methods have been employed to demonstrate the classical simulability…
We derive an exact closed-form representation for the Euclidean thermal Green function of the two-dimensional (2D) free massless scalar field in coordinate space. This can be interpreted as the real part of a complex analytic function of a…
The problem of the fictitious frequency spectrum resulting from numerical implementations of the boundary element method for the exterior Helmholtz problem is revisited. When the ordinary 3D free space Green's function is replaced by a…
We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with Fourier techniques since…
In this paper, we present a fast multipole method (FMM) for solving the two-dimensional Laplace equation in a half-plane with Robin boundary conditions. The method is based on a novel expansion theory for the reaction component of the…
Digital Transforms have important applications on subjects such as channel coding, cryptography and digital signal processing. In this paper, two Fourier Transforms are considered, the discrete time Fourier transform (DTFT) and the finite…
Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of…
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…
Integral transformations of the QCD invariant (running) coupling and of some related objects are discussed. Special attention is paid to the Fourier transformation, that is to transition from the space-time to the energy--momentum…
It will be shown how to map a simple one-dimensional tight binding model with a cosine potential in one dimension exactly to a two dimensional tight binding model with periodic boundary conditions with the presence of a single flux quantum…
We introduce a numerical method for the solution of the time-dependent Schrodinger equation with a smooth potential, based on its reformulation as a Volterra integral equation. We present versions of the method both for periodic boundary…
This work illustrates the possibility to apply the Fast Fourier Transformation to obtain the integrals of the Boundary Element Method (BEM) on arbitrary shapes. The procedure is inspired by the technique used with great success within the…
Numerical simulations of merging compact objects and their remnants form the theoretical foundation for gravitational wave and multi-messenger astronomy. While Cartesian-coordinate-based adaptive mesh refinement is commonly used for…
We propose a method for the realization of the two-qubit quantum Fourier transform (QFT) using a Hamiltonian which possesses the circulant symmetry. Importantly, the eigenvectors of the circulant matrices are the Fourier modes and do not…
Modeling the large-scale structure of the universe on nonlinear scales has the potential to substantially increase the science return of upcoming surveys by increasing the number of modes available for model comparisons. One way to achieve…
Fourier sine transforms containing irrational integrands are presented. Explicit closed form expressions are shown to be related to Lommel functions and in special cases to the Fresnel integrals. Such integrals arise in the semi-classical…
We define the notion of the Fourier transform for the rook monoid (also called the symmetric inverse semigroup) and provide two efficient divide-and-conquer algorithms (fast Fourier transforms, or FFTs) for computing it. This paper marks…
An efficient approach to handle localized states by using spectral methods (SM) in one and three dimensions is presented. The method consists of transformation of the infinite domain to the bounded domain in $(0, \pi)$ and using the Fourier…
The Fractional Fourier Transform (FrFT) has widespread applications in areas like signal analysis, Fourier optics, diffraction theory, etc. The Holomorphic Fractional Fourier Transform (HFrFT) proposed in the present paper may be used in…
The Fourier transform of a bounded measurable function, $f$, on the real line is shown to be the second distributional derivative of a H\"older continuous function. The Fourier transform is written as the difference of $\int_{-1}^1…