Spectral and Diffusive Properties of Silver-Mean Quasicrystals in 1,2, and 3 Dimensions

Spectral properties and anomalous diffusion in the silver-mean (octonacci) quasicrystals in d=1,2,3 are investigated using numerical simulations of the return probability C(t) and the width of the wave packet w(t) for various values of the hopping strength v. In all dimensions we find C(t)\sim t^{-\delta}, with results suggesting a crossover from \delta<1 to \delta=1 when v is varied in d=2,3, which is compatible with the change of the spectral measure from singular continuous to absolute continuous; and we find w(t)\sim t^{\beta} with 0<\beta(v)<1 corresponding to anomalous diffusion. Results strongly suggest that \beta(v) is independent of d. The scaling of the inverse participation ratio suggests that states remain delocalized even for very small hopping amplitude v. A study of the dynamics of initially localized wavepackets in large three-dimensional quasiperiodic structures furthermore reveals that wavepackets composed of eigenstates from an interval around the band edge diffuse faster than those composed of eigenstates from an interval of the band-center states: while the former diffuse anomalously, the latter appear to diffuse slower than any power law.Comment: 11 pages, 10 figures, 1 tabl

Trigonometric R Matrices related to `Dilute' Birman--Wenzl--Murakami Algebra

Explicit expressions for three series of $R$ matrices which are related to a ``dilute'' generalisation of the Birman--Wenzl--Murakami are presented. Of those, one series is equivalent to the quantum $R$ matrices of the $D^{(2)}_{n+1}$ generalised Toda systems whereas the remaining two series appear to be new.Comment: 5 page

Surface Properties of Aperiodic Ising Quantum Chains

We consider Ising quantum chains with quenched aperiodic disorder of the coupling constants given through general substitution rules. The critical scaling behaviour of several bulk and surface quantities is obtained by exact real space renormalization.Comment: 4 pages, RevTex, reference update

Anomaly Cancelation in Field Theory and F-theory on a Circle

We study the manifestation of local gauge anomalies of four- and six-dimensional field theories in the lower-dimensional Kaluza-Klein theory obtained after circle compactification. We identify a convenient set of transformations acting on the whole tower of massless and massive states and investigate their action on the low-energy effective theories in the Coulomb branch. The maps employ higher-dimensional large gauge transformations and precisely yield the anomaly cancelation conditions when acting on the one-loop induced Chern-Simons terms in the three- and five-dimensional effective theory. The arising symmetries are argued to play a key role in the study of the M-theory to F-theory limit on Calabi-Yau manifolds. For example, using the fact that all fully resolved F-theory geometries inducing multiple Abelian gauge groups or non-Abelian groups admit a certain set of symmetries, we are able to generally show the cancelation of pure Abelian or pure non-Abelian anomalies in these models.Comment: 48 pages, 2 figures; v2: typos corrected, comments on circle fluxes adde

Some comments on the inverse problem of pure point diffraction

In a recent paper, Lenz and Moody (arXiv:1111.3617) presented a method for constructing families of real solutions to the inverse problem for a given pure point diffraction measure. Applying their technique and discussing some possible extensions, we present, in a non-technical manner, some examples of homometric structures.Comment: 6 pages, contribution to Aperiodic 201

A Sphere Decoding Algorithm for Multistep Sequential Model Predictive Control

This paper investigates the combination of two model predictive control concepts, sequential model predictive control and long-horizon model predictive control for power electronics. To achieve sequential model predictive control, the optimization problem is split into two subproblems: The first one summarizes all control goals which linearly depend on the system inputs. Sequential model predictive control generally requires to obtain more than one solution for the first subproblem. Due to the mixed-integer nature of finite control set model predictive control power electronics a special sphere decoder is therefore proposed within the paper. The second subproblem consists of all those control goals which depend nonlinearly on the system inputs and is solved by an exhaustive search. The effectiveness of the proposed method is validated via numerical simulations at different scenarios on a three-level neutral point clamped permanent magnet synchronous generator wind turbine system and compared to other long-horizon model predictive control methods