Wave Function Shredding by Sparse Quantum Barriers

We discuss a model in which a quantum particle passes through $\delta$ potentials arranged in an increasingly sparse way. For infinitely many barriers we derive conditions, expressed in terms ergodic properties of wave function phases, which ensure that the point and absolutely continuous parts are absent leaving a purely singularly continuous spectrum. For a finite number of barriers, the transmission coefficient shows extreme sensitivity to the particle momentum with fluctuation in many different scales. We discuss a potential application of this behavior for erasing the information carried by the wave function.Comment: 4 pages ReVTeX with 3 epsf figure

Built-up structure criticality

The built-up land represents an important type of overall landscape. In this paper the built-up land structure in the largest cities in the Czech Republic and selected cities in the U.S.A. is analysed using the framework of statistical physics. We calculate the variance of the built-up area and the number variance of built-up landed plots in discs. In both cases the variance as a function of a disc radius follows a power law. The obtained values of power law exponents are comparable through different cities. The study is based on cadastral data from the Czech Republic and building footprints from GIS data in the U.S.A.Comment: 14 pages, 11 figure

Approximations by graphs and emergence of global structures

We study approximations of billiard systems by lattice graphs. It is demonstrated that under natural assumptions the graph wavefunctions approximate solutions of the Schroedinger equation with energy rescaled by the billiard dimension. As an example, we analyze a Sinai billiard with attached leads. The results illustrate emergence of global structures in large quantum graphs and offer interesting comparisons with patterns observed in complex networks of a different nature.Comment: 6 pages, RevTeX with 5 ps figure

The distribution of landed property

The distribution of property is established through various mechanisms. In this paper we study the acreage distribution of land plots owned by natural persons in the Zl\'{\i}n Region of the Czech Republic. We show that the data are explained in terms of a simple model in which the inheritance and market behavior are combined.Comment: The distribution of landed propert

Chaos in a one-dimensional integrable quantum system

We study a simple one-dimensional quantum system on a circle with n scale free point interactions. The spectrum of this system is discrete and expressible as a solution of an explicit secular equation. However, its statistical properties are nontrivial. The level spacing distribution between its neighboring odd and even levels displays a surprising agreement with the prediction obtained for the Gaussian Orthogonal Ensemble of random matrices.Comment: 11 pages, 5 figure

Parking and the visual perception of space

Using measured data we demonstrate that there is an amazing correspondence among the statistical properties of spacings between parked cars and the distances between birds perching on a power line. We show that this observation is easily explained by the fact that birds and human use the same mechanism of distance estimation. We give a simple mathematical model of this phenomenon and prove its validity using measured data

Effective Coupling for Open Billiards

We derive an explicit expression for the coupling constants of individual eigenstates of a closed billiard which is opened by attaching a waveguide. The Wigner time delay and the resonance positions resulting from the coupling constants are compared to an exact numerical calculation. Deviations can be attributed to evanescent modes in the waveguide and to the finite number of eigenstates taken into account. The influence of the shape of the billiard and of the boundary conditions at the mouth of the waveguide are also discussed. Finally we show that the mean value of the dimensionless coupling constants tends to the critical value when the eigenstates of the billiard follow random-matrix theory

Frobenius-Perron Resonances for Maps with a Mixed Phase Space

Resonances of the time evolution (Frobenius-Perron) operator P for phase space densities have recently been shown to play a key role for the interrelations of classical, semiclassical and quantum dynamics. Efficient methods to determine resonances are thus in demand, in particular for Hamiltonian systems displaying a mix of chaotic and regular behavior. We present a powerful method based on truncating P to a finite matrix which not only allows to identify resonances but also the associated phase space structures. It is demonstrated to work well for a prototypical dynamical system.Comment: 5 pages, 2 figures, 2nd version as published (minor changes

Force plate monitoring of human hemodynamics

which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Background: Noninvasive recording of movements caused by the heartbeat and the blood circulation is known as ballistocardiography. Several studies have shown the capability of a force plate to detect cardiac activity in the human body. The aim of this paper is to present a new method based on differential geometry of curves to handle multivariate time series obtained by ballistocardiographic force plate measurements. Results: We show that the recoils of the body caused by cardiac motion and blood circulation provide a noninvasive method of displaying the motions of the heart muscle and the propagation of the pulse wave along the aorta and its branches. The results are compared with the data obtained invasively during a cardiac catheterization. We show that the described noninvasive method is able to determine the moment of a particular heart movement or the time when the pulse wave reaches certain morphological structure. Conclusions: Monitoring of heart movements and pulse wave propagation may be used e.g. to estimate the aortic pulse wave velocity, which is widely accepted as an index of aortic stiffness wit