103 research outputs found
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.
Memory Function versus Binary Correlator in Additive Markov Chains
We study properties of the additive binary Markov chain with short and
long-range correlations. A new approach is suggested that allows one to express
global statistical properties of a binary chain in terms of the so-called
memory function. The latter is directly connected with the pair correlator of a
chain via the integral equation that is analyzed in great detail. To elucidate
the relation between the memory function and pair correlator, some specific
cases were considered that may have important applications in different fields.Comment: 31 pages, 1 figur
One-dimensional tight-binding models with correlated diagonal and off-diagonal disorder
We study localization properties of electronic states in one-dimensional
lattices with nearest-neighbour interaction. Both the site energies and the
hopping amplitudes are supposed to be of arbitrary form. A few cases are
considered in details. We discuss first the case in which both the diagonal
potential and the fluctuating part of the hopping amplitudes are small. In this
case we derive a general analytical expression for the localization length,
which depends on the pair correlators of the diagonal and off-diagonal matrix
elements. The second case we investigate is that of strong uncorrelated
disorder, for which approximate analytical estimates are given and compared
with numerical data. Finally, we study the model with short-range correlations
which constitutes an extension with off-diagonal disorder of the random dimer
model.Comment: 11 pages, 7 EPS figures; submitted to "Physica E
Electronic states and transport properties in the Kronig-Penney model with correlated compositional and structural disorder
We study the structure of the electronic states and the transport properties
of a Kronig-Penney model with weak compositional and structural disorder. Using
a perturbative approach we obtain an analytical expression for the localisation
length which is valid for disorder with arbitrary correlations. We show how to
generate disorder with self- and cross-correlations and we analyse both the
known delocalisation effects of the long-range self-correlations and new
effects produced by cross-correlations. We finally discuss how both kinds of
correlations alter the transport properties in Kronig-Penney models of finite
size.Comment: 23 pages, 5 figure
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
Spreading and localization of wavepackets in disordered wires in a magnetic field
We study the diffusive and localization properties of wavepackets in
disordered wires in a magnetic field. In contrast to a recent supersymmetry
approach our numerical results show that the decay rate of the steady state
changes {\em smoothly} at the crossover from preserved to broken time-reversal
symmetry. Scaling and fluctuation properties are also analyzed and a formula,
which was derived analytically only in the pure symmetry cases is shown to
describe also the steady state wavefunction at the crossover regime. Finally,
we present a scaling for the variance of the packet which shows again a smooth
transition due to the magnetic field.Comment: 4 pages, 4 figure
Single-Pulse Preparation of the Uniform Superpositional State used in Quantum Algorithms
We examine a single-pulse preparation of the uniform superpositional wave
function, which includes all basis states, in a spin quantum computer. The
effective energy spectrum and the errors generated by this pulse are studied in
detail. We show that, in spite of the finite width of the energy spectrum
bands, amplitude and phase errors can be made reasonably small.Comment: RevTex, 5 pages, 7 eps figure
Quantum Arnol'd diffusion in a rippled waveguide
We study the quantum Arnol'd diffusion for a particle moving in a quasi-1D
waveguide bounded by a periodically rippled surface, in the presence of the
time-periodic electric field. It was found that in a deep semiclassical region
the diffusion-like motion occurs for a particle in the region corresponding to
a stochastic layer surrounding the coupling resonance. The rate of the quantum
diffusion turns out to be less than the corresponding classical one, thus
indicating the influence of quantum coherent effects. Another result is that
even in the case when such a diffusion is possible, it terminates in time due
to the mechanism similar to that of the dynamical localization. The quantum
Arnol'd diffusion represents a new type of quantum dynamics, and may be
experimentally observed in measurements of a conductivity of low-dimensional
mesoscopic structures.Comment: 13 pages, 3 figure
On the Spectrum of the Resonant Quantum Kicked Rotor
It is proven that none of the bands in the quasi-energy spectrum of the
Quantum Kicked Rotor is flat at any primitive resonance of any order.
Perturbative estimates of bandwidths at small kick strength are established for
the case of primitive resonances of prime order. Different bands scale with
different powers of the kick strength, due to degeneracies in the spectrum of
the free rotor.Comment: Description of related published work has been expanded in the
Introductio
Dynamical Origin of Decoherence in Clasically Chaotic Systems
The decay of the overlap between a wave packet evolved with a Hamiltonian H
and the same state evolved with H}+ serves as a measure of the
decoherence time . Recent experimental and analytical evidence on
classically chaotic systems suggest that, under certain conditions,
depends on H but not on . By solving numerically a
Hamiltonian model we find evidence of that property provided that the system
shows a Wigner-Dyson spectrum (which defines quantum chaos) and the
perturbation exceeds a crytical value defined by the parametric correlations of
the spectra.Comment: Typos corrected, published versio
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