Related papers: The Gaussian Wave Packet Transform via Quadrature …
The ensemble Gaussian mixture filter combines the simplicity and power of Gaussian mixture models with the provable convergence and power of particle filters. The quality of the ensemble Gaussian mixture filter heavily depends on the choice…
Although real, normalized Gaussian wave packets minimize the product of position and momentum uncertainties, generic complex normalized Gaussian wave packets do not. We prove they minimize an alternative product of uncertainties that…
We construct a frame of complex Gaussians for the space of $L^2(\mathbb{R}^n)$ functions. When propagated along bicharacteristics for the wave equation, the frame can be used to build a parametrix with suitable error terms. When the…
The speedup of heavy numerical tasks by quantum computing is now actively investigated in various fields including data analysis in physics and astronomy. In this paper, we propose a new quantum algorithm for matched filtering in…
The direct detection of continuous gravitational waves from pulsars is a much anticipated discovery in the emerging field of multi-messenger gravitational wave (GW) astronomy. Because putative pulsar signals are exceedingly weak large…
Damped mechanical systems with various forms of damping are quantized using the path integral formalism. In particular, we obtain the path integral kernel for the linearly damped harmonic oscillator and a particle in a uniform gravitational…
On the base of a 1D Shr\"{o}dinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a…
We consider multiple collisions of quantum wave packets in one dimension. The system under investigation consists of an impenetrable wall and of two hard-core particles with very different masses. The lighter particle bounces between the…
We form wave packets in the Schwartz space of a reductive p-adic symmetric space for certain famillies of tempered functions. We show how to construct such families from Eisenstein integrals.
A product quadrature rule, based on the filtered de la Vall\'ee Poussin polynomial approximation, is proposed for evaluating the finite Hilbert transform in [-1; 1]. Convergence results are stated in weighted uniform norm for functions…
Generalised Hagedorn wave packets appear as exact solutions of Schr\"odinger equations with quadratic, possibly complex, potential, and are given by a polynomial times a Gaussian. We show that the Wigner transform of generalised Hagedorn…
Nondispersive wave packets in a fictitious time variable are calculated analytically for the field-free hydrogen atom. As is well known by means of the Kustaanheimo-Stiefel transformation the Coulomb problem can be converted into that of a…
This paper constructs the first quantum algorithm for wavelet packet transforms with a "parabolic scaling" tree structure, sometimes called wave atom transforms. Classically, wave atoms are used to construct sparse representations of…
We propose a Gauss-Legendre quadrature based sampling on the rotation group for the representation of a band-limited signal such that the Fourier transform (FT) of a signal can be exactly computed from its samples. Our figure of merit is…
Fractional wave equation arises in different type of physical problems such as the vibrating strings, propagation of electro-magnetic waves, and for many other systems. The exact analytical solution of the fractional differential equation…
This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The ``wavelet transform'' maps each $f(x)$ to its coefficients with respect to…
The semiclassically scaled time-dependent multi-particle Schr\"odinger equation describes, inter alia, quantum dynamics of nuclei in a molecule. It poses the combined computational challenges of high oscillations and high dimensions. This…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…
The aim of this paper is to develop novel quantum algorithms for Gaussian process quadrature methods. Gaussian process quadratures are numerical integration methods where Gaussian processes are used as functional priors for the integrands…