Flat singularities of chained systems, illustrated with an aircraft model

We consider flat differential control systems for which there exist flat outputs that are part of the state variables and study them using Jacobi bound. We introduce a notion of saddle Jacobi bound for an ordinary differential system for $n$ equations in $n+m$ variables. Systems with saddle Jacobi number generalize various notions of chained and diagonal systems and form the widest class of systems admitting subsets of state variables as flat output, for which flat parametrization may be computed without differentiating the initial equations. We investigate apparent and intrinsic flat singularities of such systems. As an illustration, we consider the case of a simplified aircraft model, providing new flat outputs and showing that it is flat at all points except possibly in stalling conditions. Finally, we present numerical simulations showing that a feedback using those flat outputs is robust to perturbations and can also compensate model errors, when using a more realistic aerodynamic model.Comment: 36 pages, 8 figure

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

Superfluid 4He dynamics beyond quasiparticle excitations

The dynamics of superfluid 4He at and above the Landau quasiparticle regime is investigated by high precision inelastic neutron scattering measurements of the dynamic structure factor. A highly structured response is observed above the familiar phonon-maxon-roton spectrum, characterized by sharp thresholds for phonon-phonon, maxon-roton and roton-roton coupling processes. The experimental dynamic structure factor is compared to the calculation of the same physical quantity by a Dynamic Many-body theory including three-phonon processes self-consistently. The theory is found to provide a quantitative description of the dynamics of the correlated bosons for energies up to about three times that of the Landau quasiparticles.Comment: 5 pages, 3 figure

Absence of strong magnetic fluctuations in the iron phosphide superconductors LaFePO and Sr2ScO3FeP

We report neutron inelastic scattering measurements on polycrystalline LaFePO and Sr2ScO3FeP, two members of the iron phosphide families of superconductors. No evidence is found for any magnetic fluctuations in the spectrum of either material in the energy and wavevector ranges probed. Special attention is paid to the wavevector at which spin-density-wave-like fluctuations are seen in other iron-based superconductors. We estimate that the magnetic signal, if present, is at least a factor of four (Sr2ScO3FeP) or seven (LaFePO) smaller than in the related iron arsenide and chalcogenide superconductors. These results suggest that magnetic fluctuations are not as influential on the electronic properties of the iron phosphide systems as they are in other iron-based superconductors.Comment: 7 pages, 5 figure

Haydeeite: a spin-1/2 kagome ferromagnet

The mineral haydeeite, alpha-MgCu3(OD)6Cl2, is a S=1/2 kagome ferromagnet that displays long-range magnetic order below TC=4.2 K with a strongly reduced moment. Our inelastic neutron scattering data show clear spin-wave excitations that are well described by a Heisenberg Hamiltonian with ferromagnetic nearest-neighbor exchange J1=-38 K and antiferromagnetic exchange Jd=+11 K across the hexagons of the kagome lattice. These values place haydeeite very close to the quantum phase transition between ferromagnetic order and non-coplanar twelve-sublattice cuboc2 antiferromagnetic order. Diffuse dynamic short-range ferromagnetic correlations observed above TC persist well into the ferromagnetically ordered phase with a behavior distinct from critical scattering

Environment as a Witness: Selective Proliferation of Information and Emergence of Objectivity in a Quantum Universe

We study the role of the information deposited in the environment of an open quantum system in course of the decoherence process. Redundant spreading of information -- the fact that some observables of the system can be independently ``read-off'' from many distinct fragments of the environment -- is investigated as the key to effective objectivity, the essential ingredient of ``classical reality''. This focus on the environment as a communication channel through which observers learn about physical systems underscores importance of quantum Darwinism -- selective proliferation of information about ``the fittest states'' chosen by the dynamics of decoherence at the expense of their superpositions -- as redundancy imposes the existence of preferred observables. We demonstrate that the only observables that can leave multiple imprints in the environment are the familiar pointer observables singled out by environment-induced superselection (einselection) for their predictability. Many independent observers monitoring the environment will therefore agree on properties of the system as they can only learn about preferred observables. In this operational sense, the selective spreading of information leads to appearance of an objective ``classical reality'' from within quantum substrate.Comment: New figures, to appear in PR