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