Strength Of Fluctuations Research Articles

Mathematical aspects of quantum annealing

Sufficient conditions for convergence of quantum annealing are derived for optimization problems represented by the Ising model. Three different types of time evolution are considered; the real-time Schrödinger equation, the path-integral Monte Carlo method and the Green's function Monte Carlo method. It is proved that the system under each dynamics reaches the target solution in the limit of infinite time if the transverse field, representing the strength of quantum fluctuations, decreases inversely proportionally to the power of time in the asymptotic region.

Quantum fluctuations in a scale-free network-connected Ising system

We study the effect of quantum fluctuations in an Ising spin system on a scale-free network of degree exponent γ>5 using a quantum Monte Carlo simulation technique. In our model, one can adjust the magnitude of the magnetic field perpendicular to the Ising spin direction and can therefore control the strength of quantum fluctuations for each spin. Our numerical analysis shows that quantum fluctuations reduce the transition temperature Tc of the ferromagnetic-paramagnetic phase transition. However, the phase transition belongs to the same mean-field type universality class both with and without the quantum fluctuations. We also study the role of hubs by turning on the quantum fluctuations exclusively at the nodes with the most links. When only a small number of hub spins fluctuate quantum mechanically, Tc decreases with increasing magnetic field until it saturates at high fields. This effect becomes stronger as the number of hub spins increases. In contrast, quantum fluctuations at the same number of “non-hub” spins do not affect Tc. This implies that the hubs play an important role in maintaining order in the whole network.

Dynamic permeability of porous rocks and its seismic signatures

In inhomogeneous porous media, the mechanism of wave-induced fluid flow causes significant attenuation and dispersion of seismic waves. In connection with this phenomenon, we study the impact of spatial permeability fluctuations on the dynamic behavior of porous materials. This heterogeneous permeability distribution further complicates the ongoing efforts to extract flow permeability from seismic data. Based on the method of statistical smoothing applied to Biot’s equations of poroelasticity, we derive models for the dynamic-equivalent permeability in 1D and 3D randomly inhomogeneous media. The low-frequency limit of this permeability corresponds to the flow permeability governing fluid flow in porous media. We incorporate the dynamic-equivalent permeability model into the expressions for attenuation and dispersion of P-waves, also obtained by the method of smoothing. The resulting attenuation and dispersion model is confirmed by numerical computations in randomly layered poroelastic structures. The results suggest that the effect of wave-induced fluid flow can be observed in a broader frequency range than previously thought. The peak attenuation shifts along the frequency axis depending on the strength of the permeability fluctuations. We conclude that estimation of flow permeability from seismic attenuation is only possible if permeability fluctuations are properly accounted for.

Formula omitted] study of the effects of Ce dilution on the development of the heavy-fermion state in [formula omitted

We have performed muon Knight shift measurements in the heavy-fermion compound ( Ce 1 - x La x ) 2 IrIn 8 , x = 0.1 , in 1 T magnetic field applied along the crystalline c-axis. Although the Knight shift K scales linearly with susceptibility χ above T ∼ 20 K , a breakdown of this relationship was observed below a temperature T * = 20.1 ( 8 ) K . It was found that this Knight shift anomaly occurs due to a low-temperature susceptibility component χ cf ∼ ( 1 - T / T * ) ln ( T * / T ) , corresponding to the formation of a coherent heavy-fermion state below T * , as found previously in the x = 0 compound. The characteristic temperature T * is reduced by about 4 K for 10% La doping, indicating a reduction in the strength of the intersite Ce fluctuations associated with the heavy electron state.

Convergence of Quantum Annealing with Real-Time Schrödinger Dynamics

Convergence conditions for quantum annealing are derived for optimization problems represented by the Ising model of a general form. Quantum fluctuations are introduced as a transverse field and/or transverse ferromagnetic interactions, and the time evolution follows the real-time Schrodinger equation. It is shown that the system stays arbitrarily close to the instantaneous ground state, finally reaching the target optimal state, if the strength of quantum fluctuations decreases sufficiently slowly, in particular inversely proportionally to the power of time in the asymptotic region. This is the same condition as the other implementations of quantum annealing, quantum Monte Carlo and Green's function Monte Carlo simulations, in spite of the essential difference in the type of dynamics. The method of analysis is an application of the adiabatic theorem in conjunction with an estimate of a lower bound of the energy gap based on the recently proposed idea of Somma et. al. for the analysis of classical simulated annealing using a classical-quantum correspondence.

Event-by-event fluctuations of transverse momentum and multiparticle clusters in relativistic heavy-ion collisions

We analyze the event-by-event fluctuations of mean transverse momentum measured recently by the PHENIX and STAR Collaborations at RHIC. We argue that the observed scaling of strength of dynamical fluctuations with the inverse number of particles can be naturally explained by formation of multiparticle clusters.

