669 research outputs found
Localization for Schrodinger operators with random vector potentials
We prove Anderson localization at the internal band-edges for periodic
magnetic Schr{\"o}dinger operators perturbed by random vector potentials of
Anderson-type. This is achieved by combining new results on the Lifshitz tails
behavior of the integrated density of states for random magnetic
Schr{\"o}dinger operators, thereby providing the initial length-scale estimate,
and a Wegner estimate, for such models
Lifshitz Tails in Constant Magnetic Fields
We consider the 2D Landau Hamiltonian perturbed by a random alloy-type
potential, and investigate the Lifshitz tails, i.e. the asymptotic behavior of
the corresponding integrated density of states (IDS) near the edges in the
spectrum of . If a given edge coincides with a Landau level, we obtain
different asymptotic formulae for power-like, exponential sub-Gaussian, and
super-Gaussian decay of the one-site potential. If the edge is away from the
Landau levels, we impose a rational-flux assumption on the magnetic field,
consider compactly supported one-site potentials, and formulate a theorem which
is analogous to a result obtained in the case of a vanishing magnetic field
Understanding the Random Displacement Model: From Ground-State Properties to Localization
We give a detailed survey of results obtained in the most recent half decade
which led to a deeper understanding of the random displacement model, a model
of a random Schr\"odinger operator which describes the quantum mechanics of an
electron in a structurally disordered medium. These results started by
identifying configurations which characterize minimal energy, then led to
Lifshitz tail bounds on the integrated density of states as well as a Wegner
estimate near the spectral minimum, which ultimately resulted in a proof of
spectral and dynamical localization at low energy for the multi-dimensional
random displacement model.Comment: 31 pages, 7 figures, final version, to appear in Proceedings of
"Spectral Days 2010", Santiago, Chile, September 20-24, 201
Spectral extrema and Lifshitz tails for non monotonous alloy type models
In the present note, we determine the ground state energy and study the
existence of Lifshitz tails near this energy for some non monotonous alloy type
models. Here, non monotonous means that the single site potential coming into
the alloy random potential changes sign. In particular, the random operator is
not a monotonous function of the random variables
Wegner estimate for discrete alloy-type models
We study discrete alloy-type random Schr\"odinger operators on
. Wegner estimates are bounds on the average number of
eigenvalues in an energy interval of finite box restrictions of these types of
operators. If the single site potential is compactly supported and the
distribution of the coupling constant is of bounded variation a Wegner estimate
holds. The bound is polynomial in the volume of the box and thus applicable as
an ingredient for a localisation proof via multiscale analysis.Comment: Accepted for publication in AHP. For an earlier version see
http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=09-10
Localization on quantum graphs with random vertex couplings
We consider Schr\"odinger operators on a class of periodic quantum graphs
with randomly distributed Kirchhoff coupling constants at all vertices. Using
the technique of self-adjoint extensions we obtain conditions for localization
on quantum graphs in terms of finite volume criteria for some energy-dependent
discrete Hamiltonians. These conditions hold in the strong disorder limit and
at the spectral edges
The weak localization for the alloy-type Anderson model on a cubic lattice
We consider alloy type random Schr\"odinger operators on a cubic lattice
whose randomness is generated by the sign-indefinite single-site potential. We
derive Anderson localization for this class of models in the Lifshitz tails
regime, i.e. when the coupling parameter is small, for the energies
.Comment: 45 pages, 2 figures. To appear in J. Stat. Phy
Localization for the random displacement model at weak disorder
This paper is devoted to the study of the random displacement model on
. We prove that, in the weak displacement regime, Anderson and dynamical
localization holds near the bottom of the spectrum under a generic assumption
on the single site potential and a fairly general assumption on the support of
the possible displacements. This result follows from the proof of the existence
of Lifshitz tail and of a Wegner estimate for the model under scrutiny
Absolutely continuous spectrum for the isotropic Maxwell operator with coefficients that are periodic in some directions and decay in others
The purpose of this paper is to prove that the spectrum of an isotropic
Maxwell operator with electric permittivity and magnetic permeability that are
periodic along certain directions and tending to a constant super-exponentially
fast in the remaining directions is purely absolutely continuous. The basic
technical tools is a new ``operatorial'' identity relating the Maxwell operator
to a vector-valued Schrodinger operator. The analysis of the spectrum of that
operator is then handled using ideas developed by the same authors in a
previous paper
Low lying spectrum of weak-disorder quantum waveguides
We study the low-lying spectrum of the Dirichlet Laplace operator on a
randomly wiggled strip. More precisely, our results are formulated in terms of
the eigenvalues of finite segment approximations of the infinite waveguide.
Under appropriate weak-disorder assumptions we obtain deterministic and
probabilistic bounds on the position of the lowest eigenvalue. A Combes-Thomas
argument allows us to obtain so-called 'initial length scale decay estimates'
at they are used in the proof of spectral localization using the multiscale
analysis.Comment: Accepted for publication in Journal of Statistical Physics
http://www.springerlink.com/content/0022-471
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