Geometric mutual information at classical critical points

A practical use of the entanglement entropy in a 1d quantum system is to identify the conformal field theory describing its critical behavior. It is exactly $(c/3)\ln \ell$ for an interval of length $\ell$ in an infinite system, where $c$ is the central charge of the conformal field theory. Here we define the geometric mutual information, an analogous quantity for classical critical points. We compute this for 2d conformal field theories in an arbitrary geometry, and show in particular that for a rectangle cut into two rectangles, it is proportional to $c$. This makes it possible to extract $c$ in classical simulations, which we demonstrate for the critical Ising and 3-state Potts models.Comment: 5 pages. v3: published versio

Cause and Possible Treatments of Foot Lesions in Captive Syrian Hamsters (Mesocricetus auratus)

Syrian hamsters (Mesocricetus auratus) run extensively in exercise wheels. This running may cause paw lesions. Three treatments of these wounds (topical application of vitamin E, wheel blocking, and a combination of both) were compared using both sexes. A pretreatment period with or without wheels lasted 15 days and the ensuing treatment period lasted 45 days. At the end of the pre-treatment period, none of the animals without wheels had paw wounds, whereas at least 75% of the females and 100% of the males with wheels did. Females had fewer and smaller wounds than males at this point. At the end of the treatment period, no effect of vitamin E could be discerned, but significant wound healing occurred after wheel blocking in both males and females. Wheel blocking is an easy way to prevent or treat paw wounds, but it presents problems in terms of animal welfare, as wheels are an important cage enrichment for hamsters

Observation of gravity-capillary wave turbulence

We report the observation of the cross-over between gravity and capillary wave turbulence on the surface of mercury. The probability density functions of the turbulent wave height are found to be asymmetric and thus non Gaussian. The surface wave height displays power-law spectra in both regimes. In the capillary region, the exponent is in fair agreement with weak turbulence theory. In the gravity region, it depends on the forcing parameters. This can be related to the finite size of the container. In addition, the scaling of those spectra with the mean energy flux is found in disagreement with weak turbulence theory for both regimes

Wave-vortex interaction

We present an experimental study on the effect of a electromagneticaly generated vortex flow on parametrically amplified waves at the surface of a fluid. The underlying vortex flow, generated by a periodic Lorentz force, creates spatio-temporal fluctuations that interact nonlinearly with the standing surface waves. We characterize the bifurcation diagram and measure the power spectrum density (PSD) of the local surface wave amplitude. We show that the parametric instability threshold increases with increasing intensity of the vortex flow.Comment: 8 pages, 10 figures, submitted to Phys. Rev.

A simple mechanism for the reversals of Earth's magnetic field

We show that a model, recently used to describe all the dynamical regimes of the magnetic field generated by the dynamo effect in the VKS experiment [1], also provides a simple explanation of the reversals of Earth's magnetic field, despite strong differences between both systems.Comment: update version, with new figure

The Domination Number of Grids

In this paper, we conclude the calculation of the domination number of all $n\times m$ grid graphs. Indeed, we prove Chang's conjecture saying that for every $16\le n\le m$, $\gamma(G_{n,m})=\lfloor\frac{(n+2)(m+2)}{5}\rfloor -4$.Comment: 12 pages, 4 figure

Enhanced Eshelby twist on thin wurtzite InP nanowires and measurement of local crystal rotation

We have performed a detailed study of the lattice distortions of InP wurtzite nanowires containing an axial screw dislocation. Eshelby predicted that this kind of system should show a crystal rotation due to the dislocation induced torque. We have measured the twisting rate and the dislocation Burgers vector on individual wires, revealing that nanowires with a 10-nm radius have a twist up to 100% larger than estimated from elasticity theory. The strain induced by the deformation has a Mexican-hat-like geometry, which may create a tube-like potential well for carriers

Entanglement in gapless resonating valence bond states

We study resonating-valence-bond (RVB) states on the square lattice of spins and of dimers, as well as SU(N)-invariant states that interpolate between the two. These states are ground states of gapless models, although the SU(2)-invariant spin RVB state is also believed to be a gapped liquid in its spinful sector. We show that the gapless behavior in spin and dimer RVB states is qualitatively similar by studying the R\'enyi entropy for splitting a torus into two cylinders, We compute this exactly for dimers, showing it behaves similarly to the familiar one-dimensional log term, although not identically. We extend the exact computation to an effective theory believed to interpolate among these states. By numerical calculations for the SU(2) RVB state and its SU(N)-invariant generalizations, we provide further support for this belief. We also show how the entanglement entropy behaves qualitatively differently for different values of the R\'enyi index $n$, with large values of $n$ proving a more sensitive probe here, by virtue of exhibiting a striking even/odd effect.Comment: 44 pages, 14 figures, published versio

Observation of Sommerfeld precursors on a fluid surface

We report the observation of two types of Sommerfeld precursors (or forerunners) on the surface of a layer of mercury. When the fluid depth increases, we observe a transition between these two precursor surface waves in good agreement with the predictions of asymptotic analysis. At depths thin enough compared to the capillary length, high frequency precursors propagate ahead of the ''main signal'' and their period and amplitude, measured at a fixed point, increase in time. For larger depths, low frequency ''precursors'' follow the main signal with decreasing period and amplitude. These behaviors are understood in the framework of the analysis first introduced for linear transient electromagnetic waves in a dielectric medium by Sommerfeld and Brillouin [1].Comment: to be published in Physical Review Letter

Harmonic generation with multi-layer dielectric metasurfaces

Abstract Metasurfaces have recently gained extensive interest because of their extraordinary optical behavior as artificial material interfaces with ultrahigh compactness. In this framework, dielectric platforms have newly become very promising for nonlinear nanophotonics, providing opportunities, especially for ultrafast optical switching, and high harmonic generation, opening the research field of nonlinear metaoptics. Up to now, nonlinear metaoptics have been mostly explored using single metasurfaces. However, in a long-term vision, the stacking of optical metasurfaces, very challenging in terms of fabrication, is one key goal of this research field. Here, we demonstrate a three-layer metasurface in the AlGaAs-on-insulator platform, which improves the second harmonic generation efficiency by more than one order of magnitude with respect to its one-layer counterpart. Our achievement paves the way toward phase-shaping multilayer and multifunctional all-dielectric metasurfaces