Collective Phase Sensitivity

The collective phase response to a macroscopic external perturbation of a population of interacting nonlinear elements exhibiting collective oscillations is formulated for the case of globally-coupled oscillators. The macroscopic phase sensitivity is derived from the microscopic phase sensitivity of the constituent oscillators by a two-step phase reduction. We apply this result to quantify the stability of the macroscopic common-noise induced synchronization of two uncoupled populations of oscillators undergoing coherent collective oscillations.Comment: 6 pages, 3 figure

On Detection of Black Hole Quasi-Normal Ringdowns: Detection Efficiency and Waveform Parameter Determination in Matched Filtering

Gravitational radiation from a slightly distorted black hole with ringdown waveform is well understood in general relativity. It provides a probe for direct observation of black holes and determination of their physical parameters, masses and angular momenta (Kerr parameters). For ringdown searches using data of gravitational wave detectors, matched filtering technique is useful. In this paper, we describe studies on problems in matched filtering analysis in realistic gravitational wave searches using observational data. Above all, we focus on template constructions, matches or signal-to-noise ratios (SNRs), detection probabilities for Galactic events, and accuracies in evaluation of waveform parameters or black hole hairs. We have performed matched filtering analysis for artificial ringdown signals which are generated with Monte-Carlo technique and injected into the TAMA300 observational data. It is shown that with TAMA300 sensitivity, the detection probability for Galactic ringdown events is about 50% for black holes of masses greater than $20 M_{\odot}$ with SNR $> 10$. The accuracies in waveform parameter estimations are found to be consistent with the template spacings, and resolutions for black hole masses and the Kerr parameters are evaluated as a few % and $\sim 40$, respectively. They can be improved up to $< 0.9$ and $< 24$ for events of ${\rm SNR} \ge 10$ by using fine-meshed template bank in the hierarchical search strategy.Comment: 10 pages, 10 figure

Universal Scaling Properties in Large Assemblies of Simple Dynamical Units Driven by Long-Wave Random Forcing

Large assemblies of nonlinear dynamical units driven by a long-wave fluctuating external field are found to generate strong turbulence with scaling properties. This type of turbulence is so robust that it persists over a finite parameter range with parameter-dependent exponents of singularity, and is insensitive to the specific nature of the dynamical units involved. Whether or not the units are coupled with their neighborhood is also unimportant. It is discovered numerically that the derivative of the field exhibits strong spatial intermittency with multifractal structure.Comment: 10 pages, 7 figures, submitted to PR

Diffusion and activation of n-type dopants in germanium

The diffusion and activation of $n$-type impurities (P and As) implanted into $p$-type Ge(100) substrates were examined under various dose and annealing conditions. The secondary ion mass spectrometry profiles of chemical concentrations indicated the existence of a sufficiently high number of impurities with increasing implanted doses. However, spreading resistance probe profiles of electrical concentrations showed electrical concentration saturation in spite of increasing doses and indicated poor activation of As relative to P in Ge. The relationships between the chemical and electrical concentrations of P in Ge and Si were calculated, taking into account the effect of incomplete ionization. The results indicated that the activation of P was almost the same in Ge and Si. The activation ratios obtained experimentally were similar to the calculated values, implying insufficient degeneration of Ge. The profiles of P in Ge substrates with and without damage generated by Ge ion implantation were compared, and it was clarified that the damage that may compensate the activated $n$-type dopants has no relationship with the activation of P in Ge.Comment: 6 pages, 4 figure

Slow Switching in Globally Coupled Oscillators: Robustness and Occurrence through Delayed Coupling

The phenomenon of slow switching in populations of globally coupled oscillators is discussed. This characteristic collective dynamics, which was first discovered in a particular class of the phase oscillator model, is a result of the formation of a heteroclinic loop connecting a pair of clustered states of the population. We argue that the same behavior can arise in a wider class of oscillator models with the amplitude degree of freedom. We also argue how such heteroclinic loops arise inevitably and persist robustly in a homogeneous population of globally coupled oscillators. Although the heteroclinic loop might seem to arise only exceptionally, we find that it appears rather easily by introducing the time-delay in the population which would otherwise exhibit perfect phase synchrony. We argue that the appearance of the heteroclinic loop induced by the delayed coupling is then characterized by transcritical and saddle-node bifurcations. Slow switching arises when the system with a heteroclinic loop is weakly perturbed. This will be demonstrated with a vector model by applying weak noises. Other types of weak symmetry-breaking perturbations can also cause slow switching.Comment: 10 pages, 14 figures, RevTex, twocolumn, to appear in Phys. Rev.

Effective long-time phase dynamics of limit-cycle oscillators driven by weak colored noise

An effective white-noise Langevin equation is derived that describes long-time phase dynamics of a limit-cycle oscillator subjected to weak stationary colored noise. Effective drift and diffusion coefficients are given in terms of the phase sensitivity of the oscillator and the correlation function of the noise, and are explicitly calculated for oscillators with sinusoidal phase sensitivity functions driven by two typical colored Gaussian processes. The results are verified by numerical simulations using several types of stochastic or chaotic noise. The drift and diffusion coefficients of oscillators driven by chaotic noise exhibit anomalous dependence on the oscillator frequency, reflecting the peculiar power spectrum of the chaotic noise.Comment: 16 pages, 6 figure

Noise-induced Turbulence in Nonlocally Coupled Oscillators

We demonstrate that nonlocally coupled limit-cycle oscillators subject to spatiotemporally white Gaussian noise can exhibit a noise-induced transition to turbulent states. After illustrating noise-induced turbulent states with numerical simulations using two representative models of limit-cycle oscillators, we develop a theory that clarifies the effective dynamical instabilities leading to the turbulent behavior using a hierarchy of dynamical reduction methods. We determine the parameter region where the system can exhibit noise-induced turbulent states, which is successfully confirmed by extensive numerical simulations at each level of the reduction.Comment: 23 pages, 17 figures, to appear in Phys. Rev.

Magnetic trapping of ultracold neutrons

Three-dimensional magnetic confinement of neutrons is reported. Neutrons are loaded into an Ioffe-type superconducting magnetic trap through inelastic scattering of cold neutrons with 4He. Scattered neutrons with sufficiently low energy and in the appropriate spin state are confined by the magnetic field until they decay. The electron resulting from neutron decay produces scintillations in the liquid helium bath that results in a pulse of extreme ultraviolet light. This light is frequency downconverted to the visible and detected. Results are presented in which 500 +/- 155 neutrons are magnetically trapped in each loading cycle, consistent with theoretical predictions. The lifetime of the observed signal, 660 s +290/-170 s, is consistent with the neutron beta-decay lifetime.Comment: 17 pages, 18 figures, accepted for publication in Physical Review

Stability of a metallic state in the two-orbital Hubbard model

Electron correlations in the two-orbital Hubbard model at half-filling are investigated by combining dynamical mean field theory with the exact diagonalization method. We systematically study how the interplay of the intra- and inter-band Coulomb interactions, together with the Hund coupling, affects the metal-insulator transition. It is found that if the intra- and inter-band Coulomb interactions are nearly equal, the Fermi-liquid state is stabilized due to orbital fluctuations up to fairly large interactions, while the system is immediately driven to the Mott insulating phase away from this condition. The effects of the isotropic and anisotropic Hund coupling are also addressed.Comment: 7 pages, 9 figure