Self-trapping of light and nonlinear localized modes in 2D photonic crystals and waveguides

We overview our recent results on the nonlinear localized modes in two-dimensional (2D) photonic crystals and photonic-crystal waveguides. Employing the technique based on the Green function, we describe the existence domains for nonlinear guided modes in photonic crystal waveguides and study their unique properties including bistability. We also show that low-amplitude nonlinear modes near the band edge of a reduced-symmetry 2D square-lattice photonic crystals, which are usually unstable, can be stabilized due to effective long-range linear and nonlinear interactions.Comment: 20 pages (LaTeX) with 12 figures (EPS

The Extent of Multi-particle Quantum Non-locality

It is well known that entangled quantum states can be nonlocal: the correlations between local measurements carried out on these states cannot always be reproduced by local hidden variable models. Svetlichny, followed by others, showed that multipartite quantum states are even more nonlocal than bipartite ones in the sense that nonlocal classical models with (super-luminal) communication between some of the parties cannot reproduce the quantum correlations. Here we study in detail the kinds of nonlocality present in quantum states. More precisely we enquire what kinds of classical communication patterns cannot reproduce quantum correlations. By studying the extremal points of the space of all multiparty probability distributions, in which all parties can make one of a pair of measurements each with two possible outcomes, we find a necessary condition for classical nonlocal models to reproduce the statistics of all quantum states. This condition extends and generalises work of Svetlichny and others in which it was shown that a particular class of classical nonlocal models, the ``separable'' models, cannot reproduce the statistics of all multiparticle quantum states. Our condition shows that the nonlocality present in some entangled multiparticle quantum states is much stronger than previously thought. We also study the sufficiency of our condition.Comment: 10 pages, 2 figures, journal versio

Cost-Effective HITs for Relative Similarity Comparisons

Similarity comparisons of the form "Is object a more similar to b than to c?" are useful for computer vision and machine learning applications. Unfortunately, an embedding of $n$ points is specified by $n^3$ triplets, making collecting every triplet an expensive task. In noticing this difficulty, other researchers have investigated more intelligent triplet sampling techniques, but they do not study their effectiveness or their potential drawbacks. Although it is important to reduce the number of collected triplets, it is also important to understand how best to display a triplet collection task to a user. In this work we explore an alternative display for collecting triplets and analyze the monetary cost and speed of the display. We propose best practices for creating cost effective human intelligence tasks for collecting triplets. We show that rather than changing the sampling algorithm, simple changes to the crowdsourcing UI can lead to much higher quality embeddings. We also provide a dataset as well as the labels collected from crowd workers.Comment: 7 pages, 7 figure

Levinson's theorem for Schroedinger operators with point interaction: a topological approach

In this note Levinson theorems for Schroedinger operators in R^n with one point interaction at 0 are derived using the concept of winding numbers. These results are based on new expressions for the associated wave operators.Comment: 7 page

Comment on "Demonstration of the Casimir Force in the 0.6 to 6 micrometer Range"

We comment on a recently published measurement of the Casimir force for distances in the 0.6 to 6 micrometer range between two Au surfaces (Phys. Rev. Lett. 78, 5(1997)) and the net discrepancy reported for the comparison with theoretical predictions (Phys. Rev. Lett. 81, 5475 (1998)).Comment: 1 page, LaTeX, 2 encapsulated postscript figure

The Kondo effect in bosonic spin liquids

In a metal, a magnetic impurity is fully screened by the conduction electrons at low temperature. In contrast, impurity moments coupled to spin-1 bulk bosons, such as triplet excitations in paramagnets, are only partially screened, even at the bulk quantum critical point. We argue that this difference is not due to the quantum statistics of the host particles but instead related to the structure of the impurity-host coupling, by demonstrating that frustrated magnets with bosonic spinon excitations can display a bosonic version of the Kondo effect. However, the Bose statistics of the bulk implies distinct behavior, such as a weak-coupling impurity quantum phase transition, and perfect screening for a range of impurity spin values. We discuss implications of our results for the compound Cs2CuCl4, as well as possible extensions to multicomponent bosonic gases.Comment: 4 pages, 3 figures. The weak coupling RG flow was corrected and expanded in last versio

Formation of quasi-free and bubble positronium states in water and aqueous solutions

It is shown that in aqueous solutions a positronium atom is first formed in the quasi-free state, and, after 50-100 ps, becomes localized in a nanobubble. Analysis of the annihilation spectra of NaNO3 aqueous solutions shows that the hydrated electron is not involved in the positronium (Ps) formation

Deux ou trois choses que l'on savait dans la France de l'Ouest, en 2001, a propos de la nature de certaines structures funéraires dites monumentales, ainsi que leur ordonnancement chronologique au long des Ve et IVe millenaires

On donne ici des résultats récents sur les monuments mégalithiques du Morbihan (site de Lannec Er Gadouer), et quelques idées sur la monumentalité funéraire et le Néolithique des régiones atlantiques