Role of noise in population dynamics cycles

Noise is an intrinsic feature of population dynamics and plays a crucial role in oscillations called phase-forgetting quasicycles by converting damped into sustained oscillations. This function of noise becomes evident when considering Langevin equations whose deterministic part yields only damped oscillations. We formulate here a consistent and systematic approach to population dynamics, leading to a Fokker-Planck equation and the associate Langevin equations in accordance with this conceptual framework, founded on stochastic lattice-gas models that describe spatially structured predator-prey systems. Langevin equations in the population densities and predator-prey pair density are derived in two stages. First, a birth-and-death stochastic process in the space of prey and predator numbers and predator-prey pair number is obtained by a contraction method that reduces the degrees of freedom. Second, a van Kampen expansion in the inverse of system size is then performed to get the Fokker-Planck equation. We also study the time correlation function, the asymptotic behavior of which is used to characterize the transition from the cyclic coexistence of species to the ordinary coexistence.

Perturbations of black p-branes

We consider black p-brane solutions of the low-energy string action, computing scalar perturbations. Using standard methods, we derive the wave equations obeyed by the perturbations and treat them analytically and numerically. We have found that tensorial perturbations obtained via a gauge-invariant formalism leads to the same results as scalar perturbations. No instability has been found. Asymptotically, these solutions typically reduce to a AdSd((p+2)) x Sd((8-p)) space which, in the framework of Maldacena's conjecture, can be regarded as a gravitational dual to a conformal field theory defined in a (p+1)-dimensional flat space-time. The results presented open the possibility of a better understanding the AdS/CFT correspondence, as originally formulated in terms of the relation among brane structures and gauge theories.

Field theory model for dark matter and dark energy in interaction

We propose a field theory model for dark energy and dark matter in interaction. Comparing the classical solutions of the field equations with the observations of the CMB shift parameter, baryonic acoustic oscillations, lookback time, and the Gold supernovae sample, we observe a possible interaction between dark sectors with energy decay from dark energy into dark matter. The observed interaction provides an alleviation to the coincidence problem.

KINETICS VERSUS HYDRODYNAMICS: GENERALIZATION OF LANDAU/COOPER-FRYE PRESCRIPTION FOR FREEZE-OUT

The problem of spectra formation in hydrodynamic approach to A + A collisions is considered within the Boltzmann equations. It is shown analytically and illustrated by numerical calculations that the particle momentum spectra can be presented in the Cooper-R-ye form despite freeze-out is not sharp and has the finite temporal width. The latter is equal to the inverse of the particle collision rate at points (t(sigma) (r, p), r) of the maximal emission at a fixed momentum p. The set of these points forms the hypersurfaces t(sigma)(r,p) which strongly depend on the values of p and typically do not enclose completely the initially dense matter. This is an important difference from the standard Cooper-Frye prescription (CFp), with a common freeze-out hypersurface for all p, that affects significantly the predicted spectra. Also, the well known problem of CFp as for negative contributions to the spectra from non-space-like parts of the freeze-out hypersurface is naturally eliminated in this improved prescription.

Deformations of the Tracy-Widom distribution

In random matrix theory, the Tracy-Widom (TW) distribution describes the behavior of the largest eigenvalue. We consider here two models in which TW undergoes transformations. In the first one disorder is introduced in the Gaussian ensembles by superimposing an external source of randomness. A competition between TW and a normal (Gaussian) distribution results, depending on the spreading of the disorder. The second model consists of removing at random a fraction of (correlated) eigenvalues of a random matrix. The usual formalism of Fredholm determinants extends naturally. A continuous transition from TW to the Weilbull distribution, characteristic of extreme values of an uncorrelated sequence, is obtained.

Physical approximations for the nonlinear evolution of perturbations in inhomogeneous dark energy scenarios

The abundance and distribution of collapsed objects such as galaxy clusters will become an important tool to investigate the nature of dark energy and dark matter. Number counts of very massive objects are sensitive not only to the equation of state of dark energy, which parametrizes the smooth component of its pressure, but also to the sound speed of dark energy, which determines the amount of pressure in inhomogeneous and collapsed structures. Since the evolution of these structures must be followed well into the nonlinear regime, and a fully relativistic framework for this regime does not exist yet, we compare two approximate schemes: the widely used spherical collapse model and the pseudo-Newtonian approach. We show that both approximation schemes convey identical equations for the density contrast, when the pressure perturbation of dark energy is parametrized in terms of an effective sound speed. We also make a comparison of these approximate approaches to general relativity in the linearized regime, which lends some support to the approximations.

Classical noncommutative electrodynamics with external source

In a U(1)(*)-noncommutative gauge field theory we extend the Seiberg-Witten map to include the (gauge-invariance-violating) external current and formulate-to the first order in the noncommutative parameter-gauge-covariant classical field equations. We find solutions to these equations in the vacuum and in an external magnetic field, when the 4-current is a static electric charge of a finite size a, restricted from below by the elementary length. We impose extra boundary conditions, which we use to rule out all singularities, 1/r included, from the solutions. The static charge proves to be a magnetic dipole, with its magnetic moment being inversely proportional to its size a. The external magnetic field modifies the long-range Coulomb field and some electromagnetic form factors. We also analyze the ambiguity in the Seiberg-Witten map and show that at least to the order studied here it is equivalent to the ambiguity of adding a homogeneous solution to the current-conservation equation.

