Magnetic translation groups as group extension

Extensions of a direct product T of two cyclic groups Z_n1 and Z_n2 by an Abelian (gauge) group G with the trivial action of T on G are considered. All possible (nonequivalent) factor systems are determined using the Mac Lane method. Some of resulting groups describe magnetic translation groups. As examples extensions with G=U(1) and G=Z_n are considered and discussed.Comment: 10 page

Dynamics of a localized spin excitation close to the spin-helix regime

The time evolution of a local spin excitation in a (001)-confined two-dimensional electron gas subjected to Rashba and Dresselhaus spin-orbit interactions of similar strength is investigated theoretically and compared with experimental data. Specifically, the consequences of the finite spatial extension of the initial spin polarization is studied for non-balanced Rashba and Dresselhaus terms and for finite cubic Dresselhaus spin-orbit interaction. We show that the initial out-of-plane spin polarization evolves into a helical spin pattern with a wave number that gradually approaches the value $q_0$ of the persistent spin helix mode. In addition to an exponential decay of the spin polarization that is proportional to both the spin-orbit imbalance and the cubic Dresselhaus term, the finite width $w$ of the spin excitation reduces the spin polarization by a factor that approaches $\exp(-q_0^2 w^2/2)$ at longer times.Comment: 8 pages, 7 figure

Characterizing Weak Chaos using Time Series of Lyapunov Exponents

We investigate chaos in mixed-phase-space Hamiltonian systems using time series of the finite- time Lyapunov exponents. The methodology we propose uses the number of Lyapunov exponents close to zero to define regimes of ordered (stickiness), semi-ordered (or semi-chaotic), and strongly chaotic motion. The dynamics is then investigated looking at the consecutive time spent in each regime, the transition between different regimes, and the regions in the phase-space associated to them. Applying our methodology to a chain of coupled standard maps we obtain: (i) that it allows for an improved numerical characterization of stickiness in high-dimensional Hamiltonian systems, when compared to the previous analyses based on the distribution of recurrence times; (ii) that the transition probabilities between different regimes are determined by the phase-space volume associated to the corresponding regions; (iii) the dependence of the Lyapunov exponents with the coupling strength.Comment: 8 pages, 6 figure

Re-Examination of Possible Bimodality of GALLEX Solar Neutrino Data

The histogram formed from published capture-rate measurements for the GALLEX solar neutrino experiment is bimodal, showing two distinct peaks. On the other hand, the histogram formed from published measurements derived from the similar GNO experiment is unimodal, showing only one peak. However, the two experiments differ in run durations: GALLEX runs are either three weeks or four weeks (approximately) in duration, whereas GNO runs are all about four weeks in duration. When we form 3-week and 4-week subsets of the GALLEX data, we find that the relevant histograms are unimodal. The upper peak arises mainly from the 3-week runs, and the lower peak from the 4-week runs. The 4-week subset of the GALLEX dataset is found to be similar to the GNO dataset. A recent re-analysis of GALLEX data leads to a unimodal histogram.Comment: 14 pages, 8 figure

Noise-enhanced trapping in chaotic scattering

We show that noise enhances the trapping of trajectories in scattering systems. In fully chaotic systems, the decay rate can decrease with increasing noise due to a generic mismatch between the noiseless escape rate and the value predicted by the Liouville measure of the exit set. In Hamiltonian systems with mixed phase space we show that noise leads to a slower algebraic decay due to trajectories performing a random walk inside Kolmogorov-Arnold-Moser islands. We argue that these noise-enhanced trapping mechanisms exist in most scattering systems and are likely to be dominant for small noise intensities, which is confirmed through a detailed investigation in the Henon map. Our results can be tested in fluid experiments, affect the fractal Weyl's law of quantum systems, and modify the estimations of chemical reaction rates based on phase-space transition state theory.Comment: 5 pages, 5 figure