Related papers: The VW transformation -- A Simple Alternative to t…
The tomographic invertable map of the Wigner function onto the positive probability distribution function is studied. Alternatives to the Schr\"odinger evolution equation and to the energy level equation written for the positive probability…
Next-generation gravitational wave (GW) experiments will explore higher frequency ranges, where GW wavelengths approach the size of the detector itself. In this regime, GWs may be detected not just through the well-known mechanical…
Full waveform inversion (FWI) is a large-scale nonlinear ill-posed problem for which computationally expensive Newton-type methods can become trapped in undesirable local minima, particularly when the initial model lacks a low-wavenumber…
Electromagnetic methods recently proposed for detecting gravitational waves modify the Michelson phase shift analysis (historically employed for special relativity). We suggest that a frequency modulation analysis is more suited to general…
The GW approximation is widely used for reliable and accurate modeling of single-particle excitations. It also serves as a starting point for many theoretical methods, such as its use in the Bethe-Salpeter equation (BSE) and dynamical…
The aim of this article is a comprehensive description of normal modes of molecular vibrations. The starting point is chosen to be a general molecular system with separated center of mass and an arbitrary embedding of body-fixed axes. This…
The results obtained by analyzing signals with the Square Wave Method (SWM) introduced previously can be presented in the frequency domain clearly and precisely by using the Square Wave Transform (SWT) described here. As an example, the SWT…
The authors propose a fast numerical renormalization group method --- the product wave function renormalization group (PWFRG) method --- for 1D quantum lattice models and 2D classical ones. A variational wave function, which is expressed by…
A random matrix approach is used to analyze the vibrational properties of amorphous solids. We investigated a dynamical matrix M=AA^T with non-negative eigenvalues. The matrix A is an arbitrary real NxN sparse random matrix with n…
We present a fully quantum field-theoretic framework for gravitational wave (GW) detection in which the interaction is described as photon-graviton scattering. In this picture, the GW acts as a coherent background that induces inelastic…
We introduce the Wasserstein Transform (WT), a general unsupervised framework for updating distance structures on given data sets with the purpose of enhancing features and denoising. Our framework represents each data point by a…
We present a method for detection and reconstruction of the gravitational-wave (GW) transients with the networks of advanced detectors. Originally designed to search for transients with the initial GW detectors, it uses significantly…
We introduce a novel framework for Generalized Tensor Transforms (GTTs), constructed through an $n$-fold tensor product of an arbitrary $b \times b$ unitary matrix $W$. This construction generalizes many established transforms, by providing…
The vibrating string is a source of gravitational waves which requires novel computational techniques, based on the explicit construction of a conserved and renormalized (in a classical sense) energy-momentum tensor. The renormalization is…
In this work, we propose a new source for gravitational wave (GW) radiation associated with the quantum chromodynamics (QCD) phase transition in the inner cores of neutron stars. The mechanism is based on the bubble dynamics during the…
The Wigner Transform (WT) has been extensively used in the formulation of phase-space models for a variety of wave propagation problems including high-frequency limits, nonlinear and random waves. It is well known that the WT features…
We analyze the gravitational wave signals with a model-independent time-frequency analysis, which is improved from the Hilbert-Huang transform (HHT) and optimized for characterizing the frequency variability on the time-frequency map.…
First-order phase transitions in the early Universe are a well-motivated source of gravitational waves (GWs). In this Letter, we identify a previously overlooked GW production mechanism: gravitational transition radiation, arising from…
The choice of vibrational coordinates is crucial for the accuracy, efficiency, and interpretability of molecular vibrational dynamics and spectra calculations. We explore the recently proposed normalizing-flow vibrational coordinates, which…
A new method of frequency analysis is presented in detail. This new method - Variable Sine Algorithmic Analysis, (VSAA) - is based on a single variable sine function and it is powered by the simplex algorithm. It is used in cases of…