Spin Effects in the Local Density of States of GaAs

We present spin-resolved measurements of the local density of states in Si doped GaAs. Both spin components exhibit strong mesoscopic fluctuations. In the magnetic quantum limit, the main features of the spin-up and spin-down components of the local density of states are found to be identical apart from Zeeman splitting. Based on this observation, we introduce a mesoscopic method to measure the $g$-factor in a material where macroscopic methods are severely restricted by disorder. Differences between the spin-up and spin-down components are discussed in terms of spin relaxation due to spin-orbit coupling.Comment: 4 pages and 5 figure

How to measure spatial distances?

The use of time--like geodesics to measure temporal distances is better justified than the use of space--like geodesics for a measurement of spatial distances. We give examples where a ''spatial distance'' cannot be appropriately determined by the length of a space--like geodesic.Comment: 4 pages, latex, no figure

Computer simulations of colloidal transport on a patterned magnetic substrate

We study the transport of paramagnetic colloidal particles on a patterned magnetic substrate with kinetic Monte Carlo and Brownian dynamics computer simulations. The planar substrate is decorated with point dipoles in either parallel or zigzag stripe arrangements and exposed to an additional external magnetic field that oscillates in time. For the case of parallel stripes we find that the magnitude and direction of the particle current is controlled by the tilt angle of the external magnetic field. The effect is reliably obtained in a wide range of ratios between temperature and magnetic permeability. Particle transport is achieved only when the period of oscillation of the external field is greater than a critical value. For the case of zigzag stripes a current is obtained using an oscillating external field normal to the substrate. In this case, transport is only possible in the vertex of the zigzag, giving rise to a narrow stream of particles. The magnitude and direction of the particle current are found to be controlled by a combination of the zigzag angle and the distance of the colloids from the substrate. Metropolis Monte Carlo and Brownian dynamics simulations predict results that are in good agreement with each other. Using kinetic Monte Carlo we find that at high density the particle transport is hindered by jamming.Comment: 8 pages, 9 figure