2,168 research outputs found
Aubry transition studied by direct evaluation of the modulation functions of infinite incommensurate systems
Incommensurate structures can be described by the Frenkel Kontorova model.
Aubry has shown that, at a critical value K_c of the coupling of the harmonic
chain to an incommensurate periodic potential, the system displays the
analyticity breaking transition between a sliding and pinned state. The ground
state equations coincide with the standard map in non-linear dynamics, with
smooth or chaotic orbits below and above K_c respectively. For the standard
map, Greene and MacKay have calculated the value K_c=.971635. Conversely,
evaluations based on the analyticity breaking of the modulation function have
been performed for high commensurate approximants. Here we show how the
modulation function of the infinite system can be calculated without using
approximants but by Taylor expansions of increasing order. This approach leads
to a value K_c'=.97978, implying the existence of a golden invariant circle up
to K_c' > K_c.Comment: 7 pages, 5 figures, file 'epl.cls' necessary for compilation
provided; Revised version, accepted for publication in Europhysics Letter
Ground state wavefunction of the quantum Frenkel-Kontorova model
The wavefunction of an incommensurate ground state for a one-dimensional
discrete sine-Gordon model -- the Frenkel-Kontorova (FK) model -- at zero
temperature is calculated by the quantum Monte Carlo method. It is found that
the ground state wavefunction crosses over from an extended state to a
localized state when the coupling constant exceeds a certain critical value.
So, although the quantum fluctuation has smeared out the breaking of
analyticity transition as observed in the classical case, the remnant of this
transition is still discernible in the quantum regime.Comment: 5 Europhys pages, 3 EPS figures, accepted for publication in
Europhys. Letter
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
On inward motion of the magnetopause preceding a substorm
Magnetopause inward motion preceding magnetic storms observed by means of OGO-E magnetomete
The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: I. Basic Results
The problem of finding the exact energies and configurations for the
Frenkel-Kontorova model consisting of particles in one dimension connected to
their nearest-neighbors by springs and placed in a periodic potential
consisting of segments from parabolas of identical (positive) curvature but
arbitrary height and spacing, is reduced to that of minimizing a certain convex
function defined on a finite simplex.Comment: 12 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 6
Postscript figures, accepted by Phys. Rev.
Oscillatory Instabilities of Standing Waves in One-Dimensional Nonlinear Lattices
In one-dimensional anharmonic lattices, we construct nonlinear standing waves
(SWs) reducing to harmonic SWs at small amplitude. For SWs with spatial
periodicity incommensurate with the lattice period, a transition by breaking of
analyticity versus wave amplitude is observed. As a consequence of the
discreteness, oscillatory linear instabilities, persisting for arbitrarily
small amplitude in infinite lattices, appear for all wave numbers Q not equal
to zero or \pi. Incommensurate analytic SWs with |Q|>\pi/2 may however appear
as 'quasi-stable', as their instability growth rate is of higher order.Comment: 4 pages, 6 figures, to appear in Phys. Rev. Let
Subdiffusion of nonlinear waves in quasiperiodic potentials
We study the spatio-temporal evolution of wave packets in one-dimensional
quasiperiodic lattices which localize linear waves. Nonlinearity (related to
two-body interactions) has destructive effect on localization, as recently
observed for interacting atomic condensates [Phys. Rev. Lett. 106, 230403
(2011)]. We extend the analysis of the characteristics of the subdiffusive
dynamics to large temporal and spatial scales. Our results for the second
moment consistently reveal an asymptotic and
intermediate laws. At variance to purely random systems
[Europhys. Lett. 91, 30001 (2010)] the fractal gap structure of the linear wave
spectrum strongly favors intermediate self-trapping events. Our findings give a
new dimension to the theory of wave packet spreading in localizing
environments
The quasi-periodic Bose-Hubbard model and localization in one-dimensional cold atomic gases
We compute the phase diagram of the one-dimensional Bose-Hubbard model with a
quasi-periodic potential by means of the density-matrix renormalization group
technique. This model describes the physics of cold atoms loaded in an optical
lattice in the presence of a superlattice potential whose wave length is
incommensurate with the main lattice wave length. After discussing the
conditions under which the model can be realized experimentally, the study of
the density vs. the chemical potential curves for a non-trapped system unveils
the existence of gapped phases at incommensurate densities interpreted as
incommensurate charge-density wave phases. Furthermore, a localization
transition is known to occur above a critical value of the potential depth V_2
in the case of free and hard-core bosons. We extend these results to soft-core
bosons for which the phase diagrams at fixed densities display new features
compared with the phase diagrams known for random box distribution disorder. In
particular, a direct transition from the superfluid phase to the Mott
insulating phase is found at finite V_2. Evidence for reentrances of the
superfluid phase upon increasing interactions is presented. We finally comment
on different ways to probe the emergent quantum phases and most importantly,
the existence of a critical value for the localization transition. The later
feature can be investigated by looking at the expansion of the cloud after
releasing the trap.Comment: 19 pages, 20 figure
Localization by bichromatic potentials versus Anderson localization
The one-dimensional propagation of waves in a bichromatic potential may be
modeled by the Aubry-Andr\'e Hamiltonian. The latter presents a
delocalization-localization transition, which has been observed in recent
experiments using ultracold atoms or light. It is shown here that, in contrast
to Anderson localization, this transition has a classical origin, namely the
localization mechanism is not due to a quantum suppression of a classically
allowed transport process. Explicit comparisons with the Anderson model, as
well as with experiments, are done.Comment: 8 pages, 4 figure
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