6,754 research outputs found
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
An exact-diagonalization study of rare events in disordered conductors
We determine the statistical properties of wave functions in disordered
quantum systems by exact diagonalization of one-, two- and quasi-one
dimensional tight-binding Hamiltonians. In the quasi-one dimensional case we
find that the tails of the distribution of wave-function amplitudes are
described by the non-linear sigma-model. In two dimensions, the tails of the
distribution function are consistent with a recent prediction based on a direct
optimal fluctuation method.Comment: 13 pages, 5 figure
The Anderson model of localization: a challenge for modern eigenvalue methods
We present a comparative study of the application of modern eigenvalue
algorithms to an eigenvalue problem arising in quantum physics, namely, the
computation of a few interior eigenvalues and their associated eigenvectors for
the large, sparse, real, symmetric, and indefinite matrices of the Anderson
model of localization. We compare the Lanczos algorithm in the 1987
implementation of Cullum and Willoughby with the implicitly restarted Arnoldi
method coupled with polynomial and several shift-and-invert convergence
accelerators as well as with a sparse hybrid tridiagonalization method. We
demonstrate that for our problem the Lanczos implementation is faster and more
memory efficient than the other approaches. This seemingly innocuous problem
presents a major challenge for all modern eigenvalue algorithms.Comment: 16 LaTeX pages with 3 figures include
Two-color QCD with staggered fermions at finite temperature under the influence of a magnetic field
In this paper we investigate the influence of a constant external magnetic
field on the finite-temperature phase structure and the chiral properties of a
simplified lattice model for QCD. We assume an SU(2) gauge symmetry and employ
dynamical staggered fermions of identical mass without rooting, corresponding
to Nf=4 flavors of identical electric charge. For fixed mass (given in lattice
units) the critical temperature is seen to rise with the magnetic field
strength. For three fixed beta-values, selected such that we stay (i) within
the chirally broken phase, (ii) within the transition region or (iii) within
the chirally restored phase, we study the approach to the chiral limit for
various values of the magnetic field. Within the chirally broken (confinement)
phase the chiral condensate is found to increase monotonically with a growing
magnetic field strength. In the chiral limit the increase starts linear in
agreement with a chiral model studied by Shushpanov and Smilga. Within the
chirally restored (deconfinement) phase the chiral condensate tends to zero in
the chiral limit, irrespective of the strength of the magnetic field.Comment: 15 pages, 12 figures; version accepted by Physical Review
Branching Fraction Measurements of the SM Higgs with a Mass of 160 GeV at Future Linear \ee Colliders
Assuming an integrated luminosity of 500 fb and a center-of-mass
energy of 350 GeV, we examine the prospects for measuring branching fractions
of a Standard Model-like Higgs boson with a mass of 160 GeV at the future
linear \ee collider TESLA when the Higgs is produced via the Higgsstrahlung
mechanism, \ee \pfr HZ. We study in detail the precisions achievable for the
branching fractions of the Higgs into WW, ZZ and \bb. However, the
measurement of BF(H \pfr \gaga) remains a great challence. Combined with the
expected error for the inclusive Higgsstrahlung production rate the uncertainty
for the total width of the Higgs is estimated.Comment: 17 pages Latex, including 7 figure
Localization of non-interacting electrons in thin layered disordered systems
Localization of electronic states in disordered thin layered systems with b
layers is studied within the Anderson model of localization using the
transfer-matrix method and finite-size scaling of the inverse of the smallest
Lyapunov exponent. The results support the one-parameter scaling hypothesis for
disorder strengths W studied and b=1,...,6. The obtained results for the
localization length are in good agreement with both the analytical results of
the self-consistent theory of localization and the numerical scaling studies of
the two-dimensional Anderson model. The localization length near the band
center grows exponentially with b for fixed W but no
localization-delocalization transition takes place.Comment: 6 pages, 5 figure
Energy-efficient coding with discrete stochastic events
We investigate the energy efficiency of signaling mechanisms that transfer information by means of discrete stochastic events, such as the opening or closing of an ion channel. Using a simple model for the generation of graded electrical signals by sodium and potassium channels, we find optimum numbers of channels that maximize energy efficiency. The optima depend on several factors: the relative magnitudes of the signaling cost (current flow through channels), the fixed cost of maintaining the system, the reliability of the input, additional sources of noise, and the relative costs of upstream and downstream mechanisms. We also analyze how the statistics of input signals influence energy efficiency. We find that energy-efficient signal ensembles favor a bimodal distribution of channel activations and contain only a very small fraction of large inputs when energy is scarce. We conclude that when energy use is a significant constraint, trade-offs between information transfer and energy can strongly influence the number of signaling molecules and synapses used by neurons and the manner in which these mechanisms represent information
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