Petr Seba
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…
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…
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…
We experimentally demonstrate that the statistical properties of distances between pedestrians which are hindered from avoiding each other are described by the Gaussian Unitary Ensemble of random matrices. The same result has recently been…
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…
We investigate a simple multisegment cellular automaton model of traffic flow. With the introduction of segment-dependent deceleration probability, metastable congested states in the intermediate density region emerge, and the initial state…
Resonances of the (Frobenius-Perron) evolution operator P for phase-space densities have recently attracted considerable attention, in the context of interrelations between classical and quantum dynamics. We determine these resonances as…
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…
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,…
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…
Quantum scattering is studied in a system consisting of randomly distributed point scatterers in the strip. The model is continuous yet exactly solvable. Varying the number of scatterers (the sample length) we investigate a transition…
We discuss the properties of eigenphases of S--matrices in random models simulating classically chaotic scattering. The energy dependence of the eigenphases is investigated and the corresponding velocity and curvature distributions are…
Parameter-dependent statistical properties of spectra of totally connected irregular quantum graphs with Neumann boundary conditions are studied. The autocorrelation functions of level velocities c(x) and c(w,x) as well as the distributions…
During the attempt to line up into a dense traffic people have necessarily to share a limited space under turbulent conditions. From the statistical point view it generally leads to a probability distribution of the distances between the…
We present the results of experimental and numerical study of the distribution of the reflection coefficient P(R) and the distributions of the imaginary P(v) and the real P(u) parts of the Wigner's reaction K matrix for irregular fully…
We analyze the transport properties of a set of symmetry-breaking extensions %, both spatial and temporal, of the Chirikov--Taylor Map. The spatial and temporal asymmetries result in the loss of periodicity in momentum direction in the…
Using the methods originally developed for Random Matrix Theory we derive an exact mathematical formula for number variance (introduced in [4]) describing a rigidity of particle ensembles with power-law repulsion. The resulting relation is…
We study the dependence of the spectral density of the covariance matrix ensemble on the power spectrum of the underlying multivariate signal. The white noise signal leads to the celebrated Marchenko-Pastur formula. We demonstrate results…
During the attempt to park a car in the city the drivers have to share limited resources (the available roadside). We show that this fact leads to a predictable distribution of the distances between the cars that depends on the length of…
We show that the spacing distribution between parked cars can be obtained as a solution of certain linear distributional fixed point equation. The results are compared with the data measured on the streets of Hradec Kralove. We also discuss…