50 research outputs found
1D quantum models with correlated disorder vs. classical oscillators with coloured noise
We perform an analytical study of the correspondence between a classical
oscillator with frequency perturbed by a coloured noise and the one-dimensional
Anderson-type model with correlated diagonal disorder. It is rigorously shown
that localisation of electronic states in the quantum model corresponds to
exponential divergence of nearby trajectories of the classical random
oscillator. We discuss the relation between the localisation length for the
quantum model and the rate of energy growth for the stochastic oscillator.
Finally, we examine the problem of electron transmission through a finite
disordered barrier by considering the evolution of the classical oscillator.Comment: 23 pages, LaTeX fil
Non-hermitean delocalization in an array of wells with variable-range widths
Nonhermitean hamiltonians of convection-diffusion type occur in the
description of vortex motion in the presence of a tilted magnetic field as well
as in models of driven population dynamics. We study such hamiltonians in the
case of rectangular barriers of variable size. We determine Lyapunov exponent
and wavenumber of the eigenfunctions within an adiabatic approach, allowing to
reduce the original d=2 phase space to a d=1 attractor. PACS
numbers:05.70.Ln,72.15Rn,74.60.GeComment: 20 pages,10 figure
Anderson localization as a parametric instability of the linear kicked oscillator
We rigorously analyse the correspondence between the one-dimensional standard
Anderson model and a related classical system, the `kicked oscillator' with
noisy frequency. We show that the Anderson localization corresponds to a
parametric instability of the oscillator, with the localization length
determined by an increment of the exponential growth of the energy. Analytical
expression for a weak disorder is obtained, which is valid both inside the
energy band and at the band edge.Comment: 7 pages, Revtex, no figures, submitted to Phys. Rev.
Scaling of Island Growth in Pb Overlayers on Cu(001)
The growth and ordering of a Pb layer deposited on Cu(001) at 150 K has been
studied using atom beam scattering. At low coverage, ordered Pb islands with a
large square unit cell and nearly hexagonal internal structure are formed. This
is a high order commensurate phase with 30 atoms in the unit cell. From the
measurement of the island diffraction peak profiles we find a power law for the
mean island - size versus coverage with an exponent . A
scaling behavior of growth is confirmed and a simple model describing island
growth is presented. Due to the high degeneracy of the monolayer phase,
different islands do not diffract coherently. Therefore, when islands merge
they still diffract as separate islands and coalescence effects are thus
negligible. From the result for we conclude that the island density is
approximately a constant in the coverage range where the
ordered islands are observed. We thus conclude that most islands nucleate at
and then grow in an approximately self similar fashion as
increases.Comment: 23 pages, 10 Figures (available upon request). SU-PHYS-93-443-375
Adiabatic description of nonspherical quantum dot models
Within the effective mass approximation an adiabatic description of
spheroidal and dumbbell quantum dot models in the regime of strong dimensional
quantization is presented using the expansion of the wave function in
appropriate sets of single-parameter basis functions. The comparison is given
and the peculiarities are considered for spectral and optical characteristics
of the models with axially symmetric confining potentials depending on their
geometric size making use of the total sets of exact and adiabatic quantum
numbers in appropriate analytic approximations