553 research outputs found
Fracture strength and Young's modulus of ZnO nanowires
The fracture strength of ZnO nanowires vertically grown on sapphire
substrates was measured in tensile and bending experiments. Nanowires with
diameters between 60 and 310 nm and a typical length of 2 um were manipulated
with an atomic force microscopy tip mounted on a nanomanipulator inside a
scanning electron microscope. The fracture strain of (7.7 +- 0.8)% measured in
the bending test was found close to the theoretical limit of 10% and revealed a
strength about twice as high as in the tensile test. From the tensile
experiments the Young's modulus could be measured to be within 30% of that of
bulk ZnO, contrary to the lower values found in literature.Comment: 5 pages, 3 figures, 1 tabl
Self-Similarity and Localization
The localized eigenstates of the Harper equation exhibit universal
self-similar fluctuations once the exponentially decaying part of a wave
function is factorized out. For a fixed quantum state, we show that the whole
localized phase is characterized by a single strong coupling fixed point of the
renormalization equations. This fixed point also describes the generalized
Harper model with next nearest neighbor interaction below a certain threshold.
Above the threshold, the fluctuations in the generalized Harper model are
described by a strange invariant set of the renormalization equations.Comment: 4 pages, RevTeX, 2 figures include
X-Ray Reflectivity of Fibonacci Multilayers
We have numerically computed the reflectivity of X-ray incident normally onto
Fibonacci multilayers, and compared the results with those obtained in periodic
approximant multilayers. The constituent layers are of low and high refractive
indices with the same thickness. Whereas reflectivity of periodic approximant
multilayers changes only slightly with increasing the number of layers,
Fibonacci multilayers present a completely different behaviour. In particular,
we have found a highly-fragmented and self-similar reflectivity pattern in
Fibonacci systems. The behaviour of the fragmentation pattern on increasing the
number of layers is quantitatively described using multifractal techniques. The
paper ends with a brief discussion on possible practical applications of our
results in the design of new X-ray devices.Comment: 8 pages, REVTeX 3.0, 3 figures available upon request from
[email protected]. To appear in Physics Letters
Dimer Decimation and Intricately Nested Localized-Ballistic Phases of Kicked Harper
Dimer decimation scheme is introduced in order to study the kicked quantum
systems exhibiting localization transition. The tight-binding representation of
the model is mapped to a vectorized dimer where an asymptotic dissociation of
the dimer is shown to correspond to the vanishing of the transmission
coefficient thru the system. The method unveils an intricate nesting of
extended and localized phases in two-dimensional parameter space. In addition
to computing transport characteristics with extremely high precision, the
renormalization tools also provide a new method to compute quasienergy
spectrum.Comment: There are five postscript figures. Only half of the figure (3) is
shown to reduce file size. However, missing part is the mirror image of the
part show
Hidden dimers and the matrix maps: Fibonacci chains re-visited
The existence of cycles of the matrix maps in Fibonacci class of lattices is
well established. We show that such cycles are intimately connected with the
presence of interesting positional correlations among the constituent `atoms'
in a one dimensional quasiperiodic lattice. We particularly address the
transfer model of the classic golden mean Fibonacci chain where a six cycle of
the full matrix map exists at the centre of the spectrum [Kohmoto et al, Phys.
Rev. B 35, 1020 (1987)], and for which no simple physical picture has so far
been provided, to the best of our knowledge. In addition, we show that our
prescription leads to a determination of other energy values for a mixed model
of the Fibonacci chain, for which the full matrix map may have similar cyclic
behaviour. Apart from the standard transfer-model of a golden mean Fibonacci
chain, we address a variant of it and the silver mean lattice, where the
existence of four cycles of the matrix map is already known to exist. The
underlying positional correlations for all such cases are discussed in details.Comment: 14 pages, 2 figures. Submitted to Physical Review
Competing density-wave orders in a one-dimensional hard-boson model
We describe the zero-temperature phase diagram of a model of bosons,
occupying sites of a linear chain, which obey a hard-exclusion constraint: any
two nearest-neighbor sites may have at most one boson. A special case of our
model was recently proposed as a description of a ``tilted'' Mott insulator of
atoms trapped in an optical lattice. Our quantum Hamiltonian is shown to
generate the transfer matrix of Baxter's hard-square model. Aided by exact
solutions of a number of special cases, and by numerical studies, we obtain a
phase diagram containing states with long-range density-wave order with period
2 and period 3, and also a floating incommensurate phase. Critical theories for
the various quantum phase transitions are presented. As a byproduct, we show
how to compute the Luttinger parameter in integrable theories with
hard-exclusion constraints.Comment: 16 page
The Fractal Dimension of the Spectrum of the Fibonacci Hamiltonian
We study the spectrum of the Fibonacci Hamiltonian and prove upper and lower
bounds for its fractal dimension in the large coupling regime. These bounds
show that as , converges to an explicit constant (). We also discuss
consequences of these results for the rate of propagation of a wavepacket that
evolves according to Schr\"odinger dynamics generated by the Fibonacci
Hamiltonian.Comment: 23 page
Glassiness Vs. Order in Densely Frustrated Josephson Arrays
We carry out extensive Monte Carlo simulations on the Coulomb gas dual to the
uniformly frustrated two dimensional XY model, for a sequence of frustrations f
converging to the irraltional (3-sqrt 5)/2. We find in these systems a sharp
first order equilibrium phase transition to an ordered vortex structure at a
T_c which varies only slightly with f. This ordered vortex structure remains in
general phase incoherent until a lower pinning transition T_p(f) that varies
with f. We argue that the glassy behaviors reported for this model in earlier
simulations are dynamic effects.Comment: 4 pages, 4 eps figure
Physical nature of critical wave functions in Fibonacci systems
We report on a new class of critical states in the energy spectrum of general
Fibonacci systems. By introducing a transfer matrix renormalization technique,
we prove that the charge distribution of these states spreads over the whole
system, showing transport properties characteristic of electronic extended
states. Our analytical method is a first step to find out the link between the
spatial structure of these critical wave functions and the quasiperiodic order
of the underlying lattice.Comment: REVTEX 3.0, 11 pages, 2 figures available upon request. To appear in
Phys. Rev. Let
Phonon Localization in One-Dimensional Quasiperiodic Chains
Quasiperiodic long range order is intermediate between spatial periodicity
and disorder, and the excitations in 1D quasiperiodic systems are believed to
be transitional between extended and localized. These ideas are tested with a
numerical analysis of two incommensurate 1D elastic chains: Frenkel-Kontorova
(FK) and Lennard-Jones (LJ). The ground state configurations and the
eigenfrequencies and eigenfunctions for harmonic excitations are determined.
Aubry's "transition by breaking the analyticity" is observed in the ground
state of each model, but the behavior of the excitations is qualitatively
different. Phonon localization is observed for some modes in the LJ chain on
both sides of the transition. The localization phenomenon apparently is
decoupled from the distribution of eigenfrequencies since the spectrum changes
from continuous to Cantor-set-like when the interaction parameters are varied
to cross the analyticity--breaking transition. The eigenfunctions of the FK
chain satisfy the "quasi-Bloch" theorem below the transition, but not above it,
while only a subset of the eigenfunctions of the LJ chain satisfy the theorem.Comment: This is a revised version to appear in Physical Review B; includes
additional and necessary clarifications and comments. 7 pages; requires
revtex.sty v3.0, epsf.sty; includes 6 EPS figures. Postscript version also
available at
http://lifshitz.physics.wisc.edu/www/koltenbah/koltenbah_homepage.htm
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