A Perturbative Approach to the Relativistic Harmonic Oscillator

A quantum realization of the Relativistic Harmonic Oscillator is realized in terms of the spatial variable $x$ and {\d\over \d x} (the minimal canonical representation). The eigenstates of the Hamiltonian operator are found (at lower order) by using a perturbation expansion in the constant $c^{-1}$. Unlike the Foldy-Wouthuysen transformed version of the relativistic hydrogen atom, conventional perturbation theory cannot be applied and a perturbation of the scalar product itself is required.Comment: 9 pages, latex, no figure

Quantum correlations in the temporal CHSH scenario

We consider a temporal version of the CHSH scenario using projective measurements on a single quantum system. It is known that quantum correlations in this scenario are fundamentally more general than correlations obtainable with the assumptions of macroscopic realism and non-invasive measurements. In this work, we also educe some fundamental limitations of these quantum correlations. One result is that a set of correlators can appear in the temporal CHSH scenario if and only if it can appear in the usual spatial CHSH scenario. In particular, we derive the validity of the Tsirelson bound and the impossibility of PR-box behavior. The strength of possible signaling also turns out to be surprisingly limited, giving a maximal communication capacity of approximately 0.32 bits. We also find a temporal version of Hardy's nonlocality paradox with a maximal quantum value of 1/4.Comment: corrected versio

On the Relationship between Convex Bodies Related to Correlation Experiments with Dichotomic Observables

In this paper we explore further the connections between convex bodies related to quantum correlation experiments with dichotomic variables and related bodies studied in combinatorial optimization, especially cut polyhedra. Such a relationship was established in Avis, Imai, Ito and Sasaki (2005 J. Phys. A: Math. Gen. 38 10971-87) with respect to Bell inequalities. We show that several well known bodies related to cut polyhedra are equivalent to bodies such as those defined by Tsirelson (1993 Hadronic J. S. 8 329-45) to represent hidden deterministic behaviors, quantum behaviors, and no-signalling behaviors. Among other things, our results allow a unique representation of these bodies, give a necessary condition for vertices of the no-signalling polytope, and give a method for bounding the quantum violation of Bell inequalities by means of a body that contains the set of quantum behaviors. Optimization over this latter body may be performed efficiently by semidefinite programming. In the second part of the paper we apply these results to the study of classical correlation functions. We provide a complete list of tight inequalities for the two party case with (m,n) dichotomic observables when m=4,n=4 and when min{m,n}<=3, and give a new general family of correlation inequalities.Comment: 17 pages, 2 figure

A survey of maincrop potatoes I Estimates of yield 1948–50

The survey shows that objective estimates of the yield of maincrop potatoes can be obtained from small samples carefully selected and dug by hand. Samples taken from about 1000 fields gave estimates of the mean yield of all counties sampled with a standard error due to sampling of less than ± 0·2 ton/acre. The precision of the estimate could have been improved by a better distribution of samples among counties.The results point to underestimation on the part of the official estimates, in each of the 3 years, especially in the case of high yields in particular counties, and in particular years. The discrepancy between the official and the survey yields is of the order of 1¾ tons/acre, after all necessary corrections have been applied to the survey yields.The experience gained in the survey indicates that the method of sampling adopted provides an accurate and reliable method of estimating the yields of potatoes which could supplement, and, possibly, ultimately replace the present official estimates if more accurate estimates are required. A national scheme, properly designed, which would include all the potato-growing areas in due proportion should not be unduly expensive to operate. Estimates so obtained would not only be generally more accurate than those obtained by the present official method, but, perhaps more important, would indicate far more closely the fluctuation in yield from year to year

Globalisation, neo-liberalism and vocational learning: the case of English further education colleges

Further education (FE) has traditionally been a rather unspectacular activity. Lacking the visibility of schools or the prestige of universities, for the vast majority of its existence FE has had a relatively low profile on the margins of English education. Over recent years this situation has altered significantly and further education has undergone profound change. This paper argues that a combination of related factors – neo-liberalism, globalisation, and dominant discourses of the knowledge economy – has acted in synergy to transform FE into a highly performative and marketised sector. Against this backdrop, further education has been assigned a particular role based upon certain narrow and instrumental understandings of skill, employment and economic competitiveness. The paper argues that, although it has always been predominantly working class in nature, FE is now, more than ever, positioned firmly at the lower end of the institutional hierarchy in the highly class-stratified terrain of English education

