State determination: an iterative algorithm

An iterative algorithm for state determination is presented that uses as physical input the probability distributions for the eigenvalues of two or more observables in an unknown state $\Phi$. Starting form an arbitrary state $\Psi_{0}$, a succession of states $\Psi_{n}$ is obtained that converges to $\Phi$ or to a Pauli partner. This algorithm for state reconstruction is efficient and robust as is seen in the numerical tests presented and is a useful tool not only for state determination but also for the study of Pauli partners. Its main ingredient is the Physical Imposition Operator that changes any state to have the same physical properties, with respect to an observable, of another state.Comment: 11 pages 3 figure

A semiquantitative approach to the impurity-band-related transport properties of GaMnAs nanolayers

We investigate the spin-polarized transport of GaMnAs nanolayers in which a ferromagnetic order exists below a certain transition temperature. Our calculation for the self-averaged resistivity takes into account the existence of an impurity band determining the extended ("metallic" transport) or localized (hopping by thermal excitation) nature of the states at and near the Fermi level. Magnetic order and resistivity are inter-related due to the influence of the spin polarization of the impurity band and the effect of the Zeeman splitting on the mobility edge. We obtain, for a given range of Mn concentration and carrier density, a "metallic" behavior in which the transport by extended carriers dominates at low temperature, and is dominated by the thermally excited localized carriers near and above the transition temperature. This gives rise to a conspicuous hump of the resistivity which has been experimentally observed and brings light onto the relationship between transport and magnetic properties of this material

Edgeworth expansions for slow-fast systems with finite time scale separation

We derive Edgeworth expansions that describe corrections to the Gaussian limiting behaviour of slow-fast systems. The Edgeworth expansion is achieved using a semi-group formalism for the transfer operator, where a Duhamel-Dyson series is used to asymptotically determine the corrections at any desired order of the time scale parameter ε. The corrections involve integrals over higher-order auto-correlation functions. We develop a diagrammatic representation of the series to control the combinatorial wealth of the asymptotic expansion in ε and provide explicit expressions for the first two orders. At a formal level, the expressions derived are valid in the case when the fast dynamics is stochastic as well as when the fast dynamics is entirely deterministic. We corroborate our analytical results with numerical simulations and show that our method provides an improvement on the classical homogenization limit which is restricted to the limit of infinite time scale separation