217 research outputs found
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
Dynamical phenomena in Fibonacci Semiconductor Superlattices
We present a detailed study of the dynamics of electronic wavepackets in
Fibonacci semiconductor superlattices, both in flat band conditions and subject
to homogeneous electric fields perpendicular to the layers. Coherent
propagation of electrons is described by means of a scalar Hamiltonian using
the effective-mass approximation. We have found that an initial Gaussian
wavepacket is filtered selectively when passing through the superlattice. This
means that only those components of the wavepacket whose wavenumber belong to
allowed subminibands of the fractal-like energy spectrum can propagate over the
entire superlattice. The Fourier pattern of the transmitted part of the
wavepacket presents clear evidences of fractality reproducing those of the
underlying energy spectrum. This phenomenon persists even in the presence of
unintentional disorder due to growth imperfections. Finally, we have
demonstrated that periodic coherent-field induced oscillations (Bloch
oscillations), which we are able to observe in our simulations of periodic
superlattices, are replaced in Fibonacci superlattices by more complex
oscillations displaying quasiperiodic signatures, thus sheding more light onto
the very peculiar nature of the electronic states in these systems.Comment: 7 pagex, RevTex, 5 Postscript figures. Physical Review B (in press
Fluorescence decay in aperiodic Frenkel lattices
We study motion and capture of excitons in self-similar linear systems in
which interstitial traps are arranged according to an aperiodic sequence,
focusing our attention on Fibonacci and Thue-Morse systems as canonical
examples. The decay of the fluorescence intensity following a broadband pulse
excitation is evaluated by solving the microscopic equations of motion of the
Frenkel exciton problem. We find that the average decay is exponential and
depends only on the concentration of traps and the trapping rate. In addition,
we observe small-amplitude oscillations coming from the coupling between the
low-lying mode and a few high-lying modes through the topology of the lattice.
These oscillations are characteristic of each particular arrangement of traps
and they are directly related to the Fourier transform of the underlying
lattice. Our predictions can be then used to determine experimentally the
ordering of traps.Comment: REVTeX 3.0 + 3PostScript Figures + epsf.sty (uuencoded). To appear in
Physical Review
Exciton Optical Absorption in Self-Similar Aperiodic Lattices
Exciton optical absorption in self-similar aperiodic one-dimensional systems
is considered, focusing our attention on Thue-Morse and Fibonacci lattices as
canonical examples. The absorption line shape is evaluated by solving the
microscopic equations of motion of the Frenkel-exciton problem on the lattice,
in which on-site energies take on two values, according to the Thue-Morse or
Fibonacci sequences. Results are compared to those obtained in random lattices
with the same stechiometry and size. We find that aperiodic order causes the
occurrence of well-defined characteristic features in the absorption spectra
which clearly differ from the case of random systems, indicating a most
peculiar exciton dynamics. We successfully explain the obtained spectra in
terms of the two-center problem. This allows us to establish the origin of all
the absorption lines by considering the self-similar aperiodic lattices as
composed of two-center blocks, within the same spirit of the renormalization
group ideas.Comment: 16 pages in REVTeX 3.0. 2 figures on request to F. D-A
([email protected]
Environment effects on the electric conductivity of the DNA
We present a theoretical analysis of the environment effects on charge
transport in double-stranded synthetic poly(G)-poly(C) DNA molecules attached
to two ideal leads. Coupling of the DNA to the environment results in two
effects: (i) localization of carrier functions due to the static disorder and
(ii) phonon-induced scattering of the carrier between these localized states,
resulting in hopping conductivity. A nonlinear Pauli master equation for
populations of localized states is used to describe the hopping transport and
calculate the electric current as a function of the applied bias. We
demonstrate that, although the electronic gap in the density of states shrinks
as the disorder increases, the voltage gap in the characteristics becomes
wider. Simple physical explanation of this effect is provided.Comment: 8 pages, 2 figures, to appear in J. Phys.: Condens. Matte
Anomalous optical absorption in a random system with scale-free disorder
We report on an anomalous behavior of the absorption spectrum in a
one-dimensional lattice with long-range-correlated diagonal disorder with a
power-like spectrum in the form S(k) ~ 1/k^A. These type of correlations give
rise to a phase of extended states at the band center, provided A is larger
than a critical value A_c. We show that for A < A_c the absorption spectrum is
single-peaked, while an additional peak arises when A > A_c, signalling the
occurrence of the Anderson transition. The peak is located slightly below the
low-energy mobility edge, providing a unique spectroscopic tool to monitor the
latter. We present qualitative arguments explaining this anomaly.Comment: 4 pages, 4 postscript figures, uses revtex
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
Optimising Convolutions for Deep Learning Inference on ARM Cortex-M Processors
We perform a series of optimisations on the convo lution operator within the ARM CMSIS-NN library to improve the performance of deep learning tasks on Arduino development boards equipped with ARM Cortex-M4 and M7 microcontrollers. To this end, we develop custom microkernels that efficiently handle the internal computations required by the convolution operator via the lowering approach and the direct method, and we design two techniques to avoid register spilling. We also take advantage of all the RAM on the Arduino boards by reusing it as a scratchpad for the convolution filters. The integration of these techniques into CMSIS-NN, when invoked by TensorFlow Lite for microcontrollers for quantised versions of VGG, SqueezeNet, ResNet, and MobileNet-like convolutional neural networks enhances the overall inference speed by a factor ranging from 1.13× to 1.50×.This research was funded by project TED2021-129334B-I00 supported by MCIN/AEI/10.13039/501100011033 and by the “European Union NextGenerationEU/PRTR”. Manuel F. Dolz was also supported by the Plan Gen–T grant CIDEXG/2022/13 of the Generalitat Valenciana. Antonio Macia-Lillo is a PRE2021-099284 fellow supported by MCIN/AEI/10.13039/501100011033
Energy spectra of quasiperiodic systems via information entropy
We study the relationship between the electronic spectrum structure and the
configurational order of one-dimensional quasiperiodic systems. We take the
Fibonacci case as an specific example, but the ideas outlined here may be
useful to accurately describe the energy spectra of general quasiperiodic
systems of technological interest. Our main result concerns the {\em
minimization} of the information entropy as a characteristic feature associated
to quasiperiodic arrangements. This feature is shown to be related to the
ability of quasiperiodic systems to encode more information, in the Shannon
sense, than periodic ones. In the conclusion we comment on interesting
implications of these results on further developments on the issue of
quasiperiodic order.Comment: REVTeX 3.0, 8 pages, 3 figures available on request from FD-A
([email protected]), Phys Rev E submitted, MA/UC3M/02/9
FIBONACCI SUPERLATTICES OF NARROW-GAP III-V SEMICONDUCTORS
We report theoretical electronic structure of Fibonacci superlattices of
narrow-gap III-V semiconductors. Electron dynamics is accurately described
within the envelope-function approximation in a two-band model.
Quasiperiodicity is introduced by considering two different III-V semiconductor
layers and arranging them according to the Fibonacci series along the growth
direction. The resulting energy spectrum is then found by solving exactly the
corresponding effective-mass (Dirac-like) wave equation using tranfer-matrix
techniques. We find that a self-similar electronic spectrum can be seen in the
band structure. Electronic transport properties of samples are also studied and
related to the degree of spatial localization of electronic envelope-functions
via Landauer resistance and Lyapunov coefficient. As a working example, we
consider type II InAs/GaSb superlattices and discuss in detail our results in
this system.Comment: REVTeX 3.0, 16 pages, 8 figures available upon request. To appear in
Semiconductor Science and Technolog
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