Diffusion anomaly and dynamic transitions in the Bell-Lavis water model

In this paper we investigate the dynamic properties of the minimal Bell-Lavis (BL) water model and their relation to the thermodynamic anomalies. The BL model is defined on a triangular lattice in which water molecules are represented by particles with three symmetric bonding arms interacting through van der Waals and hydrogen bonds. We have studied the model diffusivity in different regions of the phase diagram through Monte Carlo simulations. Our results show that the model displays a region of anomalous diffusion which lies inside the region of anomalous density, englobed by the line of temperatures of maximum density. Further, we have found that the diffusivity undergoes a dynamic transition which may be classified as fragile-to-strong transition at the critical line only at low pressures. At higher densities, no dynamic transition is seen on crossing the critical line. Thus evidence from this study is that relation of dynamic transitions to criticality may be discarded. (C) 2010 American Institute of Physics. [doi:10.1063/1.3479001]

Dynamic transitions in a three dimensional associating lattice gas model

The aggregation of interacting Brownian particles in sheared concentrated suspensions is an important issue in colloid and soft matter science per se. Also, it serves as a model to understand biochemical reactions occurring in vivo where both crowding and shear play an important role. We present an effective medium approach within the Smoluchowski equation with shear which allows one to calculate the encounter kinetics through a potential barrier under shear at arbitrary colloid concentrations. Experiments on a model colloidal system in simple shear flow support the validity of the model in the concentration range considered. By generalizing Kramers' rate theory to the presence of shear and collective hydrodynamics, our model explains the significant increase in the shear-induced reaction-limited aggregation kinetics upon increasing the colloid concentration.

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.

Dynamic transitions in a two dimensional associating lattice gas model

Using Monte Carlo simulations we investigate some new aspects of the phase diagram and the behavior of the diffusion coefficient in an associating lattice gas (ALG) model on different regions of the phase diagram. The ALG model combines a two dimensional lattice gas where particles interact through a soft core potential and orientational degrees of freedom. The competition between soft core potential and directional attractive forces results in a high density liquid phase, a low density liquid phase, and a gas phase. Besides anomalies in the behavior of the density with the temperature at constant pressure and of the diffusion coefficient with density at constant temperature are also found. The two liquid phases are separated by a coexistence line that ends in a bicritical point. The low density liquid phase is separated from the gas phase by a coexistence line that ends in tricritical point. The bicritical and tricritical points are linked by a critical lambda-line. The high density liquid phase and the fluid phases are separated by a second critical tau-line. We then investigate how the diffusion coefficient behaves on different regions of the chemical potential-temperature phase diagram. We find that diffusivity undergoes two types of dynamic transitions: a fragile-to-strong transition when the critical lambda-line is crossed by decreasing the temperature at a constant chemical potential; and a strong-to-strong transition when the critical tau-line is crossed by decreasing the temperature at a constant chemical potential.

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.

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.

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.

Carrier transfer in the optical recombination of quantum dots

We report a study of dynamic effects detected in the time-resolved emission from quantum dot ensembles. Experimental procedures were developed to search for common behaviors found in quantum dot systems independently of their composition: three quantum dot samples were experimentally characterized. Systems with contrasting interdot coupling are compared and their sensitivity to the excitation energy is analyzed. Our experimental results are compared and contrasted with other results available in literature. The optical recombination time dependence on system parameters is derived and compared to the experimental findings. We discuss the effects of occupation of the ground state in both valence and conduction bands of semiconductor quantum dots in the dynamics of the system relaxation as well as the nonlinear effects.

Knowledge acquisition by networks of interacting agents in the presence of observation errors

In this work we investigate knowledge acquisition as performed by multiple agents interacting as they infer, under the presence of observation errors, respective models of a complex system. We focus the specific case in which, at each time step, each agent takes into account its current observation as well as the average of the models of its neighbors. The agents are connected by a network of interaction of Erdos-Renyi or Barabasi-Albert type. First, we investigate situations in which one of the agents has a different probability of observation error (higher or lower). It is shown that the influence of this special agent over the quality of the models inferred by the rest of the network can be substantial, varying linearly with the respective degree of the agent with different estimation error. In case the degree of this agent is taken as a respective fitness parameter, the effect of the different estimation error is even more pronounced, becoming superlinear. To complement our analysis, we provide the analytical solution of the overall performance of the system. We also investigate the knowledge acquisition dynamic when the agents are grouped into communities. We verify that the inclusion of edges between agents (within a community) having higher probability of observation error promotes the loss of quality in the estimation of the agents in the other communities.

Protecting a quantum state from environmental noise by an incompatible finite-time measurement

We show that measurements of finite duration performed on an open two-state system can protect the initial state from a phase-noisy environment, provided the measured observable does not commute with the perturbing interaction. When the measured observable commutes with the environmental interaction, the finite-duration measurement accelerates the rate of decoherence induced by the phase noise. For the description of the measurement of an observable that is incompatible with the interaction between system and environment, we have found an approximate analytical expression, valid at zero temperature and weak coupling with the measuring device. We have tested the validity of the analytical predictions against an exact numerical approach, based on the superoperator-splitting method, that confirms the protection of the initial state of the system. When the coupling between the system and the measuring apparatus increases beyond the range of validity of the analytical approximation, the initial state is still protected by the finite-time measurement, according with the exact numerical calculations.

Directed Abelian algebras and their application to stochastic models

With each directed acyclic graph (this includes some D-dimensional lattices) one can associate some Abelian algebras that we call directed Abelian algebras (DAAs). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA, one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground-state wave functions (stationary state probability distributions) is an easy algebraic exercise. If one considers D-dimensional lattices and chooses Hamiltonians linear in the generators, in finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent z=D. One possible application of the DAA is to sandpile models. In the paper we present this application, considering one- and two-dimensional lattices. In the one-dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent sigma(tau)=3/2). We study the local density of particles inside large avalanches, showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found sigma(tau)=1.780 +/- 0.005.

Evolutionary dynamics on rugged fitness landscapes: Exact dynamics and information theoretical aspects

The parallel mutation-selection evolutionary dynamics, in which mutation and replication are independent events, is solved exactly in the case that the Malthusian fitnesses associated to the genomes are described by the random energy model (REM) and by a ferromagnetic version of the REM. The solution method uses the mapping of the evolutionary dynamics into a quantum Ising chain in a transverse field and the Suzuki-Trotter formalism to calculate the transition probabilities between configurations at different times. We find that in the case of the REM landscape the dynamics can exhibit three distinct regimes: pure diffusion or stasis for short times, depending on the fitness of the initial configuration, and a spin-glass regime for large times. The dynamic transition between these dynamical regimes is marked by discontinuities in the mean-fitness as well as in the overlap with the initial reference sequence. The relaxation to equilibrium is described by an inverse time decay. In the ferromagnetic REM, we find in addition to these three regimes, a ferromagnetic regime where the overlap and the mean-fitness are frozen. In this case, the system relaxes to equilibrium in a finite time. The relevance of our results to information processing aspects of evolution is discussed.