Spreading of Perturbations in Long-Range Interacting Classical Lattice Models

Lieb-Robinson-type bounds are reported for a large class of classical Hamiltonian lattice models. By a suitable rescaling of energy or time, such bounds can be constructed for interactions of arbitrarily long range. The bound quantifies the dependence of the system's dynamics on a perturbation of the initial state. The effect of the perturbation is found to be effectively restricted to the interior of a causal region of logarithmic shape, with only small, algebraically decaying effects in the exterior. A refined bound, sharper than conventional Lieb-Robinson bounds, is required to correctly capture the shape of the causal region, as confirmed by numerical results for classical long-range $XY$ chains. We discuss the relevance of our findings for the relaxation to equilibrium of long-range interacting lattice models.Comment: 4+6 pages, 3+2 figure

Poincar\'e profiles of groups and spaces

We introduce a spectrum of monotone coarse invariants for metric measure spaces called Poincar\'{e} profiles. The two extremes of this spectrum determine the growth of the space, and the separation profile as defined by Benjamini--Schramm--Tim\'{a}r. In this paper we focus on properties of the Poincar\'{e} profiles of groups with polynomial growth, and of hyperbolic spaces, where we deduce a connection between these profiles and conformal dimension. As applications, we use these invariants to show the non-existence of coarse embeddings in a variety of examples.Comment: 55 pages. To appear in Revista Matem\'atica Iberoamerican

Is nonlinear propagation responsible for the brassiness of elephant trumpet calls?

African elephants (Loxodonta africana) produce a broad diversity of sounds ranging from infrasonic rumbles to much higher frequency trumpets. Trumpet calls are very loud voiced signals given by highly aroused elephants, and appear to be produced by a forceful expulsion of air through the trunk. Some trumpet calls have a very distinctive quality that is unique in the animal kingdom, but resemble the "brassy" sounds that can be produced with brass musical instruments such as trumpets or trombones. Brassy musical sounds are characterised by a flat spectral slope caused by the nonlinear propagation of the source wave as it travels through the long bore of the instrument. The extent of this phenomenon, which normally occurs at high intensity levels (e.g. fortissimo), depends on the fundamental frequency (F0) of the source as well as on the length of the resonating tube. Interestingly, the length of the vocal tract of the elephant (as measured from the vocal folds to the end of the trunk) approximates the critical length for shockwave formation, given the fundamental frequency and intensity of trumpet calls. We suggest that this phenomenon could explain the unique, distinctive brassy quality of elephant trumpet calls

Hydrodynamics of operator spreading and quasiparticle diffusion in interacting integrable systems

We address the hydrodynamics of operator spreading in interacting integrable lattice models. In these models, operators spread through the ballistic propagation of quasiparticles, with an operator front whose velocity is locally set by the fastest quasiparticle velocity. In interacting integrable systems, this velocity depends on the density of the other quasiparticles, so equilibrium density fluctuations cause the front to follow a biased random walk, and therefore to broaden diffusively. Ballistic front propagation and diffusive front broadening are also generically present in non-integrable systems in one dimension; thus, although the mechanisms for operator spreading are distinct in the two cases, these coarse grained measures of the operator front do not distinguish between the two cases. We present an expression for the front-broadening rate; we explicitly derive this for a particular integrable model (the "Floquet-Fredrickson-Andersen" model), and argue on kinetic grounds that it should apply generally. Our results elucidate the microscopic mechanism for diffusive corrections to ballistic transport in interacting integrable models.Comment: Published versio

Beyond the 2nd Fermi Pulsar Catalog

Over thirteen times more gamma-ray pulsars have now been studied with the Large Area Telescope on NASA's Fermi satellite than the ten seen with the Compton Gamma-Ray Observatory in the nineteen-nineties. The large sample is diverse, allowing better understanding both of the pulsars themselves and of their roles in various cosmic processes. Here we explore the prospects for even more gamma-ray pulsars as Fermi enters the 2nd half of its nominal ten-year mission. New pulsars will naturally tend to be fainter than the first ones discovered. Some of them will have unusual characteristics compared to the current population, which may help discriminate between models. We illustrate a vision of the future with a sample of six pulsars discovered after the 2nd Fermi Pulsar Catalog was written.Comment: 6 pages, to appear in the proceedings of "The Fast and the Furious: Energetic Phenomena in Isolated Neutron Stars, Pulsar Wind Nebulae and Supernova Remnants",ESAC, Madrid, Spain, 22 - 24 May 2013 http://xmm.esac.esa.int/external/xmm_science/workshops/2013_science/, to be published as a regular issue of the Astronomische Nachrichten / Astronomical Notes (AN

The geographical significance of the first five-year development programme of Trinidad and Tobago 1958 to 1962

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Inhomogeneous Gain Saturation in EDF: Experiment and Modeling

Erbium-Doped Fiber Amplifiers can present holes in spectral gain in Wavelength Division Multiplexing operation. The origin of this inhomogeneous saturation behavior is still a subject of controversy. In this paper we present both an experimental methods and a gain's model. Our experimental method allow us to measure the first homogeneous linewidth of the 1.5 $\mu$m erbium emission with gain spectral hole burning consistently with the other measurement in the literature and the model explains the differences observed in literature between GSHB and other measurement methods