Stochastic Green's function approach to disordered systems

Based on distributions of local Green's functions we present a stochastic approach to disordered systems. Specifically we address Anderson localisation and cluster effects in binary alloys. Taking Anderson localisation of Holstein polarons as an example we discuss how this stochastic approach can be used for the investigation of interacting disordered systems.Comment: 12 pages, 7 figures, conference proceedings: Progress in Nonequilibrium Green's Functions III, 22-26 August 2005, University of Kiel, German

High-order commutator-free exponential time-propagation of driven quantum systems

We discuss the numerical solution of the Schr\"odinger equation with a time-dependent Hamilton operator using commutator-free time-propagators. These propagators are constructed as products of exponentials of simple weighted sums of the Hamilton operator. Owing to their exponential form they strictly preserve the unitarity of time-propagation. The absence of commutators or other computationally involved operations allows for straightforward implementation and application also to large scale and sparse matrix problems. We explain the derivation of commutator-free exponential time-propagators in the context of the Magnus expansion, and provide optimized propagators up to order eight. An extensive theoretical error analysis is presented together with practical efficiency tests for different problems. Issues of practical implementation, in particular the use of the Krylov technique for the calculation of exponentials, are discussed. We demonstrate for two advanced examples, the hydrogen atom in an electric field and pumped systems of multiple interacting two-level systems or spins that this approach enables fast and accurate computations.Comment: 32 pages, 12 figures. Final version as published in J. Comp. Phy

Local distribution approach to disordered binary alloys

We study the electronic structure of the binary alloy and (quantum) percolation model. Our study is based on a self-consistent scheme for the distribution of local Green functions. We obtain detailed results for the density of states, from which the phase diagram of the binary alloy model is constructed, and discuss the existence of a quantum percolation threshold.Comment: 9 pages, 8 figures. A few minor changes, 1 figure adde

A student's perspective on literacy teaching and learning: starting a conversation through six suggestions

The authors featured in this department column share instructional practices that support transformative literacy teaching and disrupt “struggling reader” and “struggling writer” labels.Accepted manuscrip

Non-equilibrium current and electron pumping in nanostructures

We discuss a numerical method to study electron transport in mesoscopic devices out of equilibrium. The method is based on the solution of operator equations of motion, using efficient Chebyshev time propagation techniques. Its peculiar feature is the propagation of operators backwards in time. In this way the resource consumption scales linearly with the number of states used to represent the system. This allows us to calculate the current for non-interacting electrons in large one-, two- and three-dimensional lead-device configurations with time-dependent voltages or potentials. We discuss the technical aspects of the method and present results for an electron pump device and a disordered system, where we find transient behaviour that exists for a very long time and may be accessible to experiments.Comment: 4 pages, 3 figures. Contribution to the International Conference on Magnetism (ICM) 2009 in Karlsruh

Exciton mass and exciton spectrum in the cuprous oxide

Excitons with a radius of a few lattice constants can be affected by strong central-cell corrections, leading to significant deviations of the optical spectrum from the hydrogen-like Rydberg series, and also to an enhancement of the exciton mass. We present an approach to this situation based on a lattice model that incorporates the effects of a non-parabolic band structure, short distance corrections to the Coulomb interaction between electrons and holes, spin-orbit and exchange coupling. The lattice model allows for observation of the crossover from large radius Wannier to small radius Frenkel excitons without invoking a continuum approximation. We apply the lattice model approach especially to the yellow exciton series in the cuprous oxide, for which the optical spectrum and exciton mass enhancement are obtained through adaptation of only a few model parameters to material-specific values. Our results predict a strongly anisotropic ortho-exciton mass.Comment: 10 pages, 7 figures. Final version as publishe