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Adaptive mesh refinement efficiently facilitates the computation of gravitational waveforms in numerical relativity. However, determining precisely when, where, and to what extent to refine when solving the Einstein equations poses…
Standard practice attempts to remove coordinate influence in physics through the use of invariant equations. Trans-coordinate physics proceeds differently by not introducing space-time coordinates in the first place. Differentials taken…
The Wilson fermion determinant can be written in the form of a series expansion in fugacity $\xi=\exp(\mu/T)$, provided that the eigenmodes of the temporally reduced operator are obtained. Since the calculation of all eigenmodes rapidly…
We describe a new approach based on semiclassical molecular dynamics that allows to simulate infrared absorption or emission spectra of molecular systems with inclusion of anharmonic intensities. This is achieved from semiclassical power…
We propose a novel method for detecting gravitational waves (GW), where a light signal emitted from a distant star interacts with a local (also distant) GW source and travels towards the Earth, where it is detected. While traveling in the…
Classical communication schemes that exploit wave modulation are the basis of the information era. The transfer of information based on the quantum properties of photons revolutionized these modern communication techniques. Here we…
It is standard practice to study the lensing of gravitational waves (GW) using the geometric optics regime. However, in many astrophysical configurations this regime breaks down as the wavelength becomes comparable to the Schwarzschild…
An alternative method is introduced to solve a simple two-dimensional models describing vibrational excitation and dissociation processes during the electron-molecule collisions. The model works with one electronic and one nuclear degree of…
In this article, exact traveling wave solutions of a Wick-type stochastic nonlinear Schr\"{o}dinger equation and of a Wick-type stochastic fractional Regularized Long Wave-Burgers (RLW-Burgers) equation have been obtained by using an…
The Wheeler-DeWitt (WdW) equation does not describe any explicit time evolution of the wave function, and somehow related to this issue, there is no natural way of defining an invariant inner product that provides a viable probability…
In this paper, a new simple but yet efficient spectral expression of the frequency-limited H2-norm, denoted H2w-norm, is introduced. The proposed new formulation requires the computation of the system eigenvalues and eigenvectors only, and…
A family of Variational Quantum Eigensolver (VQE) methods is designed to maximize the resource of existing noisy intermediate-scale quantum (NISQ) devices. However, VQE approaches encounter various difficulties in simulating molecules of…
We consider the single eigenvalue fluctuations of random matrices of general Wigner-type, under a one-cut assumption on the density of states. For eigenvalues in the bulk, we prove that the asymptotic fluctuations of a single eigenvalue…
The VB-QMC method is presented in this chapter. It consists of using in quantum Monte Carlo (QMC) approaches with a wave function expressed as a usually short expansion of classical Valence-Bond (VB) structures supplemented by a Jastrow…
Gravitational waves (GWs) are fluctuations in the fabric of spacetime predicted by Einstein's theory of general relativity. Using a collection of millisecond pulsars as high-precision clocks, the nanohertz band of this radiation is likely…
In a modified gravity theory, the propagation equation of gravitational waves will be presented in a non-standard way. Therefore this tenor mode perturbation of time-space, as a complement to the scalar mode perturbation, provides a unique…
Large biomolecular systems, whose function may involve thousands of atoms, cannot easily be addressed with parameter-free density functional theory (DFT) calculations. Until recently a central problem was that such systems possess an…
The detection of gravitational waves (GWs) propagating through cosmic structures can provide invaluable information on the geometry and content of our Universe, as well as on the fundamental theory of gravity. In order to test possible…
I present the mathematical structure of classical phonon theory in a general form, which emphasizes the wave natures of phonons, and which can serve as a robust foundation for further development of the theory of strongly interacting…
In this paper we introduce the algorithm and the fixed point hardware to calculate the normalized singular value decomposition of a non-symmetric matrices using Givens fast (approximate) rotations. This algorithm only uses the basic…