25 research outputs found
Ballistic transport in random magnetic fields with anisotropic long-ranged correlations
We present exact theoretical results about energetic and dynamic properties
of a spinless charged quantum particle on the Euclidean plane subjected to a
perpendicular random magnetic field of Gaussian type with non-zero mean. Our
results refer to the simplifying but remarkably illuminating limiting case of
an infinite correlation length along one direction and a finite but strictly
positive correlation length along the perpendicular direction in the plane.
They are therefore ``random analogs'' of results first obtained by A. Iwatsuka
in 1985 and by J. E. M\"uller in 1992, which are greatly esteemed, in
particular for providing a basic understanding of transport properties in
certain quasi-two-dimensional semiconductor heterostructures subjected to
non-random inhomogeneous magnetic fields
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
Quasi-classical versus non-classical spectral asymptotics for magnetic Schroedinger operators with decreasing electric potentials
We consider the Schroedinger operator H on L^2(R^2) or L^2(R^3) with constant
magnetic field and electric potential V which typically decays at infinity
exponentially fast or has a compact support. We investigate the asymptotic
behaviour of the discrete spectrum of H near the boundary points of its
essential spectrum. If the decay of V is Gaussian or faster, this behaviour is
non-classical in the sense that it is not described by the quasi-classical
formulas known for the case where V admits a power-like decay.Comment: Corrected versio
On Bernoulli Decompositions for Random Variables, Concentration Bounds, and Spectral Localization
As was noted already by A. N. Kolmogorov, any random variable has a Bernoulli
component. This observation provides a tool for the extension of results which
are known for Bernoulli random variables to arbitrary distributions. Two
applications are provided here: i. an anti-concentration bound for a class of
functions of independent random variables, where probabilistic bounds are
extracted from combinatorial results, and ii. a proof, based on the Bernoulli
case, of spectral localization for random Schroedinger operators with arbitrary
probability distributions for the single site coupling constants. For a general
random variable, the Bernoulli component may be defined so that its conditional
variance is uniformly positive. The natural maximization problem is an optimal
transport question which is also addressed here
Bounds on the heat kernel of the Schroedinger operator in a random electromagnetic field
We obtain lower and upper bounds on the heat kernel and Green functions of
the Schroedinger operator in a random Gaussian magnetic field and a fixed
scalar potential. We apply stochastic Feynman-Kac representation, diamagnetic
upper bounds and the Jensen inequality for the lower bound. We show that if the
covariance of the electromagnetic (vector) potential is increasing at large
distances then the lower bound is decreasing exponentially fast for large
distances and a large time.Comment: some technical improvements, new references, to appear in
Journ.Phys.
Localization Bounds for Multiparticle Systems
We consider the spectral and dynamical properties of quantum systems of
particles on the lattice , of arbitrary dimension, with a Hamiltonian
which in addition to the kinetic term includes a random potential with iid
values at the lattice sites and a finite-range interaction. Two basic
parameters of the model are the strength of the disorder and the strength of
the interparticle interaction. It is established here that for all there
are regimes of high disorder, and/or weak enough interactions, for which the
system exhibits spectral and dynamical localization. The localization is
expressed through bounds on the transition amplitudes, which are uniform in
time and decay exponentially in the Hausdorff distance in the configuration
space. The results are derived through the analysis of fractional moments of
the -particle Green function, and related bounds on the eigenfunction
correlators
Upper bounds on the density of states of single Landau levels broadened by Gaussian random potentials
We study a non-relativistic charged particle on the Euclidean plane R^2
subject to a perpendicular constant magnetic field and an R^2-homogeneous
random potential in the approximation that the corresponding random Landau
Hamiltonian on the Hilbert space L^2(R^2) is restricted to the eigenspace of a
single but arbitrary Landau level. For a wide class of Gaussian random
potentials we rigorously prove that the associated restricted integrated
density of states is absolutely continuous with respect to the Lebesgue
measure. We construct explicit upper bounds on the resulting derivative, the
restricted density of states. As a consequence, any given energy is seen to be
almost surely not an eigenvalue of the restricted random Landau Hamiltonian.Comment: 16 pages, to appear in "Journal of Mathematical Physics
A small new species of Crenicichla Heckel, 1840 from middle rio Xingu, Brazil (Teleostei: Cichlidae)
A new species of Crenicichla is described from the middle rio Xingu and tributaries, upstream from Volta Grande do Xingu. The largest specimen measured 47.8 mm SL. The new species can be distinguished from all other Crenicichla species by the combination of the following character states: presence of serrae on supracleithrum (diagnostic of Crenicichla wallacii species group), large caudal blotch centrally located on caudal lateral line (shared with C. urosema and C. virgatula), vertical dark stripes on the caudal fin and up to three series of teeth on premaxilla and maxilla (vs. more than four series of teeth). The new species described herein is the eleventh species of Crenicichla listed from the rio Xingu basin. Similarities of color pattern among small species of Crenicichla is discussed. © 2015, Sociedade Brasileira de Ictiologia