72 research outputs found
Absence of mobility edge for the Anderson random potential on tree graphs at weak disorder
Our recently established criterion for the formation of extended states on
tree graphs in the presence of disorder is shown to have the surprising
implication that for bounded random potentials, as in the Anderson model, there
is no transition to a spectral regime of Anderson localization, in the form
usually envisioned, unless the disorder is strong enough
Stochastic Green's function approach to disordered systems
Based on distributions of local Green's functions we present a stochastic
approach to disordered systems. Specifically we address Anderson localisation
and cluster effects in binary alloys. Taking Anderson localisation of Holstein
polarons as an example we discuss how this stochastic approach can be used for
the investigation of interacting disordered systems.Comment: 12 pages, 7 figures, conference proceedings: Progress in
Nonequilibrium Green's Functions III, 22-26 August 2005, University of Kiel,
German
Anderson transition on the Cayley tree as a traveling wave critical point for various probability distributions
For Anderson localization on the Cayley tree, we study the statistics of
various observables as a function of the disorder strength and the number
of generations. We first consider the Landauer transmission . In the
localized phase, its logarithm follows the traveling wave form where (i) the disorder-averaged value moves linearly
and the localization length
diverges as with (ii) the
variable is a fixed random variable with a power-law tail for large with , so that all
integer moments of are governed by rare events. In the delocalized phase,
the transmission remains a finite random variable as , and
we measure near criticality the essential singularity with . We then consider the
statistical properties of normalized eigenstates, in particular the entropy and
the Inverse Participation Ratios (I.P.R.). In the localized phase, the typical
entropy diverges as with , whereas it grows
linearly in in the delocalized phase. Finally for the I.P.R., we explain
how closely related variables propagate as traveling waves in the delocalized
phase. In conclusion, both the localized phase and the delocalized phase are
characterized by the traveling wave propagation of some probability
distributions, and the Anderson localization/delocalization transition then
corresponds to a traveling/non-traveling critical point. Moreover, our results
point towards the existence of several exponents at criticality.Comment: 28 pages, 21 figures, comments welcom
Transport in the 3-dimensional Anderson model: an analysis of the dynamics on scales below the localization length
Single-particle transport in disordered potentials is investigated on scales
below the localization length. The dynamics on those scales is concretely
analyzed for the 3-dimensional Anderson model with Gaussian on-site disorder.
This analysis particularly includes the dependence of characteristic transport
quantities on the amount of disorder and the energy interval, e.g., the mean
free path which separates ballistic and diffusive transport regimes. For these
regimes mean velocities, respectively diffusion constants are quantitatively
given. By the use of the Boltzmann equation in the limit of weak disorder we
reveal the known energy-dependencies of transport quantities. By an application
of the time-convolutionless (TCL) projection operator technique in the limit of
strong disorder we find evidence for much less pronounced energy dependencies.
All our results are partially confirmed by the numerically exact solution of
the time-dependent Schroedinger equation or by approximative numerical
integrators. A comparison with other findings in the literature is additionally
provided.Comment: 23 pages, 10 figure
Spectra of Modular and Small-World Matrices
We compute spectra of symmetric random matrices describing graphs with
general modular structure and arbitrary inter- and intra-module degree
distributions, subject only to the constraint of finite mean connectivities. We
also evaluate spectra of a certain class of small-world matrices generated from
random graphs by introducing short-cuts via additional random connectivity
components. Both adjacency matrices and the associated graph Laplacians are
investigated. For the Laplacians, we find Lifshitz type singular behaviour of
the spectral density in a localised region of small values. In the
case of modular networks, we can identify contributions local densities of
state from individual modules. For small-world networks, we find that the
introduction of short cuts can lead to the creation of satellite bands outside
the central band of extended states, exhibiting only localised states in the
band-gaps. Results for the ensemble in the thermodynamic limit are in excellent
agreement with those obtained via a cavity approach for large finite single
instances, and with direct diagonalisation results.Comment: 18 pages, 5 figure
Ergodicity breaking in a model showing many-body localization
We study the breaking of ergodicity measured in terms of return probability
in the evolution of a quantum state of a spin chain. In the non ergodic phase a
quantum state evolves in a much smaller fraction of the Hilbert space than
would be allowed by the conservation of extensive observables. By the anomalous
scaling of the participation ratios with system size we are led to consider the
distribution of the wave function coefficients, a standard observable in modern
studies of Anderson localization. We finally present a criterion for the
identification of the ergodicity breaking (many-body localization) transition
based on these distributions which is quite robust and well suited for
numerical investigations of a broad class of problems.Comment: 5 pages, 5 figures, final versio
A single defect approximation for localized states on random lattices
Geometrical disorder is present in many physical situations giving rise to
eigenvalue problems. The simplest case of diffusion on a random lattice with
fluctuating site connectivities is studied analytically and by exact numerical
diagonalizations. Localization of eigenmodes is shown to be induced by
geometrical defects, that is sites with abnormally low or large connectivities.
We expose a ``single defect approximation'' (SDA) scheme founded on this
mechanism that provides an accurate quantitative description of both extended
and localized regions of the spectrum. We then present a systematic
diagrammatic expansion allowing to use SDA for finite-dimensional problems,
e.g. to determine the localized harmonic modes of amorphous media.Comment: final version as published, 6 pages, 1 ps-figur
Properties of low-lying states in a diffusive quantum dot and Fock-space localization
Motivated by an experiment by Sivan et al. (Europhys. Lett. 25, 605 (1994))
and by subsequent theoretical work on localization in Fock space, we study
numerically a hierarchical model for a finite many-body system of Fermions
moving in a disordered potential and coupled by a two-body interaction. We
focus attention on the low-lying states close to the Fermi energy. Both the
spreading width and the participation number depend smoothly on excitation
energy. This behavior is in keeping with naive expectations and does not
display Anderson localization. We show that the model reproduces essential
features of the experiment by Sivan et al.Comment: 4 pages, 3 figures, accepted for publication in Phys. Rev. Let
“Teaches People That I'm More Than a Disability”: Using Nominal Group Technique in Patient-Oriented Research for People With Intellectual and Developmental Disabilities
Individuals with intellectual and developmental disabilities (IDD) have complex healthcare needs, which are often unmet. Nominal group technique (NGT) uses a mixed-methods approach, which may engage the IDD population in the research process in a person-centered manner and address the shortcomings of traditional research methods with this population. NGT was used with a group of 10 self-advocates to evaluate a series of healthcare tools created by and for individuals with IDD. Participants provided helpful input about the strengths of these tools and suggestions to improve them. NGT was found to be an effective way to engage all participants in the research process
Analytic computation of the Instantaneous Normal Modes spectrum in low density liquids
We analytically compute the spectrum of the Hessian of the Hamiltonian for a
system of N particles interacting via a purely repulsive potential in one
dimension. Our approach is valid in the low density regime, where we compute
the exact spectrum also in the localized sector. We finally perform a numerical
analysis of the localization properties of the eigenfunctions.Comment: 4 RevTeX pages, 4 EPS figures. Revised version to appear on Phys.
Rev. Let
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