相关论文: Physical wavelets and their sources: Real physics …
Diffraction tomography aims to recover an object's scattering potential from measured wave fields. In the classical setting, the object is illuminated by plane waves from many directions, and the Fourier diffraction theorem provides a…
Motivated by the product of periodic distributions, we give a new description of the wave front and the Sobolev-type wave front of a distribution $f\in\mathscr{D}'(\mathbb{R}^d)$ in terms of Fourier series coefficients.
We study a class of localized solutions of the wave equation, called eigenwavelets, obtained by extending its fundamental solutions to complex spacetime in the sense of hyperfunctions. The imaginary spacetime variables y, which form a…
Detecting gravitational waves above 100 kHz would constitute a major discovery, as any observable signal would have to arise from new physics within the late universe. Although many technologies have been identified to explore this…
Temperature and polarization variations across the microwave sky include the fingerprints of quantum fluctuations in the early universe. They may soon reveal physics at unprecedented energy scales.
Scattering of electromagnetic waves lies at the heart of most experimental techniques over nearly the entire electromagnetic spectrum, ranging from radio waves to optics and X-rays. Hence, deep insight into the basics of scattering theory…
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…
It is demonstrated how quantum mechanics is generated by stochastic momentum kicks from the force carriers, transmitting the fundamental interactions between the point particles. The picture is consistent with quantum field theory and…
Using waves to explore our environment is a widely used paradigm, ranging from seismology to radar technology, and from bio-medical imaging to precision measurements. In all of these fields, the central aim is to gather as much information…
A wave propagating through a scattering medium typically yields a complex temporal field distribution. Over the years, a number of procedures have emerged to shape the temporal profile of the field in order to temporally focus its energy on…
I give an overview of the motivations for gravitational-wave research, concentrating on the aspects related to ``fundamental'' physics.
We study orthogonality relations for Fourier frequencies and complex exponentials in Hilbert spaces $L^2(\mu)$ with measures $\mu$ arising from iterated function systems (IFS). This includes equilibrium measures in complex dynamics.…
Motivated by a revision of the classical equations of electromagnetism that allow for the inclusion of solitary waves in the solution space, the material collected in these notes examines the consequences of adopting the modified model in…
In the present paper, details are given on the implementation of a wavelet-based analysis tailored to the processing of acoustical signals. The family of the suitable wavelets (`Reimann wavelets') are obtained in the time domain from a…
Exploring the interaction of light with time-varying media is an intellectual challenge that, in addition to fundamental aspects, provides a pathway to multiple promising applications. Time modulation constitutes here a fundamental handle…
The observation of electromagnetic radiation emitted or absorbed by matter was instrumental in revealing the quantum properties of atoms and molecules in the early XX century, and constituted a turning-point in the development of the…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
Photons are the elementary quantum excitations of the electromagnetic field. Quantization is usually constructed on the basis of an expansion in eigenmodes, in the form of plane waves. Since they form a basis, other electromagnetic…
We present analytical and numerical studies of the Fourier transform (FT) of the gravitational wave (GW) signal from a pulsar, taking into account the rotation and orbital motion of the Earth. We also briefly discuss the Zak-Gelfand…
Given near or far field wave measurements generated by some unknown time- and space-dependent acoustic source, we seek to rapidly determine a domain in space-time, as small as possible, that contains the support of a source radiating these…