A molecular dynamics simulation of ion flow past dust grains is used to investigate the interaction between a pair of charged dust particles and streaming ions. The charging and dynamics of the grains are coupled and derived from the ion–dust interactions, allowing for detailed analysis of the ion wakefield structure and wakefield-mediated interaction as the dust particles change position. When a downstream grain oscillates vertically within the wake, it decharges by up to 30% as it approaches the upstream grain and then recharges as it recedes. There is an apparent hysteresis in charging depending on whether the grain is approaching or receding from a region of higher ion density. Maps of the ion-mediated dust–dust interaction force show that the radial extent of the wake region, which provides an attractive restoring force on the downstream particle, increases as the ion flow velocity decreases, though the restoring effect becomes weaker. As also shown in recent numerical results, there is no net attractive vertical force between the two grains. Instead, the reduced ion drag on the downstream particle allows it to “draft” in the wakefield of the upstream particle.

Abstract. In this paper we introduce the spectral approach to delocalization in infinite disordered systems and provide a physical interpretation in context of the classical model of Edwards and Thouless. We argue that spectral analysis is an important contribution to localization problems since it avoids issues related to the use of boundary conditions. Applying the method to 2D and 3D numerical simulations with various amount of disorder shows that delocalization occurs for ≤ 0.6 in 2D and for ≤ 5 for 3D.

This work extends the applications of Anderson-type Hamiltonians to include transport characterized by anomalous diffusion. Herein, we investigate the transport properties of a onedimensional disordered system that employs the discrete fractional Laplacian, (−∆) s , s ∈ (0, 2), in combination with results from spectral and measure theory. It is a classical mathematical result that the standard Anderson model exhibits localization of energy states for all nonzero disorder in one-dimensional systems. Numerical simulations utilizing our proposed model demonstrate that this localization effect is enhanced for sub-diffusive realizations of the operator, s ∈ (1, 2), and that the super-diffusive realizations of the operator, s ∈ (0, 1), can exhibit energy states with less localized features. These results suggest that the proposed method can be used to examine anomalous diffusion in physical systems where strong interactions, structural defects, and correlated effects are present.

The self-diffusion phenomenon in a two-dimensional dusty plasma at extremely strong (effective) magnetic fields is studied experimentally and by means of molecular dynamics simulations. In the experiment the high magnetic field is introduced by rotating the particle cloud and observing the particle trajectories in a co-rotating frame, which allows reaching effective magnetic fields up to 3000 Tesla. The experimental results confirm the predictions of the simulations: (i) super-diffusive behavior is found at intermediate timescales and (ii) the dependence of the self-diffusion coefficient on the magnetic field is well reproduced.

Abstract. The spectral approach to infinite disordered crystals is applied to an Anderson-type Hamiltonian to demonstrate the existence of extended states for nonzero disorder in 2D lattices of different geometries. The numerical simulations shown prove that extended states exist for disordered honeycomb, triangular, and square crystals. This observation stands in contrast to the predictions of scaling theory, and aligns with experiments in photonic lattices and electron systems. The method used is the only theoretical approach aimed at showing delocalization. A comparison of the results for the three geometries indicates that the triangular and honeycomb lattices experience transition in the transport behavior for same amount of disorder, which is to be expected from planar duality. This provides justification for the use of artificially-prepared triangular lattices as analogues for honeycomb materials, such as graphene. The analysis also shows that the transition in the honeycomb case happens more abruptly as compared to the other two geometries, which can be attributed to the number of nearest neighbors. We outline the advantages of the spectral approach as a viable alternative to scaling theory and discuss its applicability to transport problems in both quantum and classical 2D systems.