Critical behavior of the susceptible-infected-recovered model on a square lattice

By means of numerical simulations and epidemic analysis, the transition point of the stochastic asynchronous susceptible-infected-recovered model on a square lattice is found to be c(0)=0.176 500 5(10), where c is the probability a chosen infected site spontaneously recovers rather than tries to infect one neighbor. This point corresponds to an infection/recovery rate of lambda(c)=(1-c(0))/c(0)=4.665 71(3) and a net transmissibility of (1-c(0))/(1+3c(0))=0.538 410(2), which falls between the rigorous bounds of the site and bond thresholds. The critical behavior of the model is consistent with the two-dimensional percolation universality class, but local growth probabilities differ from those of dynamic percolation cluster growth, as is demonstrated explicitly.

Charged Kaon Interferometric Probes of Space-Time Evolution in Au plus Au Collisions at s(NN)=200 GeV

Bose-Einstein correlations of charged kaons are used to probe Au+Au collisions at s(NN)=200 GeV and are compared to charged pion probes, which have a larger hadronic scattering cross section. Three-dimensional Gaussian source radii are extracted, along with a one-dimensional kaon emission source function. The centrality dependences of the three Gaussian radii are well described by a single linear function of N(part)(1/3) with a zero intercept. Imaging analysis shows a deviation from a Gaussian tail at r greater than or similar to 10 fm, although the bulk emission at lower radius is well described by a Gaussian. The presence of a non-Gaussian tail in the kaon source reaffirms that the particle emission region in a heavy-ion collision is extended, and that similar measurements with pions are not solely due to the decay of long-lived resonances.

Time correlation function in systems with two coexisting biological species

We study a stochastic lattice model describing the dynamics of coexistence of two interacting biological species. The model comprehends the local processes of birth, death, and diffusion of individuals of each species and is grounded on interaction of the predator-prey type. The species coexistence can be of two types: With self-sustained coupled time oscillations of population densities and without oscillations. We perform numerical simulations of the model on a square lattice and analyze the temporal behavior of each species by computing the time correlation functions as well as the spectral densities. This analysis provides an appropriate characterization of the different types of coexistence. It is also used to examine linked population cycles in nature and in experiment.

Transition amplitude for two-time physics

We present the transition amplitude for a particle moving in a space with two times and D space dimensions having an Sp(2, R) local symmetry and an SO(D, 2) rigid symmetry. It was obtained from the BRST-BFV quantization with a unique gauge choice. We show that by constraining the initial and final points of this amplitude to lie on some hypersurface of the D + 2 space the resulting amplitude reproduces well-known systems in lower dimensions. This work provides an alternative way to derive the effects of two-time physics where all the results come from a single transition amplitude.

Critical behavior of the magnetization in the spin-gapped system NiCl(2)-4SC (NH(2))(2)

We report accurate magnetization measurements on the spin-gap compound NiCl(2)-4SC (NH(2))(2) around the low portion of the magnetic induced phase ordering. The critical density of the magnetization at the phase boundary is analyzed in terms of a Bose-Einstein condensation (BEC) of bosonic particles, and the boson interaction strength is obtained as upsilon(0)=0.61 meV. The detailed analysis of the magnetization data across the transition leads to the conclusion for the preservation of the U(1) symmetry, as required for BEC. (c) 2009 American Institute of Physics. [DOI: 10.1063/1.3055265]

Critical Properties at the Field-Induced Bose-Einstein Condensation in NiCl(2)-4SC(NH(2))(2)

We report new magnetization measurements on the spin-gap compound NiCl(2)-4SC(NH(2))(2) at the low-field boundary of the magnetic field-induced ordering. The critical density of the magnetization is analyzed in terms of a Bose-Einstein condensation of bosonic quasiparticles. The analysis of the magnetization at the transition leads to the conclusion for the preservation of the U(1) symmetry, as required for Bose-Einstein condensation. The experimental data are well described by quantum Monte Carlo simulations.

