Exact results for the star lattice chiral spin liquid

We examine the star lattice Kitaev model whose ground state is a a chiral spin liquid. We fermionize the model such that the fermionic vacua are toric code states on an effective Kagome lattice. This implies that the Abelian phase of the system is inherited from the fermionic vacua and that time reversal symmetry is spontaneously broken at the level of the vacuum. In terms of these fermions we derive the Bloch-matrix Hamiltonians for the vortex free sector and its time reversed counterpart and illuminate the relationships between the sectors. The phase diagram for the model is shown to be a sphere in the space of coupling parameters around the triangles of the lattices. The abelian phase lies inside the sphere and the critical boundary between topologically distinct Abelian and non-Abelian phases lies on the surface. Outside the sphere the system is generically gapped except in the planes where the coupling parameters are zero. These cases correspond to bipartite lattice structures and the dispersion relations are similar to that of the original Kitaev honeycomb model. In a further analysis we demonstrate the three-fold non-Abelian groundstate degeneracy on a torus by explicit calculation.Comment: 7 pages, 8 figure

Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons

Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk. Here, we propose and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems. We first introduce the mean chiral displacement, and we show that it rapidly approaches a multiple of the Zak phase in the long time limit. Then we measure the Zak phase in a photonic quantum walk, by direct observation of the mean chiral displacement in its bulk. Next, we measure the Zak phase in an alternative, inequivalent timeframe, and combine the two windings to characterize the full phase diagram of this Floquet system. Finally, we prove the robustness of the measure by introducing dynamical disorder in the system. This detection method is extremely general, as it can be applied to all one-dimensional platforms simulating static or Floquet chiral systems.Comment: 10 pages, 7 color figures (incl. appendices) Close to the published versio

Relative Equilibria in the Four-Vortex Problem with Two Pairs of Equal Vorticities

We examine in detail the relative equilibria in the four-vortex problem where two pairs of vortices have equal strength, that is, \Gamma_1 = \Gamma_2 = 1 and \Gamma_3 = \Gamma_4 = m where m is a nonzero real parameter. One main result is that for m > 0, the convex configurations all contain a line of symmetry, forming a rhombus or an isosceles trapezoid. The rhombus solutions exist for all m but the isosceles trapezoid case exists only when m is positive. In fact, there exist asymmetric convex configurations when m < 0. In contrast to the Newtonian four-body problem with two equal pairs of masses, where the symmetry of all convex central configurations is unproven, the equations in the vortex case are easier to handle, allowing for a complete classification of all solutions. Precise counts on the number and type of solutions (equivalence classes) for different values of m, as well as a description of some of the bifurcations that occur, are provided. Our techniques involve a combination of analysis and modern and computational algebraic geometry

Trends in mortality by labour market position around retirement ages in three European countries with different welfare regimes

&lt;p&gt;Objectives: In the face of economic downturn and increasing life expectancy, many industrial nations are adopting a policy of postponing the retirement age. However, questions still remain around the consequence of working longer into old age. We examine mortality by work status around retirement ages in countries with different welfare regimes; Finland (social democratic), Turin (Italy; conservative), and England and Wales (liberal).&lt;/p&gt; &lt;p&gt;Methods: Death rates and rate ratios (RRs) (reference rates = ‘in-work’), 1970 s–2000 s, were estimated for those aged 45–64 years using the England and Wales longitudinal study, Turin longitudinal study, and the Finnish linked register study.&lt;/p&gt; &lt;p&gt;Results: Mortality of the not-in-work was consistently higher than the in-work. Death rates for the not-in-work were lowest in Turin and highest in Finland. Rate ratios were smallest in Turin (RR men 1972–76 1.73; 2002–06 1.63; women 1.22; 1.68) and largest in Finland (RR men 1991–95 3.03; 2001–05 3.80; women 3.62; 4.11). Unlike RRs for men, RRs for women increased in every country (greatest in Finland).&lt;/p&gt; &lt;p&gt;Conclusions: These findings signal that overall, employment in later life is associated with lower mortality, regardless of welfare regime.&lt;/p&gt

Dose–Volume Constraints fOr oRganS At risk In Radiotherapy (CORSAIR): An “All-in-One” Multicenter–Multidisciplinary Practical Summary

BACKGROUND: The safe use of radiotherapy (RT) requires compliance with dose/volume constraints (DVCs) for organs at risk (OaRs). However, the available recommendations are sometimes conflicting and scattered across a number of different documents. Therefore, the aim of this work is to provide, in a single document, practical indications on DVCs for OaRs in external beam RT available in the literature.MATERIAL AND METHODS: A multidisciplinary team collected bibliographic information on the anatomical definition of OaRs, on the imaging methods needed for their definition, and on DVCs in general and in specific settings (curative RT of Hodgkin's lymphomas, postoperative RT of breast tumors, curative RT of pediatric cancers, stereotactic ablative RT of ventricular arrythmia). The information provided in terms of DVCs was graded based on levels of evidence.RESULTS: Over 650 papers/documents/websites were examined. The search results, together with the levels of evidence, are presented in tabular form.CONCLUSIONS: A working tool, based on collected guidelines on DVCs in different settings, is provided to help in daily clinical practice of RT departments. This could be a first step for further optimizations

First observation of the quantized exciton-polariton field and effect of interactions on a single polariton.

© 2018 The Authors. Published by Science. This is an open access article available under a Creative Commons licence. The published version can be accessed at the following link on the publisher’s website: https://doi.org/10.1126/sciadv.aao6814Polaritons are quasi-particles that originate from the coupling of light with matter and that demonstrate quantum phenomena at the many-particle mesoscopic level, such as Bose-Einstein condensation and superfluidity. A highly sought and long-time missing feature of polaritons is a genuine quantum manifestation of their dynamics at the single-particle level. Although they are conceptually perceived as entangled states and theoretical proposals abound for an explicit manifestation of their single-particle properties, so far their behavior has remained fully accounted for by classical and mean-field theories. We report the first experimental demonstration of a genuinely quantum state of the microcavity polariton field, by swapping a photon for a polariton in a two-photon entangled state generated by parametric downconversion. When bringing this single-polariton quantum state in contact with a polariton condensate, we observe a disentangling with the external photon. This manifestation of a polariton quantum state involving a single quantum unlocks new possibilities for quantum information processing with interacting bosons