Finite-Size Scaling Exponents in the Dicke Model

We consider the finite-size corrections in the Dicke model and determine the scaling exponents at the critical point for several quantities such as the ground state energy or the gap. Therefore, we use the Holstein-Primakoff representation of the angular momentum and introduce a nonlinear transformation to diagonalize the Hamiltonian in the normal phase. As already observed in several systems, these corrections turn out to be singular at the transition point and thus lead to nontrivial exponents. We show that for the atomic observables, these exponents are the same as in the Lipkin-Meshkov-Glick model, in agreement with numerical results. We also investigate the behavior of the order parameter related to the radiation mode and show that it is driven by the same scaling variable as the atomic one.Comment: 4 pages, published versio

Long-Time Tails and Anomalous Slowing Down in the Relaxation of Spatially Inhomogeneous Excitations in Quantum Spin Chains

Exact analytic calculations in spin-1/2 XY chains, show the presence of long-time tails in the asymptotic dynamics of spatially inhomogeneous excitations. The decay of inhomogeneities, for $t\to \infty$, is given in the form of a power law $$(t/\tau_{Q}) ^{-\nu_{Q}}$$ where the relaxation time $\tau_{Q}$ and the exponent $\nu_{Q}$ depend on the wave vector $Q$, characterizing the spatial modulation of the initial excitation. We consider several variants of the XY model (dimerized, with staggered magnetic field, with bond alternation, and with isotropic and uniform interactions), that are grouped into two families, whether the energy spectrum has a gap or not. Once the initial condition is given, the non-equilibrium problem for the magnetization is solved in closed form, without any other assumption. The long-time behavior for $t\to \infty$ can be obtained systematically in a form of an asymptotic series through the stationary phase method. We found that gapped models show critical behavior with respect to $Q$, in the sense that there exist critical values $Q_{c}$, where the relaxation time $\tau_{Q}$ diverges and the exponent $\nu_{Q}$ changes discontinuously. At those points, a slowing down of the relaxation process is induced, similarly to phenomena occurring near phase transitions. Long-lived excitations are identified as incommensurate spin density waves that emerge in systems undergoing the Peierls transition. In contrast, gapless models do not present the above anomalies as a function of the wave vector $Q$.Comment: 25 pages, 2 postscript figures. Manuscript submitted to Physical Review

Responses of grape berry anthocyanin and tritratable acidity to the projected climate change across the Western Australian wine regions

More than a century of observations has established that climate influences grape berry composition. Accordingly, the projected global climate change is expected to impact on grape berry composition although the magnitude and direction of impact at regional and subregional scales are not fully known. The aim of this study was to assess potential impacts of climate change on levels of berry anthocyanin and titratable acidity (TA) of the major grapevine varieties grown across all of the Western Australian (WA) wine regions. Grape berry anthocyanin and TA responses across all WA wine regions were projected for 2030, 2050 and 2070 by utilising empirical models that link these berry attributes and climate data downscaled (to ∼5 km resolution) from the csiro_mk3_5 and miroc3_2_medres global climate model outputs under IPCC SRES A2 emissions scenario. Due to the dependence of berry composition on maturity, climate impacts on anthocyanin and TA levels were assessed at a common maturity of 22 °Brix total soluble solids (TSS), which necessitated the determination of when this maturity will be reached for each variety, region and warming scenario, and future period.The results indicate that both anthocyanin and TA levels will be affected negatively by a warming climate, but the magnitude of the impacts will differ between varieties and wine regions. Compared to 1990 levels, median anthocyanins concentrations are projected to decrease, depending on global climate model, by up to 3–12 % and 9–33 % for the northern wine regions by 2030 and 2070, respectively while 2–18 % reductions are projected in the southern wine regions for the same time periods. Patterns of reductions in the median Shiraz berry anthocyanin concentrations are similar to that of Cabernet Sauvignon; however, the magnitude is lower (up to 9–18 % in southern and northern wine regions respectively by 2070). Similarly, uneven declines in TA levels are projected across the study regions. The largest reductions in median TA are likely to occur in the present day warmer wine regions, up to 40 % for Chardonnay followed by 15 % and 12 % for Shiraz and Cabernet Sauvignon, respectively, by 2070 under the high warming projection (csiro_mk3_5). It is concluded that, under existing management practices, some of the key grape attributes that are integral to premium wine production will be affected negatively by a warming climate, but the magnitudes of the impacts vary across the established wine regions, varieties, the magnitude of warming and future periods considered

Assessment of examiner leniency and stringency ('hawk-dove effect') in the MRCP(UK) clinical examination (PACES) using multi-facet Rasch modelling

