253 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
Staggered and extreme localization of electron states in fractal space
We present exact analytical results revealing the existence of a countable
infinity of unusual single particle states, which are localized with a
multitude of localization lengths in a Vicsek fractal network with diamond
shaped loops as the 'unit cells'. The family of localized states form clusters
of increasing size, much in the sense of Aharonov-Bohm cages [J. Vidal et al.,
Phys. Rev. Lett. 81, 5888 (1998)], but now without a magnetic field. The length
scale at which the localization effect for each of these states sets in can be
uniquely predicted following a well defined prescription developed within the
framework of real space renormalization group. The scheme allows an exact
evaluation of the energy eigenvalue for every such state which is ensured to
remain in the spectrum of the system even in the thermodynamic limit. In
addition, we discuss the existence of a perfectly conducting state at the band
center of this geometry and the influence of a uniform magnetic field threading
each elementary plaquette of the lattice on its spectral properties. Of
particular interest is the case of extreme localization of single particle
states when the magnetic flux equals half the fundamental flux quantum.Comment: 9 pages, 8 figure
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
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
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]
Long range correlations in DNA : scaling properties and charge transfer efficiency
We address the relation between long range correlations and charge transfer
efficiency in aperiodic artificial or genomic DNA sequences. Coherent charge
transfer through the HOMO states of the guanine nucleotide is studied using the
transmission approach, and focus is made on how the sequence-dependent
backscattering profile can be inferred from correlations between base pairs.Comment: Submitted to Phys. Rev. Let
Wave interactions in localizing media - a coin with many faces
A variety of heterogeneous potentials are capable of localizing linear
non-interacting waves. In this work, we review different examples of
heterogeneous localizing potentials which were realized in experiments. We then
discuss the impact of nonlinearity induced by wave interactions, in particular
its destructive effect on the localizing properties of the heterogeneous
potentials.Comment: Review submitted to Intl. Journal of Bifurcation and Chaos Special
Issue edited by G. Nicolis, M. Robnik, V. Rothos and Ch. Skokos 21 Pages, 8
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
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