105 research outputs found

### Crossover from Regular to Chaotic Behavior in the Conductance of Periodic Quantum Chains

The conductance of a waveguide containing finite number of periodically
placed identical point-like impurities is investigated. It has been calculated
as a function of both the impurity strength and the number of impurities using
the Landauer-B\"uttiker formula. In the case of few impurities the conductance
is proportional to the number of the open channels $N$ of the empty waveguide
and shows a regular staircase like behavior with step heights $\approx 2e^2/h$.
For large number of impurities the influence of the band structure of the
infinite periodic chain can be observed and the conductance is approximately
the number of energy bands (smaller than $N$) times the universal constant
$2e^2/h$. This lower value is reached exponentially with increasing number of
impurities. As the strength of the impurity is increased the system passes from
integrable to quantum-chaotic. The conductance, in units of $2e^2/h$, changes
from $N$ corresponding to the empty waveguide to $\sim N/2$ corresponding to
chaotic or disordered system. It turnes out, that the conductance can be
expressed as $(1-c/2)N$ where the parameter $0<c<1$ measures the chaoticity of
the system.Comment: 5 pages Revte

### Diffraction in the semiclassical description of mesoscopic devices

In pseudo integrable systems diffractive scattering caused by wedges and
impurities can be described within the framework of Geometric Theory of
Diffraction (GDT) in a way similar to the one used in the Periodic Orbit Theory
of Diffraction (POTD). We derive formulas expressing the reflection and
transition matrix elements for one and many diffractive points and apply it for
impurity and wedge diffraction. Diffraction can cause backscattering in
situations, where usual semiclassical backscattering is absent causing an
erodation of ideal conductance steps. The length of diffractive periodic orbits
and diffractive loops can be detected in the power spectrum of the reflection
matrix elements. The tail of the power spectrum shows $\sim 1/l^{1/2}$ decay
due to impurity scattering and $\sim 1/l^{3/2}$ decay due to wedge scattering.
We think this is a universal sign of the presence of diffractive scattering in
pseudo integrable waveguides.Comment: 18 pages, Latex , ep

### Spectral Determinant Method for Interacting N-body Systems Including Impurities

A general expression for the Green's function of a system of $N$ particles
(bosons/fermions) interacting by contact potentials, including impurities with
Dirac-delta type potentials is derived. In one dimension for $N>2$ bosons from
our {\it spectral determinant method} the numerically calculated energy levels
agree very well with those obtained from the exact Bethe ansatz solutions while
they are an order of magnitude more accurate than those found by direct
diagonalization. For N=2 bosons the agreement is shown analytically. In the
case of N=2 interacting bosons and one impurity, the energy levels are
calculated numerically from the spectral determinant of the system. The
spectral determinant method is applied to an interacting fermion system
including an impurity to calculate the persistent current at the presence of
magnetic field.Comment: revtex, 19 pages, 4 figure

### Turbulent helium gas cell as a new paradigm of daily meteorological fluctuations?

We compare the spectral properties of long meteorological temperature records
with laboratory measurements in small convection cells. Surprisingly, the
atmospheric boundary layer sampled on a daily scale shares the statistical
properties of temperature fluctuations in small-scale experiments. This fact
can be explained by the hydrodynamical similarity between these seemingly very
different systems. The results suggest that the dynamics of daily temperature
fluctuations is determined by the soft turbulent state of the atmospheric
boundary layer in continental climate.Comment: 10 pages Late

### Inclusion of Diffraction Effects in the Gutzwiller Trace Formula

The Gutzwiller trace formula is extended to include diffraction effects. The
new trace formula involves periodic rays which have non-geometrical segments as
a result of diffraction on the surfaces and edges of the scatter.Comment: 4 pages, LaTeX, 1 ps figur

### Trace formula for noise corrections to trace formulas

We consider an evolution operator for a discrete Langevin equation with a
strongly hyperbolic classical dynamics and Gaussian noise. Using an integral
representation of the evolution operator we investigate the high order
corrections to the trace of arbitary power of the operator.
The asymptotic behaviour is found to be controlled by sub-dominant saddle
points previously neglected in the perturbative expansion. We show that a trace
formula can be derived to describe the high order noise corrections.Comment: 4 pages, 2 figure

### Self-generated Self-similar Traffic

Self-similarity in the network traffic has been studied from several aspects:
both at the user side and at the network side there are many sources of the
long range dependence. Recently some dynamical origins are also identified: the
TCP adaptive congestion avoidance algorithm itself can produce chaotic and long
range dependent throughput behavior, if the loss rate is very high. In this
paper we show that there is a close connection between the static and dynamic
origins of self-similarity: parallel TCPs can generate the self-similarity
themselves, they can introduce heavily fluctuations into the background traffic
and produce high effective loss rate causing a long range dependent TCP flow,
however, the dropped packet ratio is low.Comment: 8 pages, 12 Postscript figures, accepted in Nonlinear Phenomena in
Complex System

### Transition from Poissonian to GOE level statistics in a modified Artin's billiard

One wall of Artin's billiard on the Poincar\'e half plane is replaced by a
one-parameter ($c_p$) family of nongeodetic walls. A brief description of the
classical phase space of this system is given. In the quantum domain, the
continuousand gradual transition from the Poisson like to GOE level statistics
due to the small perturbations breaking the symmetry responsible for the
'arithmetic chaos' at $c_p=1$ is studied. Another GOE \rightrrow Poisson
transition due to the mixed phase space for large perturbations is also
investigated. A satisfactory description of the intermediate level statistics
by the Brody distribution was found in boh cases. The study supports the
existence of a scaling region around $c_p=1$. A finite size scaling relation
for the Brody-parameter as a function of $1-c_p$ and the number of levels
considered can be established

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