Spectral Properties and Synchronization in Coupled Map Lattices

Spectral properties of Coupled Map Lattices are described. Conditions for the stability of spatially homogeneous chaotic solutions are derived using linear stability analysis. Global stability analysis results are also presented. The analytical results are supplemented with numerical examples. The quadratic map is used for the site dynamics with different coupling schemes such as global coupling, nearest neighbor coupling, intermediate range coupling, random coupling, small world coupling and scale free coupling.Comment: 10 pages with 15 figures (Postscript), REVTEX format. To appear in PR

Some generic aspects of bosonic excitations in disordered systems

We consider non-interacting bosonic excitations in disordered systems, emphasising generic features of quadratic Hamiltonians in the absence of Goldstone modes. We discuss relationships between such Hamiltonians and the symmetry classes established for fermionic systems. We examine the density \rho(\omega) of excitation frequencies \omega, showing how the universal behavior \rho(\omega) ~ \omega^4 for small \omega can be obtained both from general arguments and by detailed calculations for one-dimensional models

Synchronisation in Coupled Sine Circle Maps

We study the spatially synchronized and temporally periodic solutions of a 1-d lattice of coupled sine circle maps. We carry out an analytic stability analysis of this spatially synchronized and temporally periodic case and obtain the stability matrix in a neat block diagonal form. We find spatially synchronized behaviour over a substantial range of parameter space. We have also extended the analysis to higher spatial periods with similar results. Numerical simulations for various temporal periods of the synchronized solution, reveal that the entire structure of the Arnold tongues and the devil's staircase seen in the case of the single circle map can also be observed for the synchronized coupled sine circle map lattice. Our formalism should be useful in the study of spatially periodic behaviour in other coupled map lattices.Comment: uuencoded, 1 rextex file 14 pages, 3 postscript figure

Is the structure of 42Si understood?

A more detailed test of the implementation of nuclear forces that drive shell evolution in the pivotal nucleus \nuc{42}{Si} -- going beyond earlier comparisons of excited-state energies -- is important. The two leading shell-model effective interactions, SDPF-MU and SDPF-U-Si, both of which reproduce the low-lying \nuc{42}{Si}($2^+_1$) energy, but whose predictions for other observables differ significantly, are interrogated by the population of states in neutron-rich \nuc{42}{Si} with a one-proton removal reaction from \nuc{43}{P} projectiles at 81~MeV/nucleon. The measured cross sections to the individual \nuc{42}{Si} final states are compared to calculations that combine eikonal reaction dynamics with these shell-model nuclear structure overlaps. The differences in the two shell-model descriptions are examined and linked to predicted low-lying excited $0^+$ states and shape coexistence. Based on the present data, which are in better agreement with the SDPF-MU calculations, the state observed at 2150(13)~keV in \nuc{42}{Si} is proposed to be the ($0^+_2$) level.Comment: accepted in Physical Review Letter

Population of neutron unbound states via two-proton knockout reactions

The two-proton knockout reaction 9Be(26Ne,O2p) was used to explore excited unbound states of 23O and 24O. In 23O a state at an excitation energy of 2.79(13) MeV was observed. There was no conclusive evidence for the population of excited states in 24O.Comment: 6 pages, 3 figures, Proc. 9th Int. Spring Seminar on Nucl. Phys. Changing Facets of Nuclear Structure, May 20-34, 200

Griffiths effects and quantum critical points in dirty superconductors without spin-rotation invariance: One-dimensional examples

We introduce a strong-disorder renormalization group (RG) approach suitable for investigating the quasiparticle excitations of disordered superconductors in which the quasiparticle spin is not conserved. We analyze one-dimensional models with this RG and with elementary transfer matrix methods. We find that such models with broken spin rotation invariance {\it generically} lie in one of two topologically distinct localized phases. Close enough to the critical point separating the two phases, the system has a power-law divergent low-energy density of states (with a non-universal continuously varying power-law) in either phase, due to quantum Griffiths singularities. This critical point belongs to the same infinite-disorder universality class as the one dimensional particle-hole symmetric Anderson localization problem, while the Griffiths phases in the vicinity of the transition are controlled by lines of strong (but not infinite) disorder fixed points terminating in the critical point.Comment: 14 pages (two-column PRB format), 9 eps figure

Coupled Maps on Trees

We study coupled maps on a Cayley tree, with local (nearest-neighbor) interactions, and with a variety of boundary conditions. The homogeneous state (where every lattice site has the same value) and the node-synchronized state (where sites of a given generation have the same value) are both shown to occur for particular values of the parameters and coupling constants. We study the stability of these states and their domains of attraction. As the number of sites that become synchronized is much higher compared to that on a regular lattice, control is easier to effect. A general procedure is given to deduce the eigenvalue spectrum for these states. Perturbations of the synchronized state lead to different spatio-temporal structures. We find that a mean-field like treatment is valid on this (effectively infinite dimensional) lattice.Comment: latex file (25 pages), 4 figures included. To be published in Phys. Rev.

Exploring Neutron-Rich Oxygen Isotopes with MoNA

The Modular Neutron Array (MoNA) was used in conjunction with a large-gap dipole magnet (Sweeper) to measure neutron-unbound states in oxygen isotopes close to the neutron dripline. While no excited states were observed in 24O, a resonance at 45(2) keV above the neutron separation energy was observed in 23O.Comment: 6 pages, 4 Figures, submitted to Proc. Int. Conf. on Proton Emitting Nuclei and Related Topics, PROCON0

Energy distributions from three-body decaying many-body resonances

We compute energy distributions of three particles emerging from decaying many-body resonances. We reproduce the measured energy distributions from decays of two archetypal states chosen as the lowest $0^{+}$ and $1^{+}$-resonances in $^{12}$C populated in $\beta$-decays. These states are dominated by sequential, through the $^{8}$Be ground state, and direct decays, respectively. These decay mechanisms are reflected in the ``dynamic'' evolution from small, cluster or shell-model states, to large distances, where the coordinate or momentum space continuum wavefunctions are accurately computed.Comment: 4 pages, 4 figures. Accepted for publication in Physical Review Letter