We determine analytically the phase diagram of the toric code model in a parallel magnetic field which displays three distinct regions. Our study relies on two high-order perturbative expansions in the strong- and weak-field limit, as well as a large
-spin analysis. Calculations in the topological phase establish a quasiparticle picture for the anyonic excitations. We obtain two second-order transition lines that merge with a first-order line giving rise to a multicritical point as recently suggested by numerical simulations. We compute the values of the corresponding critical fields and exponents that drive the closure of the gap. We also give the one-particle dispersions of the anyonic quasiparticles inside the topological phase.
We investigate a new oriented variant of the Firefighter Problem. In the traditional Firefighter Problem, a fire breaks out at a given vertex of a graph, and at each time interval spreads to neighbouring vertices that have not been protected, while a
constant number of vertices are protected at each time interval. In the version of the problem considered here, the firefighters are able to orient the edges of the graph before the fire breaks out, but the fire could start at any vertex. We consider this problem when played on a graph in one of several graph classes, and give upper and lower bounds on the number of vertices that can be saved. In particular, when one firefighter is available at each time interval, and the given graph is a complete graph, or a complete bipartite graph, we present firefighting strategies that are provably optimal. We also provide lower bounds on the number of vertices that can be saved as a function of the chromatic number, of the maximum degree, and of the treewidth of a graph. For a subcubic graph, we show that the firefighters can save all but two vertices, and this is best possible.
In this paper, we study the Besov regularity of Levy white noises on the $d$-dimensional torus. Due to their rough sample paths, the white noises that we consider are defined as generalized stochastic fields. We, initially, obtain regularity results
for general Levy white noises. Then, we focus on two subclasses of noises: compound Poisson and symmetric-$alpha$-stable (including Gaussian), for which we make more precise statements. Before measuring regularity, we show that the question is well-posed; we prove that Besov spaces are in the cylindrical $sigma$-field of the space of generalized functions. These results pave the way to the characterization of the $n$-term wavelet approximation properties of stochastic processes.
We propose a simple mean-field ansatz to study phase transitions from a topological phase to a trivial phase. We probe the efficiency of this approach by considering the string-net model in the presence of a string tension for any anyon theory. Such
a perturbation is known to be responsible for a deconfinement-confinement phase transition which is well described by the present variational setup. We argue that mean-field results become exact in the limit of large total quantum dimension.
Embedded RF contacts are integrated within the ITER ICRH launcher to allow assembling, sliding and to lower the thermo-mechanical stress. They have to withstand a peak RF current up to 2.5 kA at 55 MHz in steady-state conditions, in the vacuum enviro
nment of themachine.The contacts have to sustain a temperature up to 250{textdegree}Cduring several days in baking operations and have to be reliable during the whole life of the launcher without degradation. The RF contacts are critical components for the launcher performance and intensive R&D is therefore required, since no RF contactshave so far been qualified at these specifications. In order to test and validate the anticipated RF contacts in operational conditions, CEA has prepared a test platform consisting of a steady-state vacuum pumped RF resonator. In collaboration with ITER Organization and the CYCLE consortium (CYclotronCLuster for Europe), an R&D program has been conducted to develop RF contacts that meet the ITER ICRH launcher specifications. A design proposed by CYCLE consortium, using brazed lamellas supported by a spring to improve thermal exchange efficiency while guaranteeing high contact force, was tested successfully in the T-resonator up to 1.7 kA during 1200 s, but failed for larger current values due to a degradation of the contacts. Details concerning the manufacturing of the brazed contacts on its titanium holder, the RF tests results performed on the resonator and the non-destructive tests analysis of the contacts are given in this paper.
The Jahn-Teller distortion, by its very nature, is often at the heart of the various electronic properties displayed by perovskites and related materials. Despite the Jahn-Teller mode being non- polar in nature, we devise and demonstrate in the prese
nt letter an electric field control of Jahn-Teller distortions in bulk perovskites. The electric field control is enabled through an anharmonic lattice mode coupling between the Jahn-Teller distortion and a polar mode. We confirm this coupling, and explicitly an electric field effect, through first principles calculations. The coupling will always exist within the P b2 1 m space group, which is found to be the favoured ground state for various perovskites under sufficient tensile epitaxial strain. Intriguingly, the calculations reveal that this mechanism is not only restricted to Jahn-Teller active systems, promising a general route to tune or induce novel electronic functionality in perovskites as a whole.
We compare three methods to measure the count-in-cell probability density function of galaxies in a spectroscopic redshift survey. From this comparison we found that when the sampling is low (the average number of object per cell is around unity) it
is necessary to use a parametric method to model the galaxy distribution. We used a set of mock catalogues of VIPERS, in order to verify if we were able to reconstruct the cell-count probability distribution once the observational strategy is applied. We find that in the simulated catalogues, the probability distribution of galaxies is better represented by a Gamma expansion than a Skewed Log-Normal. Finally, we correct the cell-count probability distribution function from the angular selection effect of the VIMOS instrument and study the redshift and absolute magnitude dependency of the underlying galaxy density function in VIPERS from redshift $0.5$ to $1.1$. We found very weak evolution of the probability density distribution function and that it is well approximated, independently from the chosen tracers, by a Gamma distribution.
Compressed sensing theory is slowly making its way to solve more and more astronomical inverse problems. We address here the application of sparse representations, convex optimization and proximal theory to radio interferometric imaging. First, we ex
pose the theory behind interferometric imaging, sparse representations and convex optimization, and second, we illustrate their application with numerical tests with SASIR, an implementation of the FISTA, a Forward-Backward splitting algorithm hosted in a LOFAR imager. Various tests have been conducted in Garsden et al., 2015. The main results are: i) an improved angular resolution (super resolution of a factor ~2) with point sources as compared to CLEAN on the same data, ii) correct photometry measurements on a field of point sources at high dynamic range and iii) the imaging of extended sources with improved fidelity. SASIR provides better reconstructions (five time less residuals) of the extended emission as compared to CLEAN. With the advent of large radiotelescopes, there is scope for improving classical imaging methods with convex optimization methods combined with sparse representations.
The full structuration of light in the transverse plane, including intensity, phase and polarization, holds the promise of unprecedented capabilities for applications in classical optics as well as in quantum optics and information sciences. Harnessi
ng special topologies can lead to enhanced focusing, data multiplexing or advanced sensing and metrology. Here we experimentally demonstrate the storage of such spatio-polarization-patterned beams into an optical memory. A set of vectorial vortex modes is generated via liquid crystal cell with topological charge in the optic axis distribution, and preservation of the phase and polarization singularities is demonstrated after retrieval, at the single-photon level. The realized multiple-degree-of-freedom memory can find applications in classical data processing but also in quantum network scenarios where structured states have been shown to provide promising attributes, such as rotational invariance.
We investigate a regenerative memory based upon a time-delayed neuromorphic photonic oscillator and discuss the link with temporal localized structures. Our experimental implementation is based upon a optoelectronic system composed of a nanoscale non
linear resonant tunneling diode coupled to a laser that we link to the paradigm of neuronal activity, the FitzHugh-Nagumo model with delayed feedback.
