Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators

We study synchronization properties of general uncoupled limit-cycle oscillators driven by common and independent Gaussian white noises. Using phase reduction and averaging methods, we analytically derive the stationary distribution of the phase difference between oscillators for weak noise intensity. We demonstrate that in addition to synchronization, clustering, or more generally coherence, always results from arbitrary initial conditions, irrespective of the details of the oscillators.Comment: 6 pages, 2 figure

Can Gravitational Waves Prevent Inflation?

To investigate the cosmic no hair conjecture, we analyze numerically 1-dimensional plane symmetrical inhomogeneities due to gravitational waves in vacuum spacetimes with a positive cosmological constant. Assuming periodic gravitational pulse waves initially, we study the time evolution of those waves and the nature of their collisions. As measures of inhomogeneity on each hypersurface, we use the 3-dimensional Riemann invariant ${\cal I}\equiv {}~^{(3)\!}R_{ijkl}~^{(3)\!}R^{ijkl}$ and the electric and magnetic parts of the Weyl tensor. We find a temporal growth of the curvature in the waves' collision region, but the overall expansion of the universe later overcomes this effect. No singularity appears and the result is a ``no hair" de Sitter spacetime. The waves we study have amplitudes between $0.020\Lambda \leq {\cal I}^{1/2} \leq 125.0\Lambda$ and widths between $0.080l_H \leq l \leq 2.5l_H$, where $l_H=(\Lambda/3)^{-1/2}$, the horizon scale of de Sitter spacetime. This supports the cosmic no hair conjecture.Comment: LaTeX, 11 pages, 3 figures are available on request <To [email protected] (Hisa-aki SHINKAI)>, WU-AP/29/9

Clinical application of somatosensory amplification in psychosomatic medicine

Many patients with somatoform disorders are frequently encountered in psychosomatic clinics as well as in primary care clinics. To assess such patients objectively, the concept of somatosensory amplification may be useful. Somatosensory amplification refers to the tendency to experience a somatic sensation as intense, noxious, and disturbing. It may have a role in a variety of medical conditions characterized by somatic symptoms that are disproportionate to demonstrable organ pathology. It may also explain some of the variability in somatic symptomatology found among different patients with the same serious medical disorder. It has been assessed with a self-report questionnaire, the Somatosensory Amplification Scale. This instrument was developed in a clinical setting in the U.S., and the reliability and validity of the Japanese and Turkish versions have been confirmed as well

Two Boosted Black Holes in Asymptotically de Sitter Space-Time - Relation between Mass and Apparent Horizon Formation -

We study the apparent horizon for two boosted black holes in the asymptotically de Sitter space-time by solving the initial data on a space with punctures. We show that the apparent horizon enclosing both black holes is not formed if the conserved mass of the system (Abbott-Deser mass) is larger than a critical mass. The black hole with too large AD mass therefore cannot be formed in the asymptotically de Sitter space-time even though each black hole has any inward momentum. We also discuss the dynamical meaning of AD mass by examining the electric part of the Weyl tensor (the tidal force) for various initial data.Comment: 15 pages, accepted for publication in PR

(Semi)classical limit of the Hartree equation with harmonic potential

Nonlinear Schrodinger Equations (NLS) of the Hartree type occur in the modeling of quantum semiconductor devices. Their "semiclassical" limit of vanishing (scaled) Planck constant is both a mathematical challenge and practically relevant when coupling quantum models to classical models. With the aim of describing the semi-classical limit of the 3D Schrodinger--Poisson system with an additional harmonic potential, we study some semi-classical limits of the Hartree equation with harmonic potential in space dimension n>1. The harmonic potential is confining, and causes focusing periodically in time. We prove asymptotics in several cases, showing different possible nonlinear phenomena according to the interplay of the size of the initial data and the power of the Hartree potential. In the case of the 3D Schrodinger-Poisson system with harmonic potential, we can only give a formal computation since the need of modified scattering operators for this long range scattering case goes beyond current theory. We also deal with the case of an additional "local" nonlinearity given by a power of the local density - a model that is relevant when incorporating the Pauli principle in the simplest model given by the "Schrodinger-Poisson-X$\alpha$ equation". Further we discuss the connection of our WKB based analysis to the Wigner function approach to semiclassical limits.Comment: 26 page

Independent Component Analysis of Spatiotemporal Chaos

Two types of spatiotemporal chaos exhibited by ensembles of coupled nonlinear oscillators are analyzed using independent component analysis (ICA). For diffusively coupled complex Ginzburg-Landau oscillators that exhibit smooth amplitude patterns, ICA extracts localized one-humped basis vectors that reflect the characteristic hole structures of the system, and for nonlocally coupled complex Ginzburg-Landau oscillators with fractal amplitude patterns, ICA extracts localized basis vectors with characteristic gap structures. Statistics of the decomposed signals also provide insight into the complex dynamics of the spatiotemporal chaos.Comment: 5 pages, 6 figures, JPSJ Vol 74, No.

Langevin Analysis of Eternal Inflation

It has been widely claimed that inflation is generically eternal to the future, even in models where the inflaton potential monotonically increases away from its minimum. The idea is that quantum fluctuations allow the field to jump uphill, thereby continually revitalizing the inflationary process in some regions. In this paper we investigate a simple model of this process, pertaining to inflation with a quartic potential, in which analytic progress may be made. We calculate several quantities of interest, such as the expected number of inflationary efolds, first without and then with various selection effects. With no additional weighting, the stochastic noise has little impact on the total number of inflationary efoldings even if the inflaton starts with a Planckian energy density. A "rolling" volume factor, i.e. weighting in proportion to the volume at that time, also leads to a monotonically decreasing Hubble constant and hence no eternal inflation. We show how stronger selection effects including a constraint on the initial and final states and weighting with the final volume factor can lead to a picture similar to that usually associated with eternal inflation.Comment: 22 pages, 2 figure

Existence and uniqueness of the integrated density of states for Schr\"odinger operators with magnetic fields and unbounded random potentials

The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schr\"odinger operator with a constant magnetic field and a random potential which may be unbounded from above and from below. For an ergodic random potential satisfying a simple moment condition, we give a detailed proof that the infinite-volume limits of spatial eigenvalue concentrations of finite-volume operators with different boundary conditions exist almost surely. Since all these limits are shown to coincide with the expectation of the trace of the spatially localized spectral family of the infinite-volume operator, the integrated density of states is almost surely non-random and independent of the chosen boundary condition. Our proof of the independence of the boundary condition builds on and generalizes certain results by S. Doi, A. Iwatsuka and T. Mine [Math. Z. {\bf 237} (2001) 335-371] and S. Nakamura [J. Funct. Anal. {\bf 173} (2001) 136-152].Comment: This paper is a revised version of the first part of the first version of math-ph/0010013. For a revised version of the second part, see math-ph/0105046. To appear in Reviews in Mathematical Physic

Dynamical renormalization group methods in theory of eternal inflation

Dynamics of eternal inflation on the landscape admits description in terms of the Martin-Siggia-Rose (MSR) effective field theory that is in one-to-one correspondence with vacuum dynamics equations. On those sectors of the landscape, where transport properties of the probability measure for eternal inflation are important, renormalization group fixed points of the MSR effective action determine late time behavior of the probability measure. I argue that these RG fixed points may be relevant for the solution of the gauge invariance problem for eternal inflation.Comment: 11 pages; invited mini-review for Grav.Cos