Experimental investigation of the instability of a sedimenting suspension of fibres

Observations of the flow structures formed by rigid fibres of high aspect ratio sedimenting within a viscous fluid at a Reynolds number of approximately 10−4 confirm the existence of an instability as reported in previous theories, experiments, and numerical simulations. Using data generated from particle image velocimetry measurements, we quantify the sedimentation structures over a wide range of parameters, which include the height of fluid, cross-section of the sedimentation cell, fibre dimensions, fluid properties, and volume fractions ranging from dilute to semi-dilute. Alternating structures of streamers and backflow regions which span the height of the sedimentation cell form at short times and transition from large wavelengths to smaller wavelength as the sedimentation proceeds. No simple dependence of the horizontal wavelength on the length scales and concentration was observed in the experiments, suggesting the need for additional analysis. We also report the mean velocities and velocity fluctuations; the strength of the velocity fluctuations strongly correlates with the size of the vertical component of the sedimentation structure. Measurements of the orientation distribution, using an efficient and newly employed technique, agree with previously published results. A movie is available with the online version of the paper.

Dipole induced photodetachment dynamics of halide anions

In this article the dynamics of photodetachment from closed shell anion in the presence of two color (bichromatic) laser field have been explored in the context of polar environmental situation. The electronic states of halide ions are modeled by a one dimensional Hamiltonian with a potential V(x) = −V0e. The two parameters V0 and σ are fixed by requiring V(x) to reproduce the experimentally observed ground state ionization energy of the halide ion concerned. The potential so generated are shown to support only one bound state. The time-dependent Fourier grid Hamiltonian method is used to follow the detachment dynamics with fairly high intensities of light. The environmental effects on the dynamics are sought to be modeled by two ways i) allowing the well depth (V0) to fluctuate randomly V0(t) = V0[1+ΔVR(t)]; R(t) randomly fluctuates between +1 and −1 with time, when ΔV (strength of fluctuation) is fixed and ii) in the presence of perturbation produced by a neighboring solvent dipole, which changes the effective potential. The detachment rate constant is studied as a function of important system parameters of the used light field. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

The PMD of sinusoidally spun fibers in the presence of random birefringence perturbations

Although fiber spinning is known to reduce polarization mode dispersion (PMD) effects in optical fibers, relatively few studies have been performed of the dependence of the reduction factor on the strength of random birefringence fluctuations. In this paper, we apply a general mathematical model of random fiber birefringence to sinusoidally spun fibers. We find that while even in the presence of random birefringence perturbations the maximum reduction of PMD is still obtained when the phase matching condition is satisfied, the degree of PMD reduction and the probability distribution function of the DGD both vary with the random birefringence profiles.

Event-by-event fluctuation in K/π ratio at RHIC

We present the first results from the measurement of event-by-event fluctuation in the K/π ratio for Au+Au collisions at , 130 and 200 GeV at the Relativistic Heavy Ion Collider. We observe that the strength of dynamical fluctuation decreases with increasing centrality for all centre-of-mass energies of the collisions. The excitation function for the dynamical fluctuation in the event-by-event K/π ratio for central collisions will be presented. The results will be compared with fluctuations obtained at SPS energies.

Strong Self-Similar Fluctuations of Target Fragments inRing-like Events in Ultra-Relativistic Nuclear Collision

The intermittent fluctuation of target evaporated particles is studied inboth ring-like and jet-like events emitted in 32S–emulsioninteractions at 200 AGeV within the framework of multi-dimensionalfactorial moment methodology using the concept of the Hurst exponent. It isobserved that the intermittent fluctuation in the ring-like event isself-similar, whereas in the jet-like event fluctuation is self-affine.However, study indicates that the strength of fluctuation in the ring-likeevents is much stronger than that in the jet-like events.

Vortex flow and shot noise in the quantum-liquid phase of thick amorphous superconducting films

We measure the fluctuations (noise) of the vortex-flow voltage in the low-temperature liquid phase of thick amorphous $(a\text{\ensuremath{-}}){\mathrm{Mg}}_{x}{\mathrm{B}}_{1\ensuremath{-}x}$ and $a\text{\ensuremath{-}}{\mathrm{Mo}}_{x}{\mathrm{Si}}_{1\ensuremath{-}x}$ films with different transition temperatures and widths of the quantum-vortex-liquid (QVL) phase. An anomalous vortex flow with an asymmetric distribution of (real-time) voltage fluctuations is commonly observed in the QVL phase, independent of material as well as strength of quantum fluctuations. In the QVL phase we observe the Lorentzian-type noise spectra indicative of shot noise, whose origin is attributed to the vortex bundles that are depinned and pinned randomly in the stationary flow of QVL.

