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The purpose of this effort is to investigate if the use of quaternion mathematics can be used to better model and simulate the electromagnetic fields that occur from moving electromagnetic charges. One observed deficiency with the commonly…
The Coulomb phase, with its dipolar correlations and pinch-point-scattering patterns, is central to discussions of geometrically frustrated systems, from water ice to binary and mixed-valence alloys, as well as numerous examples of…
A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space…
The three dimensional harmonic oscillator model including a cranking term is used for an energy variational calculation. Energy minima are found under variation of the three oscillator frequencies determining the shape of the system for…
Pair production due to the Schwinger mechanism is modeled in a self-consistent approach taking into account the backreaction of the created particles on the field. The model uses the Boltzmann kinetic equation for the electrons and…
Exact analytical expressions for the matrix elements of the Uehling potential in a basis of explicitly correlated exponential wave functions are presented. The obtained formulas are then used to compute with an improved accuracy the vacuum…
An alternative description of quantum scattering processes rests on inhomogeneous terms amended to the Schroedinger equation. We detail the structure of sources that give rise to multipole scattering waves of definite angular momentum, and…
The orbit-averaged fluxes of energy and angular momentum generated by a compact binary system of nonspinning particles are obtained in a popular class of massless scalar-tensor theories with first-and-a-half post-Newtonian (1.5PN) accuracy,…
A fundamentally new understanding of the classical electromagetic interaction of a point charge and a magnetic moment through order second order in 1/c is suggested. This relativistic analysis connects together hidden momentum in magnets,…
Courses on undergraduate quantum mechanics usually focus on solutions of the Schr\"odinger equation for several simple one-dimensional examples. When the notion of a Hilbert space is introduced only academic examples are used, such as the…
We prove Lieb-Thirring inequalities for Schr\"odinger operators with a homogeneous magnetic field in two and three space dimensions. The inequalities bound sums of eigenvalues by a semi-classical approximation which depends on the strength…
Spin and orbital angular momenta are fundamental physical characteristics described by polarization and spatial degrees of freedom, respectively. Polarization is a feature of vector fields while spatial phase gradient determines the orbital…
A simple approach for understanding the quantum nature of angular momentum and its reduction to the classical limit is presented based on Schwinger's coupled-boson representation. This approach leads to a straightforward explanation of why…
In this work we study symplectic unitary representations for the Galilei group. As a consequence the Schr\"odinger equation is derived in phase space. The formalism is based on the non-commutative structure of the star-product, and using…
Integral transforms arising from the separable solutions to the Helmholtz differential equation are presented. Pairs of these integral transforms are related via Plancherel theorem and, ultimately, any of these integral transforms may be…
We present a numerical method for the solution of linear magnetostatic problems in domains with a symmetry direction, including axial and translational symmetry. The approach uses a Fourier series decomposition of the vector potential…
We formulate a generalized continuum theory of phonon angular momentum in crystals by introducing a local SO(3) material frame in addition to the macroscopic displacement field. The local frame represents rotational optical degrees of…
For paraxial and non-paraxial light, numerous measures of electromagnetic attribute are expressible in terms of photon annihilation and creation. Accordingly, energy, angular momentum and chirality measures acquire a consistent…
High harmonic generation (HHG) is a manifestation of the strongly nonlinear response of matter to intense laser fields and has, as the basis for coherent XUV sources a variety of applications. Recently, HHG from atoms in a phase and…
A new theory for the dynamics of the magnetic particles and their magnetic moments in ferrofluids is developed. Based on a generalized Lagrangian formulation for the equations of motion of the colloidal particle, we introduce its…