Recent progress in mathematical diffraction

A brief summary of recent developments in mathematical diffraction theory is given. Particular emphasis is placed on systems with aperiodic order and continuous spectral components. We restrict ourselves to some key results and refer to the literature for further details

Noncollinear magnetic order in quasicrystals

Based on Monte-Carlo simulations, the stable magnetization configurations of an antiferromagnet on a quasiperiodic tiling are derived theoretically. The exchange coupling is assumed to decrease exponentially with the distance between magnetic moments. It is demonstrated that the superposition of geometric frustration with the quasiperiodic ordering leads to a three-dimensional noncollinear antiferromagnetic spin structure. The structure can be divided into several ordered interpenetrating magnetic supertilings of different energy and characteristic wave vector. The number and the symmetry of subtilings depend on the quasiperiodic ordering of atoms.Comment: RevTeX, 4 pages, 5 low-resolution color figures (due to size restrictions); to appear in Physical Review Letter

Spectrum of a duality-twisted Ising quantum chain

The Ising quantum chain with a peculiar twisted boundary condition is considered. This boundary condition, first introduced in the framework of the spin-1/2 XXZ Heisenberg quantum chain, is related to the duality transformation, which becomes a symmetry of the model at the critical point. Thus, at the critical point, the Ising quantum chain with the duality-twisted boundary is translationally invariant, similar as in the case of the usual periodic or antiperiodic boundary conditions. The complete energy spectrum of the Ising quantum chain is calculated analytically for finite systems, and the conformal properties of the scaling limit are investigated. This provides an explicit example of a conformal twisted boundary condition and a corresponding generalised twisted partition function.Comment: LaTeX, 7 pages, using IOP style

Scaling of the Thue-Morse diffraction measure

We revisit the well-known and much studied Riesz product representation of the Thue-Morse diffraction measure, which is also the maximal spectral measure for the corresponding dynamical spectrum in the complement of the pure point part. The known scaling relations are summarised, and some new findings are explained

Cold inelastic collisions between lithium and cesium in a two-species magneto-optical trap

We investigate collisional properties of lithium and cesium which are simultaneously confined in a combined magneto-optical trap. Trap-loss collisions between the two species are comprehensively studied. Different inelastic collision channels are identified, and inter-species rate coefficients as well as cross sections are determined. It is found that loss rates are independent of the optical excitation of Li, as a consequence of the repulsive Li$^*$-Cs interaction. Li and Cs loss by inelastic inter-species collisions can completely be attributed to processes involving optically excited cesium (fine-structure changing collisions and radiative escape). By lowering the trap depth for Li, an additional loss channel of Li is observed which results from ground-state Li-Cs collisions changing the hyperfine state of cesium.Comment: submitted to Euro. Phys. J. D, special issue on Laser Cooling and Trappin

A critical Ising model on the Labyrinth

A zero-field Ising model with ferromagnetic coupling constants on the so-called Labyrinth tiling is investigated. Alternatively, this can be regarded as an Ising model on a square lattice with a quasi-periodic distribution of up to eight different coupling constants. The duality transformation on this tiling is considered and the self-dual couplings are determined. Furthermore, we analyze the subclass of exactly solvable models in detail parametrizing the coupling constants in terms of four rapidity parameters. For those, the self-dual couplings correspond to the critical points which, as expected, belong to the Onsager universality class.Comment: 25 pages, 6 figure

Financing SMEs: a model for optimising the capital structure

This paper argues that the existing finance literature is inadequate with respect to its cov-erage of capital structure of small and medium sized enterprises (SMEs). In particular it is argued that the cost of equity (being both conceptually ill defined and empirically non quantifiable) is not applicable to the capital structure decisions for a large proportion of SMEs and the optimal capital structure depends only on the mix of short and long term debt. The paper then presents a model for optimising the debt mix and demonstrates its practical application using an Italian firm’s debt structure as a case study

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

Integrable impurities for an open fermion chain

Employing the graded versions of the Yang-Baxter equation and the reflection equations, we construct two kinds of integrable impurities for a small-polaron model with general open boundary conditions: (a) we shift the spectral parameter of the local Lax operator at arbitrary sites in the bulk, and (b) we embed the impurity fermion vertex at each boundary of the chain. The Hamiltonians with different types of impurity terms are given explicitly. The Bethe ansatz equations, as well as the eigenvalues of the Hamiltonians, are constructed by means of the quantum inverse scattering method. In addition, we discuss the ground-state properties in the thermodynamic limit.Comment: 20 pages, 4 figure