Detecting gravitational waves from inspiraling binaries with a network of detectors : coherent versus coincident strategies

We compare two strategies of multi-detector detection of compact binary inspiral signals, namely, the coincidence and the coherent. For simplicity we consider here two identical detectors having the same power spectral density of noise, that of initial LIGO, located in the same place and having the same orientation. We consider the cases of independent noise as well as that of correlated noise. The coincident strategy involves separately making two candidate event lists, one for each detector, and from these choosing those pairs of events from the two lists which lie within a suitable parameter window, which then are called as coincidence detections. The coherent strategy on the other hand involves combining the data phase coherently, so as to obtain a single network statistic which is then compared with a single threshold. Here we attempt to shed light on the question as to which strategy is better. We compare the performances of the two methods by plotting the Receiver Operating Characteristics (ROC) for the two strategies. Several of the results are obtained analytically in order to gain insight. Further we perform numerical simulations in order to determine certain parameters in the analytic formulae and thus obtain the final complete results. We consider here several cases from the relatively simple to the astrophysically more relevant in order to establish our results. The bottom line is that the coherent strategy although more computationally expensive in general than the coincidence strategy, is superior to the coincidence strategy - considerably less false dismissal probability for the same false alarm probability in the viable false alarm regime.Comment: 18 pages, 10 figures, typo correcte

On the Role of Global Warming on the Statistics of Record-Breaking Temperatures

We theoretically study long-term trends in the statistics of record-breaking daily temperatures and validate these predictions using Monte Carlo simulations and data from the city of Philadelphia, for which 126 years of daily temperature data is available. Using extreme statistics, we derive the number and the magnitude of record temperature events, based on the observed Gaussian daily temperatures distribution in Philadelphia, as a function of the number of elapsed years from the start of the data. We further consider the case of global warming, where the mean temperature systematically increases with time. We argue that the current warming rate is insufficient to measurably influence the frequency of record temperature events over the time range of the observations, a conclusion that is supported by numerical simulations and the Philadelphia temperature data.Comment: 11 pages, 6 figures, 2-column revtex4 format. For submission to Journal of Climate. Revised version has some new results and some errors corrected. Reformatted for Journal of Climate. Second revision has an added reference. In the third revision one sentence that explains the simulations is reworded for clarity. New revision 10/3/06 has considerable additions and new results. Revision on 11/8/06 contains a number of minor corrections and is the version that will appear in Phys. Rev.

Electronic Structure of Ladder Cuprates

We study the electronic structure of the ladder compounds (SrCa)CuO 14-24-41 and SrCuO 123. LDA calculations for both give similar Cu 3d-bands near the Fermi energy. The hopping parameters estimated by fitting LDA energy bands show a strong anisotropy between the t_perp t_par intra-ladder hopping and small inter-ladder hopping. A downfolding method shows that this anisotropy arises from the ladder structure.The conductivity perpendicular to the ladders is computed assuming incoherent tunneling giving a value close to experiment.Comment: 5 pages, 3 figure

The defect variance of random spherical harmonics

The defect of a function $f:M\rightarrow \mathbb{R}$ is defined as the difference between the measure of the positive and negative regions. In this paper, we begin the analysis of the distribution of defect of random Gaussian spherical harmonics. By an easy argument, the defect is non-trivial only for even degree and the expected value always vanishes. Our principal result is obtaining the asymptotic shape of the defect variance, in the high frequency limit. As other geometric functionals of random eigenfunctions, the defect may be used as a tool to probe the statistical properties of spherical random fields, a topic of great interest for modern Cosmological data analysis.Comment: 19 page

Completely positive maps with memory

The prevailing description for dissipative quantum dynamics is given by the Lindblad form of a Markovian master equation, used under the assumption that memory effects are negligible. However, in certain physical situations, the master equation is essentially of a non-Markovian nature. This paper examines master equations that possess a memory kernel, leading to a replacement of white noise by colored noise. The conditions under which this leads to a completely positive, trace-preserving map are discussed for an exponential memory kernel. A physical model that possesses such an exponential memory kernel is presented. This model contains a classical, fluctuating environment based on random telegraph signal stochastic variables.Comment: 4 page

Statistics of the Number of Zero Crossings : from Random Polynomials to Diffusion Equation

We consider a class of real random polynomials, indexed by an integer d, of large degree n and focus on the number of real roots of such random polynomials. The probability that such polynomials have no real root in the interval [0,1] decays as a power law n^{-\theta(d)} where \theta(d)>0 is the exponent associated to the decay of the persistence probability for the diffusion equation with random initial conditions in space dimension d. For n even, the probability that such polynomials have no root on the full real axis decays as n^{-2(\theta(d) + \theta(2))}. For d=1, this connection allows for a physical realization of real random polynomials. We further show that the probability that such polynomials have exactly k real roots in [0,1] has an unusual scaling form given by n^{-\tilde \phi(k/\log n)} where \tilde \phi(x) is a universal large deviation function.Comment: 4 pages, 3 figures. Minor changes. Accepted version in Phys. Rev. Let

Bloch Equations and Completely Positive Maps

The phenomenological dissipation of the Bloch equations is reexamined in the context of completely positive maps. Such maps occur if the dissipation arises from a reduction of a unitary evolution of a system coupled to a reservoir. In such a case the reduced dynamics for the system alone will always yield completely positive maps of the density operator. We show that, for Markovian Bloch maps, the requirement of complete positivity imposes some Bloch inequalities on the phenomenological damping constants. For non-Markovian Bloch maps some kind of Bloch inequalities involving eigenvalues of the damping basis can be established as well. As an illustration of these general properties we use the depolarizing channel with white and colored stochastic noise.Comment: Talk given at the Conference "Quantum Challenges", Falenty, Poland, September 4-7, 2003. 21 pages, 3 figure

Level Crossing Analysis of Burgers Equation in 1+1 Dimensions

We investigate the average frequency of positive slope $\nu_{\alpha}^{+}$, crossing the velocity field $u(x)- \bar u = \alpha$ in the Burgers equation. The level crossing analysis in the inviscid limit and total number of positive crossing of velocity field before creation of singularities are given. The main goal of this paper is to show that this quantity, $\nu_{\alpha}^{+}$, is a good measure for the fluctuations of velocity fields in the Burgers turbulence.Comment: 5 pages, 3 figure

Density of critical points for a Gaussian random function

Critical points of a scalar quantitiy are either extremal points or saddle points. The character of the critical points is determined by the sign distribution of the eigenvalues of the Hessian matrix. For a two-dimensional homogeneous and isotropic random function topological arguments are sufficient to show that all possible sign combinations are equidistributed or with other words, the density of the saddle points and extrema agree. This argument breaks down in three dimensions. All ratios of the densities of saddle points and extrema larger than one are possible. For a homogeneous Gaussian random field one finds no longer an equidistribution of signs, saddle points are slightly more frequent.Comment: 11 pages 1 figure, changes in list of references, corrected typo

Probability distribution of the maximum of a smooth temporal signal

We present an approximate calculation for the distribution of the maximum of a smooth stationary temporal signal X(t). As an application, we compute the persistence exponent associated to the probability that the process remains below a non-zero level M. When X(t) is a Gaussian process, our results are expressed explicitly in terms of the two-time correlation function, f(t)=.Comment: Final version (1 major typo corrected; better introduction). Accepted in Phys. Rev. Let