391 research outputs found
Critical wave-packet dynamics in the power-law bond disordered Anderson Model
We investigate the wave-packet dynamics of the power-law bond disordered
one-dimensional Anderson model with hopping amplitudes decreasing as
. We consider the critical case ().
Using an exact diagonalization scheme on finite chains, we compute the
participation moments of all stationary energy eigenstates as well as the
spreading of an initially localized wave-packet. The eigenstates
multifractality is characterized by the set of fractal dimensions of the
participation moments. The wave-packet shows a diffusive-like spread developing
a power-law tail and achieves a stationary non-uniform profile after reflecting
at the chain boundaries. As a consequence, the time-dependent participation
moments exhibit two distinct scaling regimes. We formulate a finite-size
scaling hypothesis for the participation moments relating their scaling
exponents to the ones governing the return probability and wave-function
power-law decays
Bloch oscillations in an aperiodic one-dimensional potential
We study the dynamics of an electron subjected to a static uniform electric
field within a one-dimensional tight-binding model with a slowly varying
aperiodic potential. The unbiased model is known to support phases of localized
and extended one-electron states separated by two mobility edges. We show that
the electric field promotes sustained Bloch oscillations of an initial Gaussian
wave packet whose amplitude reflects the band width of extended states. The
frequency of these oscillations exhibit unique features, such as a sensitivity
to the initial wave packet position and a multimode structure for weak fields,
originating from the characteristics of the underlying aperiodic potential.Comment: 6 pages, 7 figure
Bostonia. Volume 6
Founded in 1900, Bostonia magazine is Boston University's main alumni publication, which covers alumni and student life, as well as university activities, events, and programs
Bloch-like oscillations in a one-dimensional lattice with long-range correlated disorder
We study the dynamics of an electron subjected to a uniform electric field
within a tight-binding model with long-range-correlated diagonal disorder. The
random distribution of site energies is assumed to have a power spectrum with . Moura and Lyra [Phys. Rev. Lett. {\bf
81}, 3735 (1998)] predicted that this model supports a phase of delocalized
states at the band center, separated from localized states by two mobility
edges, provided . We find clear signatures of Bloch-like
oscillations of an initial Gaussian wave packet between the two mobility edges
and determine the bandwidth of extended states, in perfect agreement with the
zero-field prediction.Comment: 4 pages, 5 figure
Rossby Wave Instability and three-dimensional vortices in accretion disks
Context. The formation of vortices in accretion disks is of high interest in
various astrophysical contexts, in particular for planet formation or in the
disks of compact objects. But despite numerous attempts it has thus far not
been possible to produce strong vortices in fully three-dimensional simulations
of disks. Aims. The aim of this paper is to present the first 3D simulation of
a strong vortex, established across the vertically stratified structure of a
disk by the Rossby Wave Instability. Methods. Using the Versatile Advection
Code (VAC), we set up a fully 3D cylindrical stratified disk potentially prone
to the Rossby Wave Instability. Results. The simulation confirms the basic
expectations obtained from previous 2D analytic and numerical works. The
simulation exhibits a strong vortex that grows rapidly and saturates at a
finite amplitude. On the other hand the third dimension shows unexpected
additional behaviours that could be of strong importance in the astrophysical
roles that such vortices can play.Comment: Accepted by Astronomy and Astrophysic
Localization properties of a one-dimensional tight-binding model with non-random long-range inter-site interactions
We perform both analytical and numerical studies of the one-dimensional
tight-binding Hamiltonian with stochastic uncorrelated on-site energies and
non-fluctuating long-range hopping integrals . It was argued recently [A.
Rodriguez at al., J. Phys. A: Math. Gen. 33, L161 (2000)] that this model
reveals a localization-delocalization transition with respect to the disorder
magnitude provided . The transition occurs at one of the band edges (the upper
one for and the lower one for). The states at the other band edge are always
localized, which hints on the existence of a single mobility edge. We analyze
the mobility edge and show that, although the number of delocalized states
tends to infinity, they form a set of null measure in the thermodynamic limit,
i.e. the mobility edge tends to the band edge. The critical magnitude of
disorder for the band edge states is computed versus the interaction exponent
by making use of the conjecture on the universality of the normalized
participation number distribution at transition.Comment: 7 pages, 6 postscript figures, uses revtex
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
A recent appreciation of the singular dynamics at the edge of chaos
We study the dynamics of iterates at the transition to chaos in the logistic
map and find that it is constituted by an infinite family of Mori's -phase
transitions. Starting from Feigenbaum's function for the diameters
ratio, we determine the atypical weak sensitivity to initial conditions associated to each -phase transition and find that it obeys the form
suggested by the Tsallis statistics. The specific values of the variable at
which the -phase transitions take place are identified with the specific
values for the Tsallis entropic index in the corresponding . We
describe too the bifurcation gap induced by external noise and show that its
properties exhibit the characteristic elements of glassy dynamics close to
vitrification in supercooled liquids, e.g. two-step relaxation, aging and a
relationship between relaxation time and entropy.Comment: Proceedings of: Verhulst 200 on Chaos, Brussels 16-18 September 2004,
Springer Verlag, in pres
Thin Domain Walls in Lyra Geometry
This paper studies thin domain walls within the frame work of Lyra Geometry.
We have considered two models. First one is the thin domain wall with
negligible pressures perpendicular and transverse direction to the wall and
secondly, we take a particular type of thin domain wall where the pressure in
the perpendicular direction is negligible but transverse pressures are existed.
It is shown that the thin domain walls have no particle horizon and the
gravitational force due to them is attractive.Comment: 8 pages, typos are corrected, published Astrophysics and Space
Sciences 305, 337 (2006
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