Frequency-dependent magnetizability

Abstract

This work discusses the theory of the magnetizability. The magnetizability is a molecular property defined as the second-order perturbation of the energy in the presence of an external magnetic field. When the magnetic field is static, perturbation and multipole theories lead to an origin-independent expression for the magnetizability, whereas for a frequency-dependent magnetic field its expression turns out to be origin dependent. Since the magnetizability in the static case is an observable quantity, the expression obtained in the dynamic case is clearly unphysical. My work discusses several approaches in order to solve this issue. The magnetizability has been analyzed in the microscopic case, within both the non-relativistic and the relativistic framework. The expression for the magnetizability proposed by Raab and de Lange has been considered, pointing out the weak points of their non-relativistic theory, and trying to recover an alternative expression in the relativistic framework. The macroscopic case has also been discussed in detail, and an origin-independent expression for the inverse permeability has been derived within a fully relativistic approach. The problem of finding an origin-independent expression for the magnetizability in the microscopic case remains unresolved, however the results obtained in the macroscopic case and the analysis done in this thesis are good starting points for further studies, and suggests that future work should start from the relativistic theory of the property.