A Dialogue of Multipoles: Matched Asymptotic Expansion for Caged Black Holes

No analytic solution is known to date for a black hole in a compact dimension. We develop an analytic perturbation theory where the small parameter is the size of the black hole relative to the size of the compact dimension. We set up a general procedure for an arbitrary order in the perturbation series based on an asymptotic matched expansion between two coordinate patches: the near horizon zone and the asymptotic zone. The procedure is ordinary perturbation expansion in each zone, where additionally some boundary data comes from the other zone, and so the procedure alternates between the zones. It can be viewed as a dialogue of multipoles where the black hole changes its shape (mass multipoles) in response to the field (multipoles) created by its periodic "mirrors", and that in turn changes its field and so on. We present the leading correction to the full metric including the first correction to the area-temperature relation, the leading term for black hole eccentricity and the "Archimedes effect". The next order corrections will appear in a sequel. On the way we determine independently the static perturbations of the Schwarzschild black hole in dimension d>=5, where the system of equations can be reduced to "a master equation" - a single ordinary differential equation. The solutions are hypergeometric functions which in some cases reduce to polynomials.Comment: 47 pages, 12 figures, minor corrections described at the end of the introductio

The critical amplitude ratio of the susceptibility in the random-site two-dimensional Ising model

We present a new way of probing the universality class of the site-diluted two-dimensional Ising model. We analyse Monte Carlo data for the magnetic susceptibility, introducing a new fitting procedure in the critical region applicable even for a single sample with quenched disorder. This gives us the possibility to fit simultaneously the critical exponent, the critical amplitude and the sample dependent pseudo-critical temperature. The critical amplitude ratio of the magnetic susceptibility is seen to be independent of the concentration $q$ of the empty sites for all investigated values of $q\le 0.25$. At the same time the average effective exponent $\gamma_{eff}$ is found to vary with the concentration $q$, which may be argued to be due to logarithmic corrections to the power law of the pure system. This corrections are canceled in the susceptibility amplitude ratio as predicted by theory. The central charge of the corresponding field theory was computed and compared well with the theoretical predictions.Comment: 6 pages, 4 figure

An entangled two photon source using biexciton emission of an asymmetric quantum dot in a cavity

A semiconductor based scheme has been proposed for generating entangled photon pairs from the radiative decay of an electrically-pumped biexciton in a quantum dot. Symmetric dots produce polarisation entanglement, but experimentally-realised asymmetric dots produce photons entangled in both polarisation and frequency. In this work, we investigate the possibility of erasing the `which-path' information contained in the frequencies of the photons produced by asymmetric quantum dots to recover polarisation-entangled photons. We consider a biexciton with non-degenerate intermediate excitonic states in a leaky optical cavity with pairs of degenerate cavity modes close to the non-degenerate exciton transition frequencies. An open quantum system approach is used to compute the polarisation entanglement of the two-photon state after it escapes from the cavity, measured by the visibility of two-photon interference fringes. We explicitly relate the two-photon visibility to the degree of Bell-inequality violation, deriving a threshold at which Bell-inequality violations will be observed. Our results show that an ideal cavity will produce maximally polarisation-entangled photon pairs, and even a non-ideal cavity will produce partially entangled photon pairs capable of violating a Bell-inequality.Comment: 16 pages, 10 figures, submitted to PR

Crossover and self-averaging in the two-dimensional site-diluted Ising model

Using the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm, we simulate the two-dimensional (2D) site-diluted Ising model. Since we can tune the critical point of each random sample automatically with the PCC algorithm, we succeed in studying the sample-dependent $T_c(L)$ and the sample average of physical quantities at each $T_c(L)$ systematically. Using the finite-size scaling (FSS) analysis for $T_c(L)$, we discuss the importance of corrections to FSS both in the strong-dilution and weak-dilution regions. The critical phenomena of the 2D site-diluted Ising model are shown to be controlled by the pure fixed point. The crossover from the percolation fixed point to the pure Ising fixed point with the system size is explicitly demonstrated by the study of the Binder parameter. We also study the distribution of critical temperature $T_c(L)$. Its variance shows the power-law $L$ dependence, $L^{-n}$, and the estimate of the exponent $n$ is consistent with the prediction of Aharony and Harris [Phys. Rev. Lett. {\bf 77}, 3700 (1996)]. Calculating the relative variance of critical magnetization at the sample-dependent $T_c(L)$, we show that the 2D site-diluted Ising model exhibits weak self-averaging.Comment: 6 pages including 6 eps figures, RevTeX, to appear in Phys. Rev.