Orientation selectivity in visual cortex by fluctuation-controlled criticality

Within a large-scale neuronal network model of macaque primary visual cortex, we examined how intrinsic dynamic fluctuations in synaptic currents modify the effect of strong recurrent excitation on orientation selectivity. Previously, we showed that, using a strong network inhibition countered by feedforward and recurrent excitation, the cortical model reproduced many observed properties of simple and complex cells. However, that network's complex cells were poorly selective for orientation, and increasing cortical self-excitation led to network instabilities and unrealistically high firing rates. Here, we show that a sparsity of connections in the network produces large, intrinsic fluctuations in the cortico-cortical conductances that can stabilize the network and that there is a critical level of fluctuations (controllable by sparsity) that allows strong cortical gain and the emergence of orientation-selective complex cells. The resultant sparse network also shows near contrast invariance in its selectivity and, in agreement with recent experiments, has extracellular tuning properties that are similar in pinwheel center and iso-orientation regions, whereas intracellular conductances show positional dependencies. Varying the strength of synaptic fluctuations by adjusting the sparsity of network connectivity, we identified a transition between the dynamics of bistability and without bistability. In a network with strong recurrent excitation, this transition is characterized by a near hysteretic behavior and a rapid rise of network firing rates as the synaptic drive or stimulus input is increased. We discuss the connection between this transition and orientation selectivity in our model of primary visual cortex.

Does Red Noise Increase or Decrease Extinction Risk? Single Extreme Events versus Series of Unfavorable Conditions

Recent theoretical studies have shown contrasting effects of temporal correlation of environmental fluctuations (red noise) on the risk of population extinction. It is still debated whether and under which conditions red noise increases or decreases extinction risk compared with uncorrelated (white) noise. Here, we explain the opposing effects by introducing two features of red noise time series. On the one hand, positive autocorrelation increases the probability of series of poor environmental conditions, implying increasing extinction risk. On the other hand, for a given time period, the probability of at least one extremely bad year ("catastrophe") is reduced compared with white noise, implying decreasing extinction risk. Which of these two features determines extinction risk depends on the strength of environmental fluctuations and the sensitivity of population dynamics to these fluctuations. If extreme (catastrophic) events can occur (strong noise) or sensitivity is high (overcompensatory density dependence), then temporal correlation decreases extinction risk; otherwise, it increases it. Thus, our results provide a simple explanation for the contrasting previous findings and are a crucial step toward a general understanding of the effect of noise color on extinction risk.

Non‐Gaussian Radio‐Wave Scattering in the Interstellar Medium

It was recently suggested by Boldyrev & Gwinn that the characteristics of radio scintillations from distant pulsars are best understood if the interstellar electron-density fluctuations that cause the time broadening of the radio pulses obey non-Gaussian statistics. In this picture the density fluctuations are inferred to be strong on very small scales ($\sim 10^8-10^{10} {cm}$). We argue that such density structures could correspond to the ionized boundaries of molecular regions (clouds) and demonstrate that the power-law distribution of scattering angles that is required to match the observations arises naturally from the expected intersections of our line of sight with randomly distributed, thin, approximately spherical ionized shells of this type. We show that the observed change in the time-broadening behavior for pulsar dispersion measures $\lesssim 30 {\rm pc} {\rm cm}^{-3}$ is consistent with the expected effect of the general ISM turbulence, which should dominate the scattering for nearby pulsars. We also point out that if the clouds are ionized by nearby stars, then their boundaries may become turbulent on account of an ionization front instability. This turbulence could be an alternative cause of the inferred density structures. An additional effect that might contribute to the strength of the small-scale fluctuations in this case is the expected flattening of the turbulent density spectrum when the eddy sizes approach the proton gyroscale.

Event-by-event [formula omitted] fluctuations and multiparticle clusters in relativistic heavy-ion collisions

We explore the centrality dependence of the pT correlations in the event-by-event analysis of relativistic heavy-ion collisions at RHIC made recently by the PHENIX and STAR Collaborations. We point out that the observed scaling of strength of dynamical fluctuations with the inverse number of the produced particles can be naturally explained by the formation of clusters. We argue that the large magnitude of the measured covariance implies that the clusters contain at least several particles. We also discuss whether the clusters may originate from jets. In addition, we provide numerical estimates of correlations coming from resonance decays and thermal clusters.

