7,749 research outputs found
On deformation and classification of V-systems
The V-systems are special finite sets of covectors which appeared in the
theory of the generalized Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations.
Several families of V-systems are known but their classification is an open
problem. We derive the relations describing the infinitesimal deformations of
V-systems and use them to study the classification problem for V-systems in
dimension 3. We discuss also possible matroidal structures of V-systems in
relation with projective geometry and give the catalogue of all known
irreducible rank 3 V-systems.Comment: Slightly revised version, one of the figures correcte
In search for a perfect shape of polyhedra: Buffon transformation
For an arbitrary polygon consider a new one by joining the centres of
consecutive edges. Iteration of this procedure leads to a shape which is affine
equivalent to a regular polygon. This regularisation effect is usually ascribed
to Count Buffon (1707-1788). We discuss a natural analogue of this procedure
for 3-dimensional polyhedra, which leads to a new notion of affine -regular
polyhedra. The main result is the proof of existence of star-shaped affine
-regular polyhedra with prescribed combinatorial structure, under partial
symmetry and simpliciality assumptions. The proof is based on deep results from
spectral graph theory due to Colin de Verdiere and Lovasz.Comment: Slightly revised version with added example of pentakis dodecahedro
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
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
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