Related papers: Simple methods for converting equations between th…
We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and…
Modern physics is largely devoted to study conservation laws, such as charge, energy, linear momentum or angular momentum, because they give us information about the symmetries of our universe. Here, we propose to add the relationship…
We investigate the possibility of using a transcorrelated Hamiltonian to describe electron correlation. Amethod to obtain transcorrelatedwavefunctionswas developed based on the mathematical framework of the bi-variational principle. This…
The Gauss-Seidel method has been used for more than 100 years as the standard method for the solution of linear systems of equations under certain restrictions. This method, as well as Cramer and Jacobi, is widely used in education and…
Geodesic metric spaces support a variety of averaging constructions for given finite sets. Computing such averages has generated extensive interest in diverse disciplines. Here we consider the inverse problem of recognizing computationally…
A common problem in a high energy physics experiment is extracting a signal from a much larger background. Posed as a classification task, there is said to be an imbalance in the number of samples belonging to the signal class versus the…
We discuss how the likely 2018 redefinition of the SI system of units might affect the ability of students to understand the link between the units and the new system. The likely redefinition will no longer define a set of base units, but…
We give a detailed description of electrodynamics as an emergent theory from condensed-matter-like structures, not only {\it per se} but also as a warm-up for the study of the much more complex case of gravity. We will concentrate on two…
The biquaternion approach is developed for building of the equations of the inter-action of different charges and currents and generated Electro-GravyMagnetic fields. The field analogues of three Newton's laws are offered free and…
We investigate two key representative semiclassical approaches for propagating resonant energy transfer between a pair of electronic two-level systems (donor and acceptor) with coupled Maxwell-Liouville equations. On the one hand, when the…
The Einstein-Langevin equation is a perturbative correction to the semiclassical Einstein equation which takes into account the lowest order quantum fluctuations of the matter stress-energy tensor. It predicts classical stochastic…
It is well-known that the equations for a simple fluid can be cast into what is called their Lagrange formulation. We introduce a notion of a generalized Lagrange formulation, which is applicable to a wide variety of systems of partial…
Electromagnetism in an inhomogeneous dielectric medium at rest is described using the methods of differential geometry. In contrast to a general relativistic approach the electromagnetic fields are discussed in three-dimensional space only.…
The formula for the electric field of a point charge moving with constant velocity is derived using the symmetry properties of Maxwell's equations - its Lorentz invariance. In contrast to conventional treatments, the derivation presented…
We consider a specific form of explicitly correlated Gaussians -- with tensor pre-factors -- which appear naturally when dealing with certain few-body systems in nuclear and particle physics. We derive analytic matrix elements with these…
Maxwell's four differential equations describing electromagnetism are amongst the most famous equations in science. Feynman said that they provide four of the seven fundamental laws of classical physics. In this paper, we derive Maxwell's…
We re-derive hydrodynamical equations in General Relativity (GR) in the comoving reference frame for spherical symmetry and obtain from them the well-known but not explicitly derived Lagrangean equations in Special Relativity (SR), that is,…
A new generalization of the Hawking-Hayward quasilocal energy to scalar-tensor gravity is proposed without assuming symmetries, asymptotic flatness, or special spacetime metrics. The procedure followed is simple but powerful and consists of…
It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is…
In this paper we use Gaussian processes (kernel methods) to learn mappings between trajectories of distinct differential equations. Our goal is to simplify both the representation and the solution of these equations. We begin by examining…