Effect of Gender, Age, and Severity of Asthma Attack on Patterns of Emergency Department Visits due to Asthma by Month and Day of the Week

To examine the pattern and strength of seasonal fluctuations in emergency department (ED) visits due to asthma, by month and day of the week, by the patient's age, gender, and severity of asthma attack. Time series analysis of ED visits was conducted among patients with asthma aged from 18 to 55 years who visited Ontario EDs between April 1, 2001 and March 31, 2004. Autoregressive regression models with months and days of the week as predictors were fitted for (1) all patients; (2) females and males separately; (3) each combination of gender and age group, and (4) each combination of gender and level of severity. The strength of seasonality in each group of patients was estimated from the R2-statistic derived from autoregression models. For all patient groups, the highest number of ED visits occurred in October and December, and on Sundays and Mondays. Month of January and Fridays were associated with a decreased number of visits. The strength of seasonality was similar in men and women (R2 = 0.52), was the highest in young patients and decreased with age, in men more rapidly than in women. Severe cases of asthma attacks exhibited weaker seasonality (R2 = 0.30) compared to mild (R2 = 0.45) or moderate (R2 = 0.53) cases. The strength of seasonal patterns of asthma ED visits is influenced by age and the severity of attack, and to a lesser extent, gender. Understanding the significance of seasonal precipitants of asthma in different patients subgroups could lead to better management strategies.

EFFECTS OF INTERFACIAL PSEUDO-SPIN COUPLING FLUCTUATIONS ON THE DIELECTRIC PROPERTIES OF FERROELECTRIC SUPERLATTICES

Using effective-field theory with correlations, we investigate the effects of interfacial pseudo-spin coupling fluctuations on the susceptibility and polarization of ferroelectric superlattices within the framework of transverse Ising model. It is found that the interfacial coupling fluctuations increase the susceptibility in the low temperature region. For a strong interfacial coupling, the phase transition temperature decreases with the strength of fluctuations of the interfacial coupling. The dependence of the susceptibility on the superlattice period of BaTiO 3/ SrTiO 3 are plotted for different interfacial coupling fluctuations strength. At room temperature, when the interfacial coupling fluctuation increases, the peak position of the susceptibility will shift to a large superlattice period.

Effects of thermal fluctuations on the magnetic behavior of mesoscopic superconductors

We study the influence of thermal fluctuations on the magnetic behavior of square mesoscopic superconductors. The strength of thermal fluctuations are parameterized using the Ginzburg number, which is small ($G_i \approx 10^{-10}$) in low-$T_c$ superconductors and large in high-$T_c$ superconductors ($G_i \approx 10^{-4}$). For low-$T_c$ mesoscopic superconductors we found that the meta-stable states due to the surface barrier have a large half-life time, which leads to the hysteresis in the magnetization curves as observed experimentally. A very different behavior appears for high-$T_c$ mesoscopic superconductors where thermally activated vortex entrance/exit through surface barriers is frequent. This leads to a reduction of the magnetization and a non-integer average number of flux quanta penetrating the superconductor. The magnetic field dependence of the probability for the occurrence of the different vortex states and the fluctuations in the number of vortices are studied.

Magnetic Fields and Ionized Gas in the Inner Galaxy: An Outer Scale for Turbulence and the Possible Role of HiiRegions

We present an analysis of rotation measure (RM) fluctuations from the test region of the Southern Galactic Plane Survey (SGPS), along with emission measure (EM) fluctuations in the same field taken from the Southern H? Sky Survey Atlas. The structure function of RM fluctuations shows a relatively steep slope at small scales (1'-5'), a break in slope to a flatter structure function at intermediate scales (5'-60'), and a systematic variation of the strength of fluctuations as a function of position angle on the sky at the largest scales (60'-200'). The structure function of EM fluctuations shows similar behavior, although the lower resolution of the data prevents detection of a possible break in the spectrum. We interpret the anisotropy in RM/EM structure on large scales as resulting from a large-scale gradient in electron density (and possibly magnetic field) across the region. The break in the slope of the RM structure function at scales of ~5' can be explained by contributions from two spatially distinct magnetoionized screens, most likely in the Local and Carina spiral arms. The observed structure function then implies that the outer scale of RM fluctuations in these screens is ~2 pc. Such behavior is in striking contrast to the expectation that interstellar turbulence forms an unbroken spectrum from kiloparsec down to AU scales. We conclude that we have identified an additional source of enhanced turbulence, injected on scales of a few pc, possibly seen only in the Galactic plane. The most likely source of such turbulence is individual H II regions from relatively low mass stars, whose characteristic scale size is similar to the outer scale of turbulence inferred here. These sources may be the dominant source of density and velocity fluctuations in warm ionized gas in the Galactic plane.