Character of magnetic excitations in a quasi-one-dimensional antiferromagnet near the quantum critical points: Impact on magnetoacoustic properties

We report results of magnetoacoustic studies in the quantum spin-chain magnet NiCl(2)-4SC(NH(2))(2) (DTN) having a field-induced ordered antiferromagnetic (AF) phase. In the vicinity of the quantum critical points (QCPs) the acoustic c(33) mode manifests a pronounced softening accompanied by energy dissipation of the sound wave. The acoustic anomalies are traced up to T > T(N), where the thermodynamic properties are determined by fermionic magnetic excitations, the ""hallmark"" of one-dimensional (1D) spin chains. On the other hand, as established in earlier studies, the AF phase in DTN is governed by bosonic magnetic excitations. Our results suggest the presence of a crossover from a 1D fermionic to a three-dimensional bosonic character of the magnetic excitations in DTN in the vicinity of the QCPs.

Identified particle production, azimuthal anisotropy, and interferometry measurements in Au plus Au collisions at root s(NN)=9.2 GeV

We present the first measurements of identified hadron production, azimuthal anisotropy, and pion interferometry from Au + Au collisions below the nominal injection energy at the BNL Relativistic Heavy-Ion Collider (RHIC) facility. The data were collected using the large acceptance solenoidal tracker at RHIC (STAR) detector at root s(NN) = 9.2 GeV from a test run of the collider in the year 2008. Midrapidity results on multiplicity density dN/dy in rapidity y, average transverse momentum < p(T)>, particle ratios, elliptic flow, and Hanbury-Brown-Twiss (HBT) radii are consistent with the corresponding results at similar root s(NN) from fixed-target experiments. Directed flow measurements are presented for both midrapidity and forward-rapidity regions. Furthermore the collision centrality dependence of identified particle dN/dy, < p(T)>, and particle ratios are discussed. These results also demonstrate that the capabilities of the STAR detector, although optimized for root s(NN) = 200 GeV, are suitable for the proposed QCD critical-point search and exploration of the QCD phase diagram at RHIC.

Numerical evidence against a conjecture on the cover time of planar graphs

We investigate a conjecture on the cover times of planar graphs by means of large Monte Carlo simulations. The conjecture states that the cover time tau (G(N)) of a planar graph G(N) of N vertices and maximal degree d is lower bounded by tau (G(N)) >= C(d)N(lnN)(2) with C(d) = (d/4 pi) tan(pi/d), with equality holding for some geometries. We tested this conjecture on the regular honeycomb (d = 3), regular square (d = 4), regular elongated triangular (d = 5), and regular triangular (d = 6) lattices, as well as on the nonregular Union Jack lattice (d(min) = 4, d(max) = 8). Indeed, the Monte Carlo data suggest that the rigorous lower bound may hold as an equality for most of these lattices, with an interesting issue in the case of the Union Jack lattice. The data for the honeycomb lattice, however, violate the bound with the conjectured constant. The empirical probability distribution function of the cover time for the square lattice is also briefly presented, since very little is known about cover time probability distribution functions in general.

Instability of the time dependent Horava-Witten model

We consider scalar perturbations in the time dependent Horava-Witten model in order to probe its stability. We show that during the nonsingular epoque the model evolves without instabilities until it encounters the curvature singularity where a big crunch is supposed to occur. We compute the frequencies of the scalar field oscillation during the stable period and show how the oscillations can be used to prove the presence of such a singularity.

Monte Carlo investigation of the critical behavior of Stavskaya's probabilistic cellular automaton

Stavskaya's model is a one-dimensional probabilistic cellular automaton (PCA) introduced in the end of the 1960s as an example of a model displaying a nonequilibrium phase transition. Although its absorbing state phase transition is well understood nowadays, the model never received a full numerical treatment to investigate its critical behavior. In this Brief Report we characterize the critical behavior of Stavskaya's PCA by means of Monte Carlo simulations and finite-size scaling analysis. The critical exponents of the model are calculated and indicate that its phase transition belongs to the directed percolation universality class of critical behavior, as would be expected on the basis of the directed percolation conjecture. We also explicitly establish the relationship of the model with the Domany-Kinzel PCA on its directed site percolation line, a connection that seems to have gone unnoticed in the literature so far.

