The Hartree equation for infinitely many particles. II. Dispersion and scattering in 2D

We consider the nonlinear Hartree equation for an interacting gas containing infinitely many particles and we investigate the large-time stability of the stationary states of the form $f(-\Delta)$, describing an homogeneous Fermi gas. Under suitable assumptions on the interaction potential and on the momentum distribution $f$, we prove that the stationary state is asymptotically stable in dimension 2. More precisely, for any initial datum which is a small perturbation of $f(-\Delta)$ in a Schatten space, the system weakly converges to the stationary state for large times

Constraining photon dispersion relations from observations of the Vela pulsar with H.E.S.S

Some approaches to Quantum Gravity (QG) predict a modification of photon dispersion relations due to a breaking of Lorentz invariance. The effect is expected to affect photons near an effective QG energy scale. This scale has been constrained by observing gamma rays emitted from variable astrophysical sources such as gamma-ray bursts and flaring active galactic nuclei. Pulsars exhibit a periodic emission of possibly ms time scale. In 2014, the H.E.S.S. experiment reported the detection down to 20 GeV of gamma rays from the Vela pulsar having a periodicity of 89 ms. Using a likelihood analysis, calibrated with a dedicated Monte-Carlo procedure, we obtain the first limit on QG energy scale with the Vela pulsar. In this paper, the method and calibration procedure in use will be described and the results will be discussed.Comment: 7 pages, 4 figures, In Proceedings of the 34th International Cosmic Ray Conference (ICRC2015), The Hague (The Netherlands

Modeling the shortening history of a fault tip fold using structural and geomorphic records of deformation

We present a methodology to derive the growth history of a fault tip fold above a basal detachment. Our approach is based on modeling the stratigraphic and geomorphic records of deformation, as well as the finite structure of the fold constrained from seismic profiles. We parameterize the spatial deformation pattern using a simple formulation of the displacement field derived from sandbox experiments. Assuming a stationary spatial pattern of deformation, we simulate the gradual warping and uplift of stratigraphic and geomorphic markers, which provides an estimate of the cumulative amounts of shortening they have recorded. This approach allows modeling of isolated terraces or growth strata. We apply this method to the study of two fault tip folds in the Tien Shan, the Yakeng and Anjihai anticlines, documenting their deformation history over the past 6–7 Myr. We show that the modern shortening rates can be estimated from the width of the fold topography provided that the sedimentation rate is known, yielding respective rates of 2.15 and 1.12 mm/yr across Yakeng and Anjihai, consistent with the deformation recorded by fluvial and alluvial terraces. This study demonstrates that the shortening rates across both folds accelerated significantly since the onset of folding. It also illustrates the usefulness of a simple geometric folding model and highlights the importance of considering local interactions between tectonic deformation, sedimentation, and erosion

The bag-of-frames approach: a not so sufficient model for urban soundscapes

The "bag-of-frames" approach (BOF), which encodes audio signals as the long-term statistical distribution of short-term spectral features, is commonly regarded as an effective and sufficient way to represent environmental sound recordings (soundscapes) since its introduction in an influential 2007 article. The present paper describes a concep-tual replication of this seminal article using several new soundscape datasets, with results strongly questioning the adequacy of the BOF approach for the task. We show that the good accuracy originally re-ported with BOF likely result from a particularly thankful dataset with low within-class variability, and that for more realistic datasets, BOF in fact does not perform significantly better than a mere one-point av-erage of the signal's features. Soundscape modeling, therefore, may not be the closed case it was once thought to be. Progress, we ar-gue, could lie in reconsidering the problem of considering individual acoustical events within each soundscape

Origin of the orbital and spin orderings in rare-earth titanates

Rare-earth titanates RTiO$_3$ are Mott insulators displaying a rich physical behavior, featuring most notably orbital and spin orders in their ground state. The origin of their ferromagnetic to antiferromagnetic transition as a function of the size of the rare-earth however remains debated. Here we show on the basis of symmetry analysis and first-principles calculations that although rare-earth titanates are nominally Jahn-Teller active, the Jahn-Teller distortion is negligible and irrelevant for the description of the ground state properties. At the same time, we demonstrate that the combination of two antipolar motions produces an effective Jahn-Teller-like motion which is the key of the varying spin-orbital orders appearing in titanates. Thus, titanates are prototypical examples illustrating how a subtle interplay between several lattice distortions commonly appearing in perovskites can produce orbital orderings and insulating phases irrespective of proper Jahn-Teller motions.Comment: Accepted in Physical Review

Semi-classical spin dynamics of the antiferromagnetic Heisenberg model on the kagome lattice

We investigate the dynamical properties of the classical antiferromagnetic Heisenberg model on the kagome lattice using a combination of Monte Carlo and molecular dynamics simulations. We find that frustration induces a distribution of timescales in the cooperative paramagnetic regime (i.e. far above the onset of coplanarity), as recently reported experimentally in deuterium jarosite. At lower temperature, when the coplanar correlations are well established, we show that the weath- ervane loop fluctuations control the system relaxation : the time distribution observed at higher temperatures splits into two distinct timescales associated with fluctuations in the plane and out of the plane of coplanarity. The temperature and wave vector dependences of these two components are qualitatively consistent with loops diffusing in the entropically dominated free energy landscape. Numerical results are discussed and compared with the $O(N)$ model and recent experiments for both classical and quantum realizations of the kagome magnets.Comment: 18 pages, 14 figure