Bilinear-biquadratic spin-1 chain undergoing quadratic Zeeman effect

The Heisenberg model for spin-1 bosons in one dimension presents many different quantum phases, including the famous topological Haldane phase. Here we study the robustness of such phases in front of a SU(2) symmetry-breaking field as well as the emergence of unique phases. Previous studies have analyzed the effect of such uniaxial anisotropy in some restricted relevant points of the phase diagram. Here we extend those studies and present the complete phase diagram of the spin-1 chain with uniaxial anisotropy. To this aim, we employ the density-matrix renormalization group together with analytical approaches. The complete phase diagram can be realized using ultracold spinor gases in the Mott insulator regime under a quadratic Zeeman effect.

Minimal Hilbert series for quadratic algebras and the Anick conjecture

We study the question on whether the famous Golod–Shafarevich estimate, which gives a lower bound for the Hilbert series of a (noncommutative) algebra, is attained. This question was considered by Anick in his 1983 paper ‘Generic algebras and CW-complexes’, Princeton Univ. Press, where he proved that the estimate is attained for the number of quadratic relations $d\leq n^2/4$
and $d\geq n^2/2$, and conjectured that it is the case for any number of quadratic relations. The particular point where the number of relations is equal to $n(n-1)/2$ was addressed by Vershik. He conjectured that a generic algebra with this number of relations is finite dimensional. We announce here the result that over any infinite field, the Anick conjecture holds for $d \geq 4(n2+n)/9$ and an arbitrary number of generators. We also discuss the result that confirms the Vershik conjecture over any field of characteristic 0, and a series of related
asymptotic results.

Finite dimensional semigroup quadratic algebras with the minimal number of relations

A quadratic semigroup algebra is an algebra over a field given by the generators x_1, . . . , x_n and a finite set of quadratic relations each of which either has the shape x_j x_k = 0 or the shape x_j x_k = x_l x_m . We prove that a quadratic semigroup algebra given by n generators and d=(n^2+n)/4 relations is always infinite dimensional. This strengthens the Golod–Shafarevich estimate for the above class of algebras. Our main result however is that for every n, there is a finite dimensional quadratic semigroup algebra with n generators and d_n relations, where d_n is the first integer greater than (n^2+n)/4 . That is, the above Golod–Shafarevich-type estimate for semigroup algebras is sharp.

Explaining Social Class Inequalities in Smoking: The Role of Education, Self-Efficacy, and Deprivation

Rates of smoking have decreased dramatically in most Northern European countries over the last 50 years or so, but manual working class groups are substantially more likely to smoke daily than are the professional and managerial classes. This article examines three hypotheses about the processes producing these inequalities. The first argues that social class inequalities reflect differences across education groups in knowledge of the risks of smoking. The second suggests that the living conditions of lower social class groups leads to the development of lower self-efficacy and a lower propensity to quit smoking. The third states that smoking has a functional use among poorer individuals. This article draws upon data from the Republic of Ireland to assess these hypotheses. Our analysis provides some support for the first hypothesis in that education independently reduces the odds of a manual class person smoking relative to a non-manual by 12 per cent. The second hypothesis is not supported by the data. The third hypothesis gains the most support: measures of disadvantage and deprivation account for almost one-third of the class differential in smoking. The results suggest that smoking cessation policy should reflect the importance of social and economic context in quitting behaviour.

Class inequalities in educational attainment among the adult population in the Republic of Ireland

Substantial increases in participation rates at secondary and third level in recent years have often been assumed to be associated with increased equality of opportunity. However, there is little evidence from elsewhere that expansion per se, except when it takes the form of saturation of the demand from higher classes, leads to a reduction in class inequalities. In exploring the factors that contribute to trends over time, or to a distinctive position in comparison with other countries, we have drawn on the recent literature to argue that the crucial factors are those which affect decisions to continue in education. We have also operated on the assumption that students and their parents rationally consider the costs and benefits associated with educational choices. The most recent evidence relating to the adult population provides no support for the existence of any trend towards equality of educational opportunity. It is, rather consistent with the class reproduction perspective that stresses the ability of privileged classes to maintain their advantages.

Selectable linear or quadratic coupling in an optomechanical system

There has been much interest recently in the analysis of optomechanical systems incorporating dielectric nano- or microspheres inside a cavity field. We analyse here the situation when one of the mirrors of the cavity itself is also allowed to move. We reveal that the interplay between the two oscillators yields a cross-coupling that results in, e.g., appreciable cooling and squeezing of the motion of the sphere, despite its nominal quadratic coupling. We also discuss a simple modification that would allow this cross-coupling to be removed at will, thereby yielding a purely quadratic coupling for the sphere.

Violation of Bell's inequalities with preamplified homodyne detection

We show that the use of probabilistic noiseless amplification in entangled coherent state-based schemes for the test of quantum nonlocality provides substantial advantages. The threshold amplitude to falsify a Bell-CHSH nonlocality test, in fact, is significantly reduced when amplification is embedded into the test itself. Such a beneficial effect holds also in the presence of detection inefficiency. Our study helps in affirming noiseless amplification as a valuable tool for coherent information processing and the generation of strongly nonclassical states of bosonic systems.

Who Feels Inferior? A Test of the Status Anxiety Hypothesis of Social Inequalities in Health

The empirical association between income inequality, population health and other social problems is now well established and the research literature suggests that the relationship is not artefactual. Debate is still ongoing as to the cause of this association. Wilkinson, Marmot and colleagues have argued for some time that the relationship stems from the psycho-social effects of status comparisons. Here, income inequality is a marker of a wider status hierarchy that provokes an emotional stress response in individuals that is harmful to health and well-being. We label this the ‘status anxiety hypothesis’. If true, this would imply a structured relationship between income inequality at the societal level, individual income rank and anxiety relating to social status. This paper sets out strong and weak forms of the hypothesis and then presents three predictions concerning the structuring of ‘status anxiety’ at the individual level given different levels of national income inequality and varying individual income. We then test these predictions using data from a cross-national survey of over 34,000 individuals carried out in 2007 in 31 European countries. Respondents from low inequality countries reported less status anxiety than those in higher inequality countries at all points on the income rank curve. This is an important precondition of support for the status anxiety hypothesis and may be seen as providing support for the weaker version of the hypothesis. However, we do not find evidence to support the stronger version of the hypothesis which requires the negative effect of income rank on status anxiety to be exacerbated by increasing income inequality.