Stability of degenerate Cauchy horizons in black hole spacetimes

In the multihorizon black hole spacetimes, it is possible that there are degenerate Cauchy horizons with vanishing surface gravities. We investigate the stability of the degenerate Cauchy horizon in black hole spacetimes. Despite the asymptotic behavior of spacetimes (flat, anti-de Sitter, or de Sitter), we find that the Cauchy horizon is stable against the classical perturbations, but unstable quantum mechanically.Comment: Revtex, 4 pages, no figures, references adde

Vacuum Polarization in an Anti-de Sitter Space as an Origin for a Cosmological Constant in a Brane World

In this Letter we show that the vacuum polarization of quantum fields in an anti-de Sitter space naturally gives rise to a small but nonzero cosmological constant in a brane world living in it. To explain the extremely small ratio of mass density in the cosmological constant to the Planck mass density in our universe (\approx 10^{-123}) as suggested by cosmological observations, all we need is a four-dimensional brane world (our universe) living in a five-dimensional anti-de Sitter space with a curvature radius r_0 \sim 10^{-3}cm and a fundamental Planck energy M_P \sim 10^9 GeV, and a scalar field with a mass m \sim r_0^{-1}\sim 10^{-2}eV. Probing gravity down to a scale \sim 10^{-3}cm, which is attainable in the near future, will provide a test of the model.Comment: 10 pages, including 1 figur

Bounds on the Complexity of Halfspace Intersections when the Bounded Faces have Small Dimension

We study the combinatorial complexity of D-dimensional polyhedra defined as the intersection of n halfspaces, with the property that the highest dimension of any bounded face is much smaller than D. We show that, if d is the maximum dimension of a bounded face, then the number of vertices of the polyhedron is O(n^d) and the total number of bounded faces of the polyhedron is O(n^d^2). For inputs in general position the number of bounded faces is O(n^d). For any fixed d, we show how to compute the set of all vertices, how to determine the maximum dimension of a bounded face of the polyhedron, and how to compute the set of bounded faces in polynomial time, by solving a polynomial number of linear programs

Comfort radicalism and NEETs: a conservative praxis

Young people who are not in education, employment or training (NEET) are construed by policy makers as a pressing problem about which something should be done. Such young people's lack of employment is thought to pose difficulties for wider society in relation to social cohesion and inclusion and it is feared that they will become a 'lost generation'. This paper(1) draws upon English research, seeking to historicise the debate whilst acknowledging that these issues have a much wider purchase. The notion of NEETs rests alongside longstanding concerns of the English state and middle classes, addressing unruly male working class youth as well as the moral turpitude of working class girls. Waged labour and domesticity are seen as a means to integrate such groups into society thereby generating social cohesion. The paper places the debate within it socio-economic context and draws on theorisations of cognitive capitalism, Italian workerism, as well as emerging theories of antiwork to analyse these. It concludes by arguing that ‘radical’ approaches to NEETs that point towards inequities embedded in the social structure and call for social democratic solutions veer towards a form of comfort radicalism. Such approaches leave in place the dominance of capitalist relations as well as productivist orientations that celebrate waged labour

Anti-de Sitter boundary in Poincare coordinates

We study the space-time boundary of a Poincare patch of Anti-de Sitter (AdS) space. We map the Poincare AdS boundary to the global coordinate chart and show why this boundary is not equivalent to the global AdS boundary. The Poincare AdS boundary is shown to contain points of the bulk of the entire AdS space. The Euclidean AdS space is also discussed. In this case one can define a semi-global chart that divides the AdS space in the same way as the corresponding Euclidean Poincare chart.Comment: In this revised version we add a discussion of the physical consequences of the choice of a coordinate system for AdS space. We changed figure 1 and added more references. Version to be published in Gen. Relat. Grav