Jezbera, Daniel, Kordek, David, Kriz, Jan, Seba, Petr, Sroll, Petr
We demonstrate experimentally that the statistical properties of distances between pedestrians that are hindered from foregoing each other are described by the Gaussian Unitary Ensemble of random...
Hul, Oleh, Seba, Petr, Sirko, Leszek
Parameter-dependent statistical properties of spectra of totally connected irregular quantum graphs with Neumann boundary conditions are studied. The autocorrelation functions of level velocities...
Traffic and the visual perception of space (2009)
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...
Lawniczak, Michal, Hul, Oleh, Bauch, Szymon, Seba, Petr, Sirko, Leszek
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...
Spectral rigidity of vehicular streams (Random Matrix Theory approach) (2008)
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...
Chaos in a one-dimensional integrable quantum system (2008)
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...
Spectral Density of Sample Covariance Matrices of Colored Noise (2008)
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...
Parking in the city: an example of limited resource sharing (2008)
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...
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...
Statistical variances in traffic data (2006)
We perform statistical analysis of the single-vehicle data measured on the Dutch freeway A9 and discussed in Ref. [2]. Using tools originating from the Random Matrix Theory we show that the...
Approximations by graphs and emergence of global structures (2005)
Exner, Pavel, Hejcik, Pavel, Seba, Petr
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...
Metastable Congested States in Multisegment Traffic Cellular Automaton (2005)
Nishimura, Yutaka, Cheon, Taksu, Seba, Petr
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...
Physics, Stability and Dynamics of Supply Networks (2004)
Helbing, Dirk, Lammer, Stefan, Seidel, Thomas, Seba, Petr, Platkowski, Tadeusz
We show how to treat supply networks as physical transport problems governed by balance equations and equations for the adaptation of production speeds. Although the non-linear behaviour is...
Extended Standard Map with Spatio-Temporal Asymmetry (2002)
Cheon, Taksu, Exner, Pavel, Seba, Petr
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...
Resonances of the Frobenius-Perron Operator for a Hamiltonian Map with a Mixed Phase Space (2001)
Weber, Joachim, Haake, Fritz, Braun, Petr A., Manderfeld, Christopher, Seba, Petr
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...
Effective Coupling for Open Billiards (2001)
Pichugin, Konstantin, Schanz, Holger, Seba, Petr
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...
Wave Function Shredding by Sparse Quantum Barriers (2000)
Cheon, Taksu, Exner, Pavel, Seba, Petr
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...
Frobenius-Perron Resonances for Maps with a Mixed Phase Space (2000)
Weber, Joachim, Haake, Fritz, Seba, Petr
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...
Quantum scattering in the strip: from ballistic to localized regimes (1998)
Gebarowski, Robert, Seba, Petr, Zyczkowski, Karol, Zakrzewski, Jakub
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...
Random matrix approach to `nonuniversal' conductance (1997)
Seba, Petr, Zyczkowski, Karol, Zakrzewski, Jakub
Recent experiments on the conductance of high quality quantum wires have revealed an unexpected feature: the quantization step of the conductance is apparently system dependent. We provide the...
Probability current tornado loops in three-dimensional scattering (1997)
We consider scattering of a three-dimensional particle on a finite family of delta potentials. For some parameter values the scattering wavenctions exhibit nodal lines in the form of closed loops,...
Statistical properties of random scattering matrices (1996)
Seba, Petr, Zyczkowski, Karol, Zakrzewski, Jakub
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...