Gravitational stability of simply rotating Myers-Perry black holes: Tensorial perturbations

We study the stability of D >= 7 asymptotically flat black holes rotating in a single two-plane against tensor-type gravitational perturbations. The extensive search of quasinormal modes for these black holes did not indicate any presence of growing modes, implying the stability of simply rotating Myers-Perry black holes against tensor-type perturbations.

Graviton emission in the bulk by a simply rotating black hole

In this work, we study the emission of tensor-type gravitational degrees of freedom from a higher-dimensional, simply rotating black hole in the bulk. The decoupled radial part of the corresponding field equation is first solved analytically in the limit of low-energy emitted particles and low-angular momentum of the black hole in order to derive the absorption probability. Both the angular and radial equations are then solved numerically, and the comparison of the analytical and numerical results shows a very good agreement in the low and intermediate energy regimes. By using our exact, numerical results we compute the energy and angular-momentum emission rates and their dependence on the spacetime parameters such as the number of additional spacelike dimensions and the angular momentum of the black hole. Particular care is given to the convergence of our results in terms of the number of modes taken into account in the calculation and the multiplicity of graviton tensor modes that correspond to the same angular-momentum numbers.

Gravitational instability of simply rotating AdS black holes in higher dimensions

We study the stability of AdS black holes rotating in a single two-plane for tensor-type gravitational perturbations in D > 6 space-time dimensions. First, by an analytic method, we show that there exists no unstable mode when the magnitude a of the angular momentum is smaller than r(h)(2)/R, where r(h) is the horizon radius and R is the AdS curvature radius. Then, by numerical calculations of quasinormal modes, using the separability of the relevant perturbation equations, we show that an instability occurs for rapidly rotating black holes with a > r(h)(2)/R, although the growth rate is tiny (of order 10(-12) of the inverse horizon radius). We give numerical evidence indicating that this instability is caused by superradiance.

Stability of higher dimensional Reissner-Nordstrom-anti-de Sitter black holes

We investigate stability of the D-dimensional Reissner-Nordstrom-anti-de Sitter metrics as solutions of the Einstein-Maxwell equations. We have shown that asymptotically anti-de Sitter (AdS) black holes are dynamically stable for all values of charge and anti-de Sitter radius in D=5,6...11 dimensional space-times. This does not contradict dynamical instability of RNAdS black holes found by Gubser in N=8 gauged supergravity, because the latter instability comes from the tachyon mode of the scalar field, coupled to the system. Asymptotically AdS black holes are known to be thermodynamically unstable for some region of parameters, yet, as we have shown here, they are stable against gravitational perturbations.

Gravitational wave recoil in Robinson-Trautman spacetimes

We consider the gravitational recoil due to nonreflection-symmetric gravitational wave emission in the context of axisymmetric Robinson-Trautman spacetimes. We show that regular initial data evolve generically into a final configuration corresponding to a Schwarzschild black hole moving with constant speed. For the case of (reflection-)symmetric initial configurations, the mass of the remnant black hole and the total energy radiated away are completely determined by the initial data, allowing us to obtain analytical expressions for some recent numerical results that have appeared in the literature. Moreover, by using the Galerkin spectral method to analyze the nonlinear regime of the Robinson-Trautman equations, we show that the recoil velocity can be estimated with good accuracy from some asymmetry measures (namely the first odd moments) of the initial data. The extension for the nonaxisymmetric case and the implications of our results for realistic situations involving head-on collision of two black holes are also discussed.

Transition to chaotic scattering: Signatures in the differential cross section

We show that bifurcations in chaotic scattering manifest themselves through the appearance of an infinitely fine-scale structure of singularities in the cross section. These ""rainbow singularities"" are created in a cascade, which is closely related to the bifurcation cascade undergone by the set of trapped orbits (the chaotic saddle). This cascade provides a signature in the differential cross section of the complex pattern of bifurcations of orbits underlying the transition to chaotic scattering. We show that there is a power law with a universal coefficient governing the sequence of births of rainbow singularities and we verify this prediction by numerical simulations.

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.

Nonlinear waves in a quark gluon plasma

We study the propagation of perturbations in the quark gluon plasma. This subject has been addressed in other works and in most of the theoretical descriptions of this phenomenon the hydrodynamic equations have been linearized for simplicity. We propose an alternative approach, also based on hydrodynamics but taking into account the nonlinear terms of the equations. We show that these terms may lead to localized waves or even solitons. We use a simple equation of state for the QGP and expand the hydrodynamic equations around equilibrium configurations. The resulting differential equations describe the propagation of perturbations in the energy density. We solve them numerically and find that localized perturbations can propagate for long distances in the plasma. Under certain conditions our solutions mimic the propagation of Korteweg-de Vries solitons.