Nonequilibrium orbital magnetization of strongly localized electrons

The magnetic response of strongly localized electrons to a time-dependent vector potential is considered. The orbital magnetic moment of the system, away from steady-state conditions, is obtained. The expression involves the tunneling and phonon-assisted hopping currents between localized states. The frequency and temperature dependence of the orbital magnetization is analyzed as function of the admittances connecting localized levels. It is shown that quantum interference of the localized wave functions contributes to the moment a term which follows adiabatically the time-dependent perturbation.Comment: RevTeX 3.

Trajectory Propagation Using Information on Periodicity

Families of methods to integrate first and second order ordinary differential equations whose solution known to be periodic will be discussed. The methods can be tuned to a possibly a-priori knowledge of the user on the location of the frequencies, that are dominant in the exact solution. On the basis of such extra information the truncation error can considerably be reduced in magnitude. The paper compares these methods to well known in integrators and discusses a simple mechanism to estimate the frequency during the integration process