Decoherence-free evolution of time-dependent superposition states of two-level systems and thermal effects

In this paper we detail some results advanced in a recent letter [Prado et al., Phys. Rev. Lett. 102, 073008 (2009).] showing how to engineer reservoirs for two-level systems at absolute zero by means of a time-dependent master equation leading to a nonstationary superposition equilibrium state. We also present a general recipe showing how to build nonadiabatic coherent evolutions of a fermionic system interacting with a bosonic mode and investigate the influence of thermal reservoirs at finite temperature on the fidelity of the protected superposition state. Our analytical results are supported by numerical analysis of the full Hamiltonian model.

Equivalence between Redfield- and master-equation approaches for a time-dependent quantum system and coherence control

We present a derivation of the Redfield formalism for treating the dissipative dynamics of a time-dependent quantum system coupled to a classical environment. We compare such a formalism with the master equation approach where the environments are treated quantum mechanically. Focusing on a time-dependent spin-1/2 system we demonstrate the equivalence between both approaches by showing that they lead to the same Bloch equations and, as a consequence, to the same characteristic times T(1) and T(2) (associated with the longitudinal and transverse relaxations, respectively). These characteristic times are shown to be related to the operator-sum representation and the equivalent phenomenological-operator approach. Finally, we present a protocol to circumvent the decoherence processes due to the loss of energy (and thus, associated with T(1)). To this end, we simply associate the time dependence of the quantum system to an easily achieved modulated frequency. A possible implementation of the protocol is also proposed in the context of nuclear magnetic resonance.

Precise determination of quantum critical points by the violation of the entropic area law

Finite-size scaling analysis turns out to be a powerful tool to calculate the phase diagram as well as the critical properties of two-dimensional classical statistical mechanics models and quantum Hamiltonians in one dimension. The most used method to locate quantum critical points is the so-called crossing method, where the estimates are obtained by comparing the mass gaps of two distinct lattice sizes. The success of this method is due to its simplicity and the ability to provide accurate results even considering relatively small lattice sizes. In this paper, we introduce an estimator that locates quantum critical points by exploring the known distinct behavior of the entanglement entropy in critical and noncritical systems. As a benchmark test, we use this new estimator to locate the critical point of the quantum Ising chain and the critical line of the spin-1 Blume-Capel quantum chain. The tricritical point of this last model is also obtained. Comparison with the standard crossing method is also presented. The method we propose is simple to implement in practice, particularly in density matrix renormalization group calculations, and provides us, like the crossing method, amazingly accurate results for quite small lattice sizes. Our applications show that the proposed method has several advantages, as compared with the standard crossing method, and we believe it will become popular in future numerical studies.

Automatic Network Fingerprinting through Single-Node Motifs

Complex networks have been characterised by their specific connectivity patterns (network motifs), but their building blocks can also be identified and described by node-motifs-a combination of local network features. One technique to identify single node-motifs has been presented by Costa et al. (L. D. F. Costa, F. A. Rodrigues, C. C. Hilgetag, and M. Kaiser, Europhys. Lett., 87, 1, 2009). Here, we first suggest improvements to the method including how its parameters can be determined automatically. Such automatic routines make high-throughput studies of many networks feasible. Second, the new routines are validated in different network-series. Third, we provide an example of how the method can be used to analyse network time-series. In conclusion, we provide a robust method for systematically discovering and classifying characteristic nodes of a network. In contrast to classical motif analysis, our approach can identify individual components (here: nodes) that are specific to a network. Such special nodes, as hubs before, might be found to play critical roles in real-world networks.