114 research outputs found
Isolated resonances in conductance fluctuations in ballistic billiards
We study numerically quantum transport through a billiard with a classically
mixed phase space. In particular, we calculate the conductance and Wigner delay
time by employing a recursive Green's function method. We find sharp, isolated
resonances with a broad distribution of resonance widths in both the
conductance and the Wigner time, in contrast to the well-known smooth
conductance fluctuations of completely chaotic billiards. In order to elucidate
the origin of the isolated resonances, we calculate the associated scattering
states as well as the eigenstates of the corresponding closed system. As a
result, we find a one-to-one correspondence between the resonant scattering
states and eigenstates of the closed system. The broad distribution of
resonance widths is traced to the structure of the classical phase space.
Husimi representations of the resonant scattering states show a strong overlap
either with the regular regions in phase space or with the hierarchical parts
surrounding the regular regions. We are thus lead to a classification of the
resonant states into regular and hierarchical, depending on their phase space
portrait.Comment: 2 pages, 5 figures, to be published in J. Phys. Soc. Jpn.,
proceedings Localisation 2002 (Tokyo, Japan
Universal Power-law Decay in Hamiltonian Systems?
The understanding of the asymptotic decay of correlations and of the
distribution of Poincar\'e recurrence times has been a major challenge
in the field of Hamiltonian chaos for more than two decades. In a recent
Letter, Chirikov and Shepelyansky claimed the universal decay for Hamiltonian systems. Their reasoning is based on renormalization
arguments and numerical findings for the sticking of chaotic trajectories near
a critical golden torus in the standard map. We performed extensive numerics
and find clear deviations from the predicted asymptotic exponent of the decay
of . We thereby demonstrate that even in the supposedly simple case, when
a critical golden torus is present, the fundamental question of asymptotic
statistics in Hamiltonian systems remains unsolved.Comment: Phys. Rev. Lett., in pres
Efficient Diagonalization of Kicked Quantum Systems
We show that the time evolution operator of kicked quantum systems, although
a full matrix of size NxN, can be diagonalized with the help of a new method
based on a suitable combination of fast Fourier transform and Lanczos algorithm
in just N^2 ln(N) operations. It allows the diagonalization of matrizes of
sizes up to N\approx 10^6 going far beyond the possibilities of standard
diagonalization techniques which need O(N^3) operations. We have applied this
method to the kicked Harper model revealing its intricate spectral properties.Comment: Text reorganized; part on the kicked Harper model extended. 13 pages
RevTex, 1 figur
Metal-insulator transitions in cyclotron resonance of periodic nanostructures due to avoided band crossings
A recently found metal-insulator transition in a model for cyclotron
resonance in a two-dimensional periodic potential is investigated by means of
spectral properties of the time evolution operator. The previously found
dynamical signatures of the transition are explained in terms of avoided band
crossings due to the change of the external electric field. The occurrence of a
cross-like transport is predicted and numerically confirmed
Dimer Decimation and Intricately Nested Localized-Ballistic Phases of Kicked Harper
Dimer decimation scheme is introduced in order to study the kicked quantum
systems exhibiting localization transition. The tight-binding representation of
the model is mapped to a vectorized dimer where an asymptotic dissociation of
the dimer is shown to correspond to the vanishing of the transmission
coefficient thru the system. The method unveils an intricate nesting of
extended and localized phases in two-dimensional parameter space. In addition
to computing transport characteristics with extremely high precision, the
renormalization tools also provide a new method to compute quasienergy
spectrum.Comment: There are five postscript figures. Only half of the figure (3) is
shown to reduce file size. However, missing part is the mirror image of the
part show
Quenched and Negative Hall Effect in Periodic Media: Application to Antidot Superlattices
We find the counterintuitive result that electrons move in OPPOSITE direction
to the free electron E x B - drift when subject to a two-dimensional periodic
potential. We show that this phenomenon arises from chaotic channeling
trajectories and by a subtle mechanism leads to a NEGATIVE value of the Hall
resistivity for small magnetic fields. The effect is present also in
experimentally recorded Hall curves in antidot arrays on semiconductor
heterojunctions but so far has remained unexplained.Comment: 10 pages, 4 figs on request, RevTeX3.0, Europhysics Letters, in pres
Quantum Diffusion in Separable d-Dimensional Quasiperiodic Tilings
We study the electronic transport in quasiperiodic separable tight-binding
models in one, two, and three dimensions. First, we investigate a
one-dimensional quasiperiodic chain, in which the atoms are coupled by weak and
strong bonds aligned according to the Fibonacci chain. The associated
d-dimensional quasiperiodic tilings are constructed from the product of d such
chains, which yields either the square/cubic Fibonacci tiling or the labyrinth
tiling. We study the scaling behavior of the mean square displacement and the
return probability of wave packets with respect to time. We also discuss
results of renormalization group approaches and lower bounds for the scaling
exponent of the width of the wave packet.Comment: 6 pages, 4 figures, conference proceedings Aperiodic 2012 (Cairns
Dynamical tunneling in mushroom billiards
We study the fundamental question of dynamical tunneling in generic
two-dimensional Hamiltonian systems by considering regular-to-chaotic tunneling
rates. Experimentally, we use microwave spectra to investigate a mushroom
billiard with adjustable foot height. Numerically, we obtain tunneling rates
from high precision eigenvalues using the improved method of particular
solutions. Analytically, a prediction is given by extending an approach using a
fictitious integrable system to billiards. In contrast to previous approaches
for billiards, we find agreement with experimental and numerical data without
any free parameter.Comment: 4 pages, 4 figure
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