Environmental disclosure in Spain: Corporate characteristics and media exposure

Social and environmental issues have become a major concern for accounting research over the past two decades. Social and Environmental Accounting has attracted the attention of a number of researchers attempting to understand, explain and predict the disclosure of information on the social and environmental implications of business activities. Empirical research has hypothesized that size, profitability and the potential environmental impact of the firm are the main factors explaining the amount of information disclosed. On the other hand, several studies have focused on the motivations for disclosing environmental information, hypothesizing that disclosures are aimed at building or sustaining corporate legitimacy. We test the main hypotheses developed to date by empirical research with regard to the disclosure of environmental information based on a sample of companies listed on the Madrid Stock Exchange. Results of a content analysis show that firms disclosing environmental information tend to be larger, have higher risk (measured by the beta coefficient) and operate in industries that have a high potential environmental impact. The environmental implications of the activities carried out by these companies also seem to receive more attention from print media. Our results also provide evidence that two factors directly associated with the amount of environmental information disclosed are the potential environmental impact of the industry and the extent of media coverage of the firms

Experimental study of the quantum driven pendulum and its classical analogue in atoms optics

We present experimental results for the dynamics of cold atoms in a far detuned amplitude-modulated optical standing wave. Phase-space resonances constitute distinct peaks in the atomic momentum distribution containing up to 65% of all atoms resulting from a mixed quantum chaotic phase space. We characterize the atomic behavior in classical and quantum regimes and we present the applicable quantum and classical theory, which we have developed and refined. We show experimental proof that the size and the position of the resonances in phase space can be controlled by varying several parameters, such as the modulation frequency, the scaled well depth, the modulation amplitude, and the scaled Planck's constant of the system. We have found a surprising stability against amplitude noise. We present methods to accurately control the momentum of an ensemble of atoms using these phase-space resonances which could be used for efficient phase-space state preparation

Critical aspects of the random-field Ising model

We investigate the critical behavior of the three-dimensional random-field Ising model (RFIM) with a Gaussian field distribution at zero temperature. By implementing a computational approach that maps the ground-state of the RFIM to the maximum-flow optimization problem of a network, we simulate large ensembles of disorder realizations of the model for a broad range of values of the disorder strength h and system sizes  = L3, with L ≤ 156. Our averaging procedure outcomes previous studies of the model, increasing the sampling of ground states by a factor of 103. Using well-established finite-size scaling schemes, the fourth-order’s Binder cumulant, and the sample-to-sample fluctuations of various thermodynamic quantities, we provide high-accuracy estimates for the critical field hc, as well as the critical exponents ν, β/ν, and γ̅/ν of the correlation length, order parameter, and disconnected susceptibility, respectively. Moreover, using properly defined noise to signal ratios, we depict the variation of the self-averaging property of the model, by crossing the phase boundary into the ordered phase. Finally, we discuss the controversial issue of the specific heat based on a scaling analysis of the bond energy, providing evidence that its critical exponent α ≈ 0−

Untangling the effects of overexploration and overexploitation on organizational performance: The moderating role of environmental dynamism

Because a firm's optimal knowledge search behavior is determined by unique firm and industry conditions, organizational performance should be contingent oil the degree to which a firm's actual level of knowledge search deviates from the optimal level. It is thus hypothesized that deviation from the optimal search, in the form of either overexploitation or overexploration, is detrimental to organizational performance. Furthermore, the negative effect of search deviation oil organizational performance varies with environmental dynamism: that is, overexploitation is expected to become more harmful. whereas overexploration becomes less so with all increase in environmental dynamism. The empirical analyses yield results consistent with these arguments. Implications for research and practice are correspondingly discussed