Differential operators and Cherednik algebras

We establish a link between two geometric approaches to the representation theory of rational Cherednik algebras of type A: one based on a noncommutative Proj construction, used in [GS]; the other involving quantum hamiltonian reduction of an algebra of differential operators, used in [GG]. In the present paper, we combine these two points of view by showing that the process of hamiltonian reduction intertwines a naturally defined geometric twist functor on D-modules with the shift functor for the Cherednik algebra. That enables us to give a direct and relatively short proof of the key result, [GS, Theorem 1.4] without recourse to Haiman's deep results on the n! theorem. We also show that the characteristic cycles defined independently in these two approaches are equal, thereby confirming a conjecture from [GG].Comment: 37 p

Quantum Necking in Stressed Metallic Nanowires

When a macroscopic metallic wire is subject to tensile stress, it necks down smoothly as it elongates. We show that nanowires with radii comparable to the Fermi wavelength display remarkably different behavior. Using concepts from fluid dynamics, a PDE for nanowire shape evolution is derived from a semiclassical energy functional that includes electron-shell effects. A rich dynamics involving movement and interaction of kinks connecting locally stable radii is found, and a new class of universal equilibrium shapes is predicted.Comment: 4 pages, 3 postscript figures. New result on universal equilibrium shape

Minor and subthreshold depressive disorders in Alzheimer's disease: a systematic review and meta-analysis of prevalence studies

Background: Depressive symptoms are common in Alzheimer's disease (AD) and negatively impact patient well-being. The main aim of the present study was to establish summary estimates for the prevalence of minor depressive disorder (MinD) and subthreshold depression in AD and synthesise evidence on prognosis and management of these symptoms in order to inform clinical guidelines. / Methods: Systematic review and meta-analysis of cross-sectional and longitudinal studies of prevalence, prognosis, and treatments for minor and subthreshold depression in AD. We searched MEDLINE, Embase, PsycINFO and CINAHL. We included studies that reported prevalence of subthreshold depressive disorders and those reporting data on validity of diagnostic criteria, mechanisms, or randomised controlled clinical trials (RCTs) testing effectiveness of interventions. Estimates of prevalence were pooled using random-effects meta-analyses. Two authors screened articles and independently extracted data on study characteristics. / Results: We reviewed 5671 abstracts, retrieved 621 full text articles and included a total of 15 studies. Pooling data from 10 studies showed that prevalence for MinD in AD was 22.0% (95% CI 16.0 to 28.0). Prevalence for a clinical diagnosis of MinD (DSM-III-R and DSM-IV) was 26.0% (95% CI 20.0 to 32.0; 6 studies). People with MinD experienced higher levels of neuropsychiatric symptoms, functional and cognitive decline, although studies remain cross-sectional. Neither sertraline nor a carer intervention were effective in reducing symptoms. / Conclusion: This review finds that MinD is prevalent in people with a diagnosis of AD and requires clinical attention. Research is warranted to develop effective interventions to treat and prevent these symptoms

The disconnect between evidence and practice: A systematic review of person-centred interventions and training manuals for care home staff working with people with dementia

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordObjective The overall objective is to determine the availability of person-centred intervention and training manuals for dementia care staff with clinical trial evidence of efficacy. Design Interventions were identified using a search of electronic databases, augmented by mainstream search engines, reference lists, hand searching for resources and consultation with an expert panel. The specific search for published manuals was complemented by a search for randomised control trials focussing on training and activity-based interventions for people with dementia in care homes. Manuals were screened for eligibility and rated to assess their quality, relevance and feasibility. Results A meta-analysis of randomised control trials indicated that person-centred training interventions conferred significant benefit in improving agitation and reducing the use of antipsychotics. Each of the efficacious packages included a sustained period of joint working and supervision with a trained mental health professional in addition to an educational element. However, of the 170 manuals that were identified, 30 met the quality criteria and only four had been evaluated in clinical trials. Conclusions Despite the availability of a small number of evidence-based training manuals, there is a widespread use of person-centred intervention and training manuals that are not evidence-based. Clearer guidance is needed to ensure that commissioned training and interventions are based on robust evidence. Copyright © 2014 John Wiley & Sons, Ltd.National Institute for Health Research (NIHR

