The magnetic field generated by an electron bound in angular-momentum eigenstates

The magnetic field generated by an electron bound in a spherically symmetric potential is calculated for eigenstates of the orbital and total angular momentum. General expressions are presented for the current density in such states and the magnetic field is calculated through the vector potential, which is obtained from the current density by direct integration. The method is applied to the hydrogen atom, for which we reproduce and extend known results.Comment: This article is a long version of our article which will appear in Eur. J.phys.20. It contains 22 pages 3 figure

Domain-wall profile in the presence of anisotropic exchange interactions: Effective on-site anisotropy

Starting from a D-dimensional XXZ ferromagnetic Heisenberg model in an hypercubic lattice, it is demonstrated that the anisotropy in the exchange coupling constant leads to a D-dependent effective on-site anisotropy interaction often ignored for D>1. As a result the effective width of the wall depends on the dimensionality of the system. It is shown that the effective one-dimensional Hamiltonian is not the one-dimensional XXZ version as assumed in previous theoretical work. We derive a new expression for the wall profile that generalizes the standard Landau-Lifshitz form. Our results are found to be in very good agreement with earlier numerical work using the Monte Carlo method. Preceding theories concerning the domain wall contribution to magnetoresistance have considered the role of D only through the modification of the density of states in the electronic band structure. This Brief Report reveals that the wall profile itself contains an additional D dependence for the case of anisotropic exchange interactions.Comment: 4 pages; new title and abstract; 1 figure comparing our results with earlier numerical work; a more general model containing the usual on-site anisotropy; new remarks and references on the following two topics: (a) experimental evidence for the existence of spin exchange anisotropy, and (b) preceding theories concerning the domain wall contribution to magnetoresistance; to appear in Phys. Rev.

Analysis for water conflict transformation

This article proposes and fleshes out an analytical method designed to support efforts to transform inequitable and unsustainable transboundary water arrangements. Such ‘transformative analysis’ leverages socio-ecological thinking to critically evaluate the processes that have established and maintain an arrangement, including hydro-diplomacy itself. Transformative analysis facilitates the interpretation of strategies to deflect transformation, identification of destructive forms of cooperation, and strategic classification of opportunities for transformation. The assertions are premised on an understanding of the particularities of water conflict, and followed by a discussion of ways researchers may overcome the challenges inherent in the method