Scaling Invariance in a Time-Dependent Elliptical Billiard

We study some dynamical properties of a classical time-dependent elliptical billiard. We consider periodically moving boundary and collisions between the particle and the boundary are assumed to be elastic. Our results confirm that although the static elliptical billiard is an integrable system, after to introduce time-dependent perturbation on the boundary the unlimited energy growth is observed. The behaviour of the average velocity is described using scaling arguments

Separating the regular and irregular energy levels and their statistics in Hamiltonian system with mixed classical dynamics

We look at the high-lying eigenstates (from the 10,001st to the 13,000th) in the Robnik billiard (defined as a quadratic conformal map of the unit disk) with the shape parameter $\lambda=0.15$. All the 3,000 eigenstates have been numerically calculated and examined in the configuration space and in the phase space which - in comparison with the classical phase space - enabled a clear cut classification of energy levels into regular and irregular. This is the first successful separation of energy levels based on purely dynamical rather than special geometrical symmetry properties. We calculate the fractional measure of regular levels as $\rho_1=0.365\pm 0.01$ which is in remarkable agreement with the classical estimate $\rho_1=0.360\pm 0.001$. This finding confirms the Percival's (1973) classification scheme, the assumption in Berry-Robnik (1984) theory and the rigorous result by Lazutkin (1981,1991). The regular levels obey the Poissonian statistics quite well whereas the irregular sequence exhibits the fractional power law level repulsion and globally Brody-like statistics with $\beta = 0.286\pm0.001$. This is due to the strong localization of irregular eigenstates in the classically chaotic regions. Therefore in the entire spectrum we see that the Berry-Robnik regime is not yet fully established so that the level spacing distribution is correctly captured by the Berry-Robnik-Brody distribution (Prosen and Robnik 1994).Comment: 20 pages, file in plain LaTeX, 7 figures upon request submitted to J. Phys. A. Math. Gen. in December 199

Electron energy level statistics in graphene quantum dots

Motivated by recent experimental observations of size quantization of electron energy levels in graphene quantum dots \cite{ponomarenko} we investigate the level statistics in the simplest tight-binding model for different dot shapes by computer simulation. The results are in a reasonable agreement with the experiment which confirms qualitatively interpretation of observed level statistics in terms of "Dirac billiards" without taking into account many-body effects. It is shown that edge effects are in general sufficient to produce the observed level distribution and that even strong bulk disorder does not change the results drastically.Comment: Published: Pis'ma v ZhETF, vol. 88, iss. 9, pp. 698 -- 701 (2008

Proučavanje 194Ir uhvatom termičkih neutrona I (d, p) reakcijom

Levels of 194Ir were studied using thermal neutron capture reaction. A pair spectrometer was used to measure the high-energy γ-ray spectrum from thermal-neutron capture in enriched 193Ir target over the energy range 4640 - 6100 keV. The low-energy γ-radiation from the reaction was studied with crystal diffraction spectrometers, and conversion electrons were observed with magnetic spectrometers. The high-sensitivity measurements at the Grenoble reactor, evaluated for transition energies up to 500 keV, are compared with lower-sensitivity measurements at the Wuerenlingen and Salaspils reactors. The comparison helped to obtain reliable isotopic identification for a number of 194Ir lines. The multipolarity admixtures for 29 γ-transitions were determined on the basis of conversion lines from different electron subshells. Prompt and delayed γ-γ coincidences were measured using semiconductor and scintillation detectors. The 193Ir(d,p) high-resolution spectra, observed with a magnetic spectrometer, are given. All these data contributed to establishing a detailed level scheme of 194Ir. Additional data and the interpretation of the results in terms of current models will be presented in a forthcoming paper.Proučavala su se stanja u 194Ir reakcijama 193Ir(n, γ) i 193Ir(d, p). Mjerenja uhvata termičkih neutrona načinjena su uz reaktore u Grenoblu, Wuerenlingenu i Salapsisu. Za mjerenja γ-zračenja visoke energije upotrebljavao se spektrometar parova, a za niske energije difraktometar. Konverzijske elektrone se mjerilo magnetskim spektrometrom. Mjerenja reakcije (d, p) visokog razlučivanja izvedena su magnetskim spektrometrom. Usporedbe tih mjerenja omogućile su pouzdano izotopno prepoznavanje prijelaza u 194 Ir, a spektri konverzijskih elektrona i određivanje multipolnosti prijelaza. Dobiveni su podaci osnova sheme raspada 194Ir

Proučavanje 194Ir uhvatom termičkih neutrona I (d, p) reakcijom

Levels of 194Ir were studied using thermal neutron capture reaction. A pair spectrometer was used to measure the high-energy γ-ray spectrum from thermal-neutron capture in enriched 193Ir target over the energy range 4640 - 6100 keV. The low-energy γ-radiation from the reaction was studied with crystal diffraction spectrometers, and conversion electrons were observed with magnetic spectrometers. The high-sensitivity measurements at the Grenoble reactor, evaluated for transition energies up to 500 keV, are compared with lower-sensitivity measurements at the Wuerenlingen and Salaspils reactors. The comparison helped to obtain reliable isotopic identification for a number of 194Ir lines. The multipolarity admixtures for 29 γ-transitions were determined on the basis of conversion lines from different electron subshells. Prompt and delayed γ-γ coincidences were measured using semiconductor and scintillation detectors. The 193Ir(d,p) high-resolution spectra, observed with a magnetic spectrometer, are given. All these data contributed to establishing a detailed level scheme of 194Ir. Additional data and the interpretation of the results in terms of current models will be presented in a forthcoming paper.Proučavala su se stanja u 194Ir reakcijama 193Ir(n, γ) i 193Ir(d, p). Mjerenja uhvata termičkih neutrona načinjena su uz reaktore u Grenoblu, Wuerenlingenu i Salapsisu. Za mjerenja γ-zračenja visoke energije upotrebljavao se spektrometar parova, a za niske energije difraktometar. Konverzijske elektrone se mjerilo magnetskim spektrometrom. Mjerenja reakcije (d, p) visokog razlučivanja izvedena su magnetskim spektrometrom. Usporedbe tih mjerenja omogućile su pouzdano izotopno prepoznavanje prijelaza u 194 Ir, a spektri konverzijskih elektrona i određivanje multipolnosti prijelaza. Dobiveni su podaci osnova sheme raspada 194Ir