On the Stability and Structural Dynamics of Metal Nanowires

This article presents a brief review of the nanoscale free-electron model, which provides a continuum description of metal nanostructures. It is argued that surface and quantum-size effects are the two dominant factors in the energetics of metal nanowires, and that much of the phenomenology of nanowire stability and structural dynamics can be understood based on the interplay of these two competing factors. A linear stability analysis reveals that metal nanocylinders with certain magic conductance values G=1, 3, 6, 12, 17, 23, 34, 42, 51, 67, 78, 96, ... times the conductance quantum are exceptionally stable. A nonlinear dynamical simulation of nanowire structural evolution reveals a universal equilibrium shape consisting of a magic cylinder suspended between unduloidal contacts. The lifetimes of these metastable structures are also computed.Comment: 8 pages, 6 figure

The Order of Phase Transitions in Barrier Crossing

A spatially extended classical system with metastable states subject to weak spatiotemporal noise can exhibit a transition in its activation behavior when one or more external parameters are varied. Depending on the potential, the transition can be first or second-order, but there exists no systematic theory of the relation between the order of the transition and the shape of the potential barrier. In this paper, we address that question in detail for a general class of systems whose order parameter is describable by a classical field that can vary both in space and time, and whose zero-noise dynamics are governed by a smooth polynomial potential. We show that a quartic potential barrier can only have second-order transitions, confirming an earlier conjecture [1]. We then derive, through a combination of analytical and numerical arguments, both necessary conditions and sufficient conditions to have a first-order vs. a second-order transition in noise-induced activation behavior, for a large class of systems with smooth polynomial potentials of arbitrary order. We find in particular that the order of the transition is especially sensitive to the potential behavior near the top of the barrier.Comment: 8 pages, 6 figures with extended introduction and discussion; version accepted for publication by Phys. Rev.

Non-trivial stably free modules over crossed products

We consider the class of crossed products of noetherian domains with universal enveloping algebras of Lie algebras. For algebras from this class we give a sufficient condition for the existence of projective non-free modules. This class includes Weyl algebras and universal envelopings of Lie algebras, for which this question, known as noncommutative Serre's problem, was extensively studied before. It turns out that the method of lifting of non-trivial stably free modules from simple Ore extensions can be applied to crossed products after an appropriate choice of filtration. The motivating examples of crossed products are provided by the class of RIT algebras, originating in non-equilibrium physics.Comment: 13 page

Melting transition of an Ising glass driven by magnetic field

The quantum critical behavior of the Ising glass in a magnetic field is investigated. We focus on the spin glass to paramagnet transition of the transverse degrees of freedom in the presence of finite longitudinal field. We use two complementary techniques, the Landau theory close to the T=0 transition and the exact diagonalization method for finite systems. This allows us to estimate the size of the critical region and characterize various crossover regimes. An unexpectedly small energy scale on the disordered side of the critical line is found, and its possible relevance to experiments on metallic glasses is briefly discussed.Comment: 4 pages, 3 figure

A note on density correlations in the half-filled Hubbard model

We consider density-density correlations in the one-dimensional Hubbard model at half filling. On intuitive grounds one might expect them to exhibit an exponential decay. However, as has been noted recently, this is not obvious from the Bethe Ansatz/conformal field theory (BA/CFT) approach. We show that by supplementing the BA/CFT analysis with simple symmetry arguments one can easily prove that correlations of the lattice density operators decay exponentially.Comment: 3 pages, RevTe

Influence of Long-Range Coulomb Interactions on the Metal-Insulator Transition in One-Dimensional Strongly Correlated Electron Systems

The influence of long-range Coulomb interactions on the properties of one-dimensional (1D) strongly correlated electron systems in vicinity of the metal-insulator phase transition is considered. It is shown that unscreened repulsive Coulomb forces lead to the formation of a 1D Wigner crystal in the metallic phase and to the transformation of the square-root singularity of the compressibility (characterizing the commensurate-incommensurate transition) to a logarