5,754 research outputs found
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
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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
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