Scalar potential

About: Scalar potential is a research topic. Over the lifetime, 3642 publications have been published within this topic receiving 78868 citations. The topic is also known as: potential.

Mixed formulations for finite element analysis of magnetostatic and electrostatic problems

Abstract: This paper presents some mixed formulations for finite element analysis of magnetostatic and electrostatic problems We employ the magnetic and electric fields as fundamental unknowns instead of the vector potential and the scalar potential, and the proposed approach appears to be desirable for three-dimensional finite element analyses We also give brief comments on the use of the vector potential for the magnetostatic problem

Weyl gauge symmetry and its spontaneous breaking in the standard model and inflation

Abstract: We discuss the local (gauged) Weyl symmetry and its spontaneous breaking and apply it to model building beyond the Standard Model (SM) and inflation. In models with non-minimal couplings of the scalar fields to the Ricci scalar, that are conformal invariant, the spontaneous generation by a scalar field(s) vev of a positive Newton constant demands a negative kinetic term for the scalar field, or vice-versa. This is naturally avoided in models with additional Weyl gauge symmetry. The Weyl gauge field $\omega_\mu$ couples to the scalar sector but not to the fermionic sector of a SM-like Lagrangian. The field $\omega_\mu$ undergoes a Stueckelberg mechanism and becomes massive after "eating" the (radial mode) would-be-Goldstone field (dilaton $\rho$) in the scalar sector. Before the decoupling of $\omega_\mu$, the dilaton can act as UV regulator and maintain the Weyl symmetry at the {\it quantum} level, with relevance for solving the hierarchy problem. After the decoupling of $\omega_\mu$, the scalar potential depends only on the remaining (angular variables) scalar fields, that can be the Higgs field, inflaton, etc. We show that successful inflation is then possible with one of these scalar fields identified as the inflaton. While our approach is derived in the Riemannian geometry with $\omega_\mu$ introduced to avoid ghosts, the natural framework is that of Weyl geometry which for the same matter spectrum is shown to generate the same Lagrangian, up to a total derivative.

First-principles approach to Non-Collinear Magnetism: towards Spin-dynamics

Abstract: A description of non-collinear magnetism in the framework of spin-density functional theory is presented for the exact exchange energy functional which depends explicitly on two-component spinor orbitals. The equations for the effective Kohn-Sham scalar potential and magnetic field are derived within the optimized effective potential (OEP) framework. With the example of a magnetically frustrated Cr monolayer it is shown that the resulting magnetization density exhibits much more non-collinear structure than standard calculations. Furthermore, a time-dependent generalization of the non-collinear OEP method is well suited for an ab-initio description of spin dynamics. We also show that the magnetic moments of solids Fe, Co and Ni are well reproduced.

On Eigenfunction Decay for Two Dimensional¶Magnetic Schrödinger Operators

Abstract: For two dimensional Schrodinger operators with a nonzero constant magnetic field perturbed by a magnetic field and a scalar potential, both vanishing arbitrarily slow at infinity, it is proved that eigenfunctions corresponding to the discrete spectrum decay faster than any exponential. Under more restrictive conditions on the perturbations, even quicker decay is obtained.