Related papers: Modeling Magnetic Fields with Helical Solutions to…
Results of a general study on the dynamics of cosmological scalar fields with arbitrary potentials are presented. Exact and approximate attractor solutions are found, with applications to quintessence, moduli stabilization and inflation.
The elliptically oscillating solutions in the Abelian Higgs-model are presented and the classical massive-dispersion-relation through the non-linear dynamics is discussed. The generated massive-dispersion-relation including a field value of…
A key question in understanding the observed magnetic field topologies of cool stars is the link between the small- and the large-scale magnetic field and the influence of the stellar parameters on the magnetic field topology. We examine…
The purpose of this article is to initiate a study of a class of Lorentz invariant, yet tractable, Lagrangian Field Theories which may be viewed as an extension of the Klein-Gordon Lagrangian to many scalar fields in a novel manner. These…
The connection between helically isotropic MHD turbulence and mean-field dynamo theory is reviewed. The nonlinearity in the mean-field theory is not yet well established, but detailed comparison with simulations begin to help select viable…
A new representation for solutions of Maxwell's equations is derived. Instead of being expanded in plane waves, the solutions are given as linear superpositions of spherical wavelets dynamically adapted to the Maxwell field and…
Both physical arguments and simulations of the global heliosphere indicate that the tailward heliopause is flattened considerably in the direction perpendicular to both the incoming flow and the large-scale interstellar magnetic field.…
A strong magnetic field can make it advantageous to work in a coordinate system aligned with dipolar field lines. This monograph collect the formulas for some of the most frequently used expressions and operations in dipole coordinates.
For the diagonalization of the Hamilton matrix in the Heisenberg model relevant dimensions are determined depending on the applicable symmetries. Results are presented, both, by general formulae in closed form and by the respective numbers…
The fact that the capacitance coefficients for a set of conductors are geometrical factors is derived in most electricity and magnetism textbooks. We present an alternative derivation based on Laplace's equation that is accessible for an…
A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…
To a first semiclassical approximation one can reduce the multi-parton light-front problem in QCD to an effective one-dimensional quantum field theory, which encodes the fundamental conformal symmetry of the classical QCD Lagrangian. This…
A linearized version of Heisenberg's fundamental equation is solved, and the solutions satisfy the axioms of a relativistic quantum field theory with a fundamental length.
The present paper is based on our graduate lectures in condensed-matter physics. We found that the mean-field solution of the Hubbard model is an excellent tool to stimulate students' reflections towards the treatment of realistic magnetic…
This review is a compilation of relevant concepts in designing Halbach multipoles for magnetic resonance applications. The main focus is on providing practical guidelines to plan, design and build such magnets. Therefore, analytical…
We obtain highly accurate solutions to the Thomas-Fermi equations for atoms and atoms in very strong magnetic fields. We apply the Pad\'e-Hankel method, numerical integration, power series with Pad\'e and Hermite-Pad\'e approximants and…
We briefly review the recent developments in magnetohydrodynamics, which in particular deal with the evolution of magnetic fields in turbulent plasmas. We especially emphasize (i) the necessity of renormalizing equations of motion in…
A connection of a variety of tight-binding models of noninteracting electrons on a rectangular lattice in a magnetic field with theta functions is established. A new spectrum generating symmetry is discovered which essentialy reduces the…
We formulate deformation of relativistic stars due to the magnetic stress, considering the magnetic fields to be perturbations from spherical stars. The ellipticity for the dipole magnetic field is calculated for some stellar models. We…
Solid state theory, density functional theory and its generalizations for correlated systems together with numerical simulations on supercomputers allow nowadays to model magnetic systems realistically and in detail and can be even used to…