Conformal dimension and random groups

We give a lower and an upper bound for the conformal dimension of the boundaries of certain small cancellation groups. We apply these bounds to the few relator and density models for random groups. This gives generic bounds of the following form, where $l$ is the relator length, going to infinity. (a) 1 + 1/C < \Cdim(\bdry G) < C l / \log(l), for the few relator model, and (b) 1 + l / (C\log(l)) < \Cdim(\bdry G) < C l, for the density model, at densities $d < 1/16$. In particular, for the density model at densities $d < 1/16$, as the relator length $l$ goes to infinity, the random groups will pass through infinitely many different quasi-isometry classes.Comment: 32 pages, 4 figures. v2: Final version. Main result improved to density < 1/16. Many minor improvements. To appear in GAF

Photometric stability analysis of the Exoplanet Characterisation Observatory

Photometric stability is a key requirement for time-resolved spectroscopic observations of transiting extrasolar planets. In the context of the Exoplanet Characterisation Observatory (EChO) mission design, we here present and investigate means of translating spacecraft pointing instabilities as well as temperature fluctuation of its optical chain into an overall error budget of the exoplanetary spectrum to be retrieved. Given the instrument specifications as of date, we investigate the magnitudes of these photometric instabilities in the context of simulated observations of the exoplanet HD189733b secondary eclipse.Comment: submitted to MNRA

Asymmetry of bipartite quantum discord

It is known from the analysis of the density matrix for bipartite systems that the quantum discord (as a measure of quantum correlations) depends on the particular subsystem chosen for the projective measurements. We study asymmetry of the discord in a simple physical model of two spin-1/2 particles with the dipole-dipole interaction governed by the XY Hamiltonian in the inhomogeneous magnetic field. The dependence of the above discord asymmetry on the Larmour frequencies at both T=0 (the ground state) and $T>0$ has been investigated. It is demonstrated, in particular, that the asymmetry is negligible for high temperatures but it may become significant with the decrease in temperature.Comment: 5 pages 3 figure

Quantum Dissension: Generalizing Quantum Discord for Three-Qubit States

We introduce the notion of quantum dissension for a three-qubit system as a measure of quantum correlations. We use three equivalent expressions of three-variable mutual information. Their differences can be zero classically but not so in quantum domain. It generalizes the notion of quantum discord to a multipartite system. There can be multiple definitions of the dissension depending on the nature of projective measurements done on the subsystems. As an illustration, we explore the consequences of these multiple definitions and compare them for three-qubit pure and mixed GHZ and W states. We find that unlike discord, dissension can be negative. This is because measurement on a subsystem may enhance the correlations in the rest of the system. This approach can pave a way to generalize the notion of quantum correlations in the multiparticle setting.Comment: 9 pages 6 figures typo fixed and some arguments adde

EChOSim: The Exoplanet Characterisation Observatory software simulator

EChOSim is the end-to-end time-domain simulator of the Exoplanet Characterisation Observatory (EChO) space mission. EChOSim has been developed to assess the capability EChO has to detect and characterize the atmospheres of transiting exoplanets, and through this revolutionize the knowledge we have of the Milky Way and of our place in the Galaxy. Here we discuss the details of the EChOSim implementation and describe the models used to represent the instrument and to simulate the detection. Software simulators have assumed a central role in the design of new instrumentation and in assessing the level of systematics affecting the measurements of existing experiments. Thanks to its high modularity, EChOSim can simulate basic aspects of several existing and proposed spectrometers for exoplanet transits, including instruments on the Hubble Space Telescope and Spitzer, or ground-based and balloon borne experiments. A discussion of different uses of EChOSim is given, including examples of simulations performed to assess the EChO mission

Magnetic excitations in a new anisotropic Kagom\'{e} antiferromagnet

The Nd-langasite compound contains planes of magnetic Nd3+ ions on a lattice topologically equivalent to a kagom\'{e} net. The magnetic susceptibility does not reveal any signature of long-range ordering down to 2 K but rather a correlated paramagnetism with significant antiferromagnetic interactions between the Nd and a single-ion anisotropy due to crystal field effect. Inelastic neutron scattering on Nd-langasite powder and single-crystal allowed to probe its very peculiar low temperature dynamical magnetic correlations. They present unusual dispersive features and are broadly localized in wave-vector Q revealing a structure factor associated to characteristics short range-correlations between the magnetic atoms. From comparison with theoretical calculations, these results are interpreted as a possible experimental observation of a spin liquid state in an anisotropic kagom\'{e} antiferromagnet.Comment: to appear in Physica

Параметрична логістична модель планування роботи різних видів транспорту

Запропонована логістична модель планування роботи різних видів транспорту вантажної станції за умов ефективного використання вантажно-розвантажувальних механізмів, вантажних фронтів та складської обробки вантажів.Предложенная логистическая модель планирования работы различных видов транспорта грузовой станции в условиях эффективного использования погрузочно-разгрузочных механизмов, грузовых фронтов и складской обработки грузов.The proposed model of logistic planning of transport modes cargo station for the effective use of material handling equipment, commercial fronts and warehouse handling

Order by Disorder and Energetic Selection of the Ground State in the XY Pyrochlore Antiferromagnet Er2Ti2O7. An Inelastic Neutron Scattering Study

Examples of materials where an "order by disorder" mechanism is at play to select a particular ground state are scarce. It has recently been proposed, however, that the antiferromagnetic XY pyrochlore Er2Ti2O7, reveals a most convincing case of this mechanism. Observation of a spin gap at zone centers has recently been interpreted as a corroboration of this physics. In this paper, we argue, however, that the anisotropy generated by the interaction-induced admixing between the crystal-field ground and excited levels provides for an alternative mechanism. It especially predicts the opening of a spin gap of about 15 micro-eV, which is of the same order of magnitude as the one observed experimentally. We report new high resolution inelastic neutron scattering data which can be well understood within this scenario.Comment: This version corrects a mistake on the numerical values of the exchange couplings $J$ in relation to the published versio