BACKGROUND: A potential problem of clinical examinations is known as the hawk-dove problem, some examiners being more stringent and requiring a higher performance than other examiners who are more lenient. Although the problem has been known qualitatively for at least a century, we know of no previous statistical estimation of the size of the effect in a large-scale, high-stakes examination. Here we use FACETS to carry out a multi-facet Rasch modelling of the paired judgements made by examiners in the clinical examination (PACES) of MRCP(UK), where identical candidates were assessed in identical situations, allowing calculation of examiner stringency. METHODS: Data were analysed from the first nine diets of PACES, which were taken between June 2001 and March 2004 by 10,145 candidates. Each candidate was assessed by two examiners on each of seven separate tasks. with the candidates assessed by a total of 1,259 examiners, resulting in a total of 142,030 marks. Examiner demographics were described in terms of age, sex, ethnicity, and total number of candidates examined. RESULTS: FACETS suggested that about 87% of main effect variance was due to candidate differences, 1% due to station differences, and 12% due to differences between examiners in leniency-stringency. Multiple regression suggested that greater examiner stringency was associated with greater examiner experience and being from an ethnic minority. Male and female examiners showed no overall difference in stringency. Examination scores were adjusted for examiner stringency and it was shown that for the present pass mark, the outcome for 95.9% of candidates would be unchanged using adjusted marks, whereas 2.6% of candidates would have passed, even though they had failed on the basis of raw marks, and 1.5% of candidates would have failed, despite passing on the basis of raw marks. CONCLUSION: Examiners do differ in their leniency or stringency, and the effect can be estimated using Rasch modelling. The reasons for differences are not clear, but there are some demographic correlates, and the effects appear to be reliable across time. Account can be taken of differences, either by adjusting marks or, perhaps more effectively and more justifiably, by pairing high and low stringency examiners, so that raw marks can be used in the determination of pass and fail

A prospective, multi-method, multi-disciplinary, multi-level, collaborative, social-organisational design for researching health sector accreditation [LP0560737]

BACKGROUND: Accreditation has become ubiquitous across the international health care landscape. Award of full accreditation status in health care is viewed, as it is in other sectors, as a valid indicator of high quality organisational performance. However, few studies have empirically demonstrated this assertion. The value of accreditation, therefore, remains uncertain, and this persists as a central legitimacy problem for accreditation providers, policymakers and researchers. The question arises as to how best to research the validity, impact and value of accreditation processes in health care. Most health care organisations participate in some sort of accreditation process and thus it is not possible to study its merits using a randomised controlled strategy. Further, tools and processes for accreditation and organisational performance are multifaceted. METHODS/DESIGN: To understand the relationship between them a multi-method research approach is required which incorporates both quantitative and qualitative data. The generic nature of accreditation standard development and inspection within different sectors enhances the extent to which the findings of in-depth study of accreditation process in one industry can be generalised to other industries. This paper presents a research design which comprises a prospective, multi-method, multi-level, multi-disciplinary approach to assess the validity, impact and value of accreditation. DISCUSSION: The accreditation program which assesses over 1,000 health services in Australia is used as an exemplar for testing this design. The paper proposes this design as a framework suitable for application to future international research into accreditation. Our aim is to stimulate debate on the role of accreditation and how to research it.Jeffrey Braithwaite, Johanna Westbrook, Marjorie Pawsey, David Greenfield, Justine Naylor, Rick Iedema, Bill Runciman, Sally Redman, Christine Jorm, Maureen Robinson, Sally Nathan and Robert Gibber

A probability analysis of some spatial interaction models

This paper derives several well-known spatial models in a framework based upon the laws of conditional probability analysis. In particular, it relates the structure of some existing models of trip distribution, elementary residential location and residential location with capacity constraints, to either the multinomial or hypergeometric probability distributions. The major changes from traditional methods for developing these models deal with the derivation and form of the objective function for each interaction model. This alternative analysis reaches a wider audience than that only familiar with entropy methods and leads to several improvements in generality. Further, when population constraints were imposed on residential location models, it was found that the model which developed naturally from the approach taken in the paper contained as a special case the model proposed by Dacey and Norcliffe and not the Wilson model.

Developments of an entropy model for residential location with maximum zonal population constraints

This paper considers recent developments of singly-constrained entropy models which are used for predicting future zonal populations, when the models are required to satisfy given inequality constraints for the maximum zonal populations. Wilson and Batty et al have shown how ad hoc algorithms could be used to modify the usual singly-constrained gravity model, whereas recently Jefferson and Scott have used geometric programming techniques to ensure that the inequality constraints are satisfied. This work develops an approach suggested by Dacey and Norcliffe whereby the inequality constraints are incorporated into the expression for the system entropy. The entropy-maximising method and the more rigorous statistical derivation considered in the paper lead to implicit expressions for the zonal populations which can be evaluated by means of a given algorithm. The asymptotic properties of the model and the inclusion of attractiveness factors are also considered. An interesting feature of this model is that it contains as special cases Wilson's doubly-constrained model and singly-constrained model.