Gerald Schubert

Distribution of the local density of states as a criterion for Anderson localization: Numerically exact results for various lattices in two and three dimensions

Numerical approaches to Anderson localization face the problem of having to treat large localization lengths while being restricted to finite system sizes. We show that by finite-size scaling of the probability distribution of the local density of states LDOS this long-standing problem can be overcome. To this end we reexamine this method, propose numerical refinements, and apply it to study the dependence of the distribution of the LDOS on the dimensionality and coordination number of the lattice. Particular attention is given to the graphene lattice. We show that the system-size dependence of the LDOS distribution is indeed an unambiguous sign of Anderson localization, irrespective of the dimension and lattice structure. The numerically exact LDOS data obtained by us agree with a log-normal distribution over up to ten orders of magnitude and thereby fulfill a nontrivial symmetry relation previously derived for the nonlinear model.

Anderson disorder in graphene nanoribbons: A local distribution approach

Disorder effects strongly influence the transport properties of graphene-based nanodevices even to the point of Anderson localization. Focusing on the local density of states and its distribution function, we analyze the localization properties of actual size graphene nanoribbons. In particular, we determine the time evolution and localization length of the single-particle wave function in dependence on the ribbon extension and edge geometry as well as on the disorder type and strength.

Delocalisation transition in chains with correlated disorder

Abstract We show that in the one-dimensional (1D) Anderson model long-range correlations within the sequence of on-site potentials may lead to a region of extended states in the vicinity of the band centre, i.e., to a correlation-induced insulator–metal transition. Thus, although still disordered, the 1D system can behave as a conductor.

Effects of disorder and contacts on transport through graphene nanoribbons

We study the transport of charge carriers through finite graphene structures. The use of numerical exact kernel polynomial and Green function techniques allows us to treat actual sized samples beyond the Dirac-cone approximation. Particularly we investigate disordered nanoribbons, normal-conductor/graphene interfaces and normal-conductor/graphene/normal-conductor junctions with a focus on the behavior of the local density of states, single-particle spectral function, optical conductivity and conductance. We demonstrate that the contacts and bulk disorder will have a major impact on the electronic properties of graphene-based devices.

Numerical approaches to time evolution of complex quantum systems

Abstract We examine several numerical techniques for the calculation of the dynamics of quantum systems. In particular, we single out an iterative method which is based on expanding the time evolution operator into a finite series of Chebyshev polynomials. The Chebyshev approach benefits from two advantages over the standard time-integration Crank–Nicholson scheme: speedup and efficiency. Potential competitors are semiclassical methods such as the Wigner–Moyal or quantum tomographic approaches. We outline the basic concepts of these techniques and benchmark their performance against the Chebyshev approach by monitoring the time evolution of a Gaussian wave packet in restricted one-dimensional (1D) geometries. Thereby the focus is on tunnelling processes and the motion in anharmonic potentials. Finally we apply the prominent Chebyshev technique to two highly non-trivial problems of current interest: (i) the injection of a particle in a disordered 2D graphene nanoribbon and (ii) the spatiotemporal evolution of polaron states in finite quantum systems. Here, depending on the disorder/electron–phonon coupling strength and the device dimensions, we observe transmission or localisation of the matter wave.

Performance Limitations for Sparse Matrix-Vector Multiplications on Current Multi-Core Environments

The increasing importance of multi-core processors calls for a reevaluation of established numerical algorithms in view of their ability to profit from this new hardware concept. In order to optimize the existent algorithms, a detailed knowledge of the different performance-limiting factors is mandatory. In this contribution we investigate sparse matrix-vector multiplications, which are the dominant operation in many sparse eigenvalue solvers. Two conceptually different storage schemes and computational kernels have been conceived in the past to target cache-based and vector architectures, respectively: compressed row and jagged diagonal storage. Starting from a series of microbenchmarks to single out performance limitations, we apply the gained insight to optimize sparse MVM implementations, reviewing serial and OpenMP-parallel performance on state-of-the-art multi-core systems.

Comment on “Anderson transition in disordered graphene” by Amini M. et al.

We comment on a recent letter by Amini et al. (EPL 87, 37002 (2009)) concerning the existence of a mobility edge in disordered graphene.

Dynamical aspects of two-dimensional quantum percolation

The existence of a quantum-percolation threshold

Quantum Percolation in Disordered Structures

{p}_{q}l1

Optical absorption and activated transport in polaronic systems

in the two-dimensional (2D) quantum site-percolation problem has been a controversial issue for a long time. By means of a highly efficient Chebyshev expansion technique we investigate numerically the time evolution of particle states on finite disordered square lattices with system sizes not reachable up to now. After a careful finite-size scaling, our results for the particles recurrence probability and the distribution function of the local particle density give evidence that indeed extended states exist in the 2D percolation model for