30 research outputs found
Delocalization in harmonic chains with long-range correlated random masses
We study the nature of collective excitations in harmonic chains with masses
exhibiting long-range correlated disorder with power spectrum proportional to
, where is the wave-vector of the modulations on the random
masses landscape. Using a transfer matrix method and exact diagonalization, we
compute the localization length and participation ratio of eigenmodes within
the band of allowed energies. We find extended vibrational modes in the
low-energy region for . In order to study the time evolution of an
initially localized energy input, we calculate the second moment of
the energy spatial distribution. We show that , besides being dependent
of the specific initial excitation and exhibiting an anomalous diffusion for
weakly correlated disorder, assumes a ballistic spread in the regime
due to the presence of extended vibrational modes.Comment: 6 pages, 9 figure
Bias driven coherent carrier dynamics in a two-dimensional aperiodic potential
We study the dynamics of an electron wave-packet in a two-dimensional square
lattice with an aperiodic site potential in the presence of an external uniform
electric field. The aperiodicity is described by at lattice sites
, with being a rational number, and and
tunable parameters, controlling the aperiodicity. Using an exact
diagonalization procedure and a finite-size scaling analysis, we show that in
the weakly aperiodic regime (), a phase of extended states
emerges in the center of the band at zero field giving support to a macroscopic
conductivity in the thermodynamic limit. Turning on the field gives rise to
Bloch oscillations of the electron wave-packet. The spectral density of these
oscillations may display a double peak structure signaling the spatial
anisotropy of the potential landscape. The frequency of the oscillations can be
understood using a semi-classical approach.Comment: 16 pages, to appear in Phys. Lett.
Delocalization and spin-wave dynamics in ferromagnetic chains with long-range correlated random exchange
We study the one-dimensional quantum Heisenberg ferromagnet with exchange
couplings exhibiting long-range correlated disorder with power spectrum
proportional to , where is the wave-vector of the modulations
on the random coupling landscape. By using renormalization group, integration
of the equations of motion and exact diagonalization, we compute the spin-wave
localization length and the mean-square displacement of the wave-packet. We
find that, associated with the emergence of extended spin-waves in the
low-energy region for , the wave-packet mean-square displacement
changes from a long-time super-diffusive behavior for to a
long-time ballistic behavior for . At the vicinity of ,
the mobility edge separating the extended and localized phases is shown to
scale with the degree of correlation as .Comment: PRB to appea
Scaling Properties of 1D Anderson Model with Correlated Diagonal Disorder
Statistical and scaling properties of the Lyapunov exponent for a
tight-binding model with the diagonal disorder described by a dichotomic
process are considered near the band edge. The effect of correlations on
scaling properties is discussed. It is shown that correlations lead to an
additional parameter governing the validity of single parameter scaling.Comment: 5 pages, 3 figures, RevTe
Universal renormalization-group dynamics at the onset of chaos in logistic maps and nonextensive statistical mechanics
We uncover the dynamics at the chaos threshold of the logistic
map and find it consists of trajectories made of intertwined power laws that
reproduce the entire period-doubling cascade that occurs for . We corroborate this structure analytically via the Feigenbaum
renormalization group (RG) transformation and find that the sensitivity to
initial conditions has precisely the form of a -exponential, of which we
determine the -index and the -generalized Lyapunov coefficient . Our results are an unequivocal validation of the applicability of the
non-extensive generalization of Boltzmann-Gibbs (BG) statistical mechanics to
critical points of nonlinear maps.Comment: Revtex, 3 figures. Updated references and some general presentation
improvements. To appear published as a Rapid communication of PR
Comment on "Critique of q-entropy for thermal statistics" by M. Nauenberg
It was recently published by M. Nauenberg [1] a quite long list of objections
about the physical validity for thermal statistics of the theory sometimes
referred to in the literature as {\it nonextensive statistical mechanics}. This
generalization of Boltzmann-Gibbs (BG) statistical mechanics is based on the
following expression for the entropy:
S_q= k\frac{1- \sum_{i=1}^Wp_i^q}{q-1} (q \in {\cal R}; S_1=S_{BG} \equiv
-k\sum_{i=1}^W p_i \ln p_i) .
The author of [1] already presented orally the essence of his arguments in
1993 during a scientific meeting in Buenos Aires. I am replying now
simultaneously to the just cited paper, as well as to the 1993 objections
(essentially, the violation of "fundamental thermodynamic concepts", as stated
in the Abstract of [1]).Comment: 7 pages including 2 figures. This is a reply to M. Nauenberg, Phys.
Rev. E 67, 036114 (2003
Electronic localization at mesoscopic length scales: different definitions of localization and contact effects in a heuristic DNA model
In this work we investigate the electronic transport along model DNA
molecules using an effective tight-binding approach that includes the backbone
on site energies. The localization length and participation number are examined
as a function of system size, energy dependence, and the contact coupling
between the leads and the DNA molecule. On one hand, the transition from an
diffusive regime to a localized regime for short systems is identified,
suggesting the necessity of a further length scale revealing the system borders
sensibility. On the other hand, we show that the lenght localization and
participation number, do not depended of system size and contact coupling in
the thermodynamic limit. Finally we discuss possible length dependent origins
for the large discrepancies among experimental results for the electronic
transport in DNA sample
Metastability, negative specific heat and weak mixing in classical long-range many-rotator system
We perform a molecular dynamical study of the isolated classical
Hamiltonian , known to
exhibit a second order phase transition, being disordered for and ordered otherwise ( total energy
and ). We focus
on the nonextensive case and observe that, for , a
basin of attraction exists for the initial conditions for which the system
quickly relaxes onto a longstanding metastable state (whose duration presumably
diverges with like ) which eventually crosses over to the
microcanonical Boltzmann-Gibbs stable state. The temperature associated with
the (scaled) average kinetic energy per particle is lower in the metastable
state than in the stable one. It is exhibited for the first time that the
appropriately scaled maximal Lyapunov exponent
, where, for all values of ,
numerically coincides with {\it one third} of its value for , hence
decreases from 1/9 to zero when increases from zero to unity,
remaining zero thereafter. This new and simple {\it connection between
anomalies above and below the critical point} reinforces the nonextensive
universality scenario.Comment: 9 pages and 4 PS figure
Extended acoustic waves in a one-dimensional aperiodic system
We numerically study the propagation of acoustic waves in a one-dimensional system with an aperiodic pseudo-random elasticity distribution. The elasticity distribution was generated
by using a sinusoidal function whose phase
varies as a power-law, , where n labels the positions along the
media. By considering a discrete one-dimensional
version of the wave equation and a matrix recursive reformulation we compute the localization length within the band of allowed frequencies. In addition, we apply a second-order finite-difference
method for both the time and spatial variables and study the nature of the waves that propagate
in the chain. Our numerical data indicates the presence of extended acoustic waves with non-zero frequency for sufficient degree of aperiodicity
Absence of localization on the 2d model with long-range correlated off-diagonal disorder
We study the one-electron eigenstates in a
two-dimensional (2d) Anderson model with long-range correlated off-diagonal
disorder, generated by a 2d
discrete Fourier method. The dynamics of an initially
localized wave packet is investigated by numerically solving the
2d time-dependent Schrödinger equation. In additional the participation number and its
scaling behavior was obtained through direct diagonalization. Our numerical data suggest that the system
exhibits a ballistic dynamics in the strongly
correlated disorder regime. Moreover, the scaling analysis of mean participation number around the band center
also indicates the presence of extended states for high degree of correlations