5,165 research outputs found
Localized and extended states in a disordered trap
We study Anderson localization in a disordered potential combined with an
inhomogeneous trap. We show that the spectrum displays both localized and
extended states, which coexist at intermediate energies. In the region of
coexistence, we find that the extended states result from confinement by the
trap and are weakly affected by the disorder. Conversely, the localized states
correspond to eigenstates of the disordered potential, which are only affected
by the trap via an inhomogeneous energy shift. These results are relevant to
disordered quantum gases and we propose a realistic scheme to observe the
coexistence of localized and extended states in these systems.Comment: Published versio
A model of dispersive transport across sharp interfaces between porous materials
Recent laboratory experiments on solute migration in composite porous columns
have shown an asymmetry in the solute arrival time upon reversal of the flow
direction, which is not explained by current paradigms of transport. In this
work, we propose a definition for the solute flux across sharp interfaces and
explore the underlying microscopic particle dynamics by applying Monte Carlo
simulation. Our results are consistent with previous experimental findings and
explain the observed transport asymmetry. An interpretation of the proposed
physical mechanism in terms of a flux rectification is also provided. The
approach is quite general and can be extended to other situations involving
transport across sharp interfaces.Comment: 4 pages, 4 figure
Localization of solitons: linear response of the mean-field ground state to weak external potentials
Two aspects of bright matter-wave solitons in weak external potentials are
discussed. First, we briefly review recent results on the Anderson localization
of an entire soliton in disordered potentials [Sacha et al. PRL 103, 210402
(2009)], as a paradigmatic showcase of genuine quantum dynamics beyond simple
perturbation theory. Second, we calculate the linear response of the mean-field
soliton shape to a weak, but otherwise arbitrary external potential, with a
detailed application to lattice potentials.Comment: Selected paper presented at the 2010 Spring Meeting of the Quantum
Optics and Photonics Section of the German Physical Society. V2: minor
changes, published versio
Anderson localization of matter waves in tailored disordered potentials
We show that, in contrast to immediate intuition, Anderson localization of
noninteracting particles induced by a disordered potential in free space can
increase (i.e., the localization length can decrease) when the particle energy
increases, for appropriately tailored disorder correlations. We predict the
effect in one, two, and three dimensions, and propose a simple method to
observe it using ultracold atoms placed in optical disorder. The increase of
localization with the particle energy can serve to discriminate quantum versus
classical localization
Tailoring Anderson localization by disorder correlations in 1D speckle potentials
We study Anderson localization of single particles in continuous, correlated,
one-dimensional disordered potentials. We show that tailored correlations can
completely change the energy-dependence of the localization length. By
considering two suitable models of disorder, we explicitly show that disorder
correlations can lead to a nonmonotonic behavior of the localization length
versus energy. Numerical calculations performed within the transfer-matrix
approach and analytical calculations performed within the phase formalism up to
order three show excellent agreement and demonstrate the effect. We finally
show how the nonmonotonic behavior of the localization length with energy can
be observed using expanding ultracold-atom gases
Quasi-localization and quasi-mobility edge for light atoms mixed with heavy ones
A mixture of light and heavy atoms is considered. We study the kinetics of
the light atoms, scattered by the heavy ones, the latter undergoing slow
diffusive motion. In three-dimensional space we claim the existence of a
crossover region (in energy), which separates the states of the light atoms
with fast diffusion and the states with slow diffusion; the latter is
determined by the dephasing time. For the two dimensional case we have a
transition between weak localization, observed when the dephasing length is
less than the localization length (calculated for static scatterers), and
strong localization observed in the opposite case.Comment: LaTeX, 5 pages, 3 figures. The manuscript has been changed following
the Referees' constructive criticism and is accepted for publication in EPJ
Exponential splitting of bound states in a waveguide with a pair of distant windows
We consider Laplacian in a straight planar strip with Dirichlet boundary
which has two Neumann ``windows'' of the same length the centers of which are
apart, and study the asymptotic behaviour of the discrete spectrum as
. It is shown that there are pairs of eigenvalues around each
isolated eigenvalue of a single-window strip and their distances vanish
exponentially in the limit . We derive an asymptotic expansion also
in the case where a single window gives rise to a threshold resonance which the
presence of the other window turns into a single isolated eigenvalue
New porous medium Poisson-Nernst-Planck equations for strongly oscillating electric potentials
We consider the Poisson-Nernst-Planck system which is well-accepted for
describing dilute electrolytes as well as transport of charged species in
homogeneous environments. Here, we study these equations in porous media whose
electric permittivities show a contrast compared to the electric permittivity
of the electrolyte phase. Our main result is the derivation of convenient
low-dimensional equations, that is, of effective macroscopic porous media
Poisson-Nernst-Planck equations, which reliably describe ionic transport. The
contrast in the electric permittivities between liquid and solid phase and the
heterogeneity of the porous medium induce strongly oscillating electric
potentials (fields). In order to account for this special physical scenario, we
introduce a modified asymptotic multiple-scale expansion which takes advantage
of the nonlinearly coupled structure of the ionic transport equations. This
allows for a systematic upscaling resulting in a new effective porous medium
formulation which shows a new transport term on the macroscale. Solvability of
all arising equations is rigorously verified. This emergence of a new transport
term indicates promising physical insights into the influence of the microscale
material properties on the macroscale. Hence, systematic upscaling strategies
provide a source and a prospective tool to capitalize intrinsic scale effects
for scientific, engineering, and industrial applications
Toughening and asymmetry in peeling of heterogeneous adhesives
The effective adhesive properties of heterogeneous thin films are
characterized through a combined experimental and theoretical investigation. By
bridging scales, we show how variations of elastic or adhesive properties at
the microscale can significantly affect the effective peeling behavior of the
adhesive at the macroscale. Our study reveals three elementary mechanisms in
heterogeneous systems involving front propagation: (i) patterning the elastic
bending stiffness of the film produces fluctuations of the driving force
resulting in dramatically enhanced resistance to peeling; (ii) optimized
arrangements of pinning sites with large adhesion energy are shown to control
the effective system resistance, allowing the design of highly anisotropic and
asymmetric adhesives; (iii) heterogeneities of both types result in front
motion instabilities producing sudden energy releases that increase the overall
adhesion energy. These findings open potentially new avenues for the design of
thin films with improved adhesion properties, and motivate new investigation of
other phenomena involving front propagation.Comment: Physical Review Letters (2012)
Electromagnetic phenomena in heterogeneous media: Effective properties and local behavior
The purpose of this paper is the use of a mathematical homogenization approach based on the multiple scale expansion theory for modeling the electromagnetic phenomena arising in heterogeneous media under an imposed magnetic flux. The attention is focused on the analysis and discussion of the merits and limits of this theoretical approach in reproducing not only the effective macroscopic properties but also the local behavior, under a wide frequency range and considering different constitutive and geometrical parameters. The results show that the proposed method is able to predict local and integral physical quantities, ranging from a substantially global behavior in the whole media to significantly localized effects determined by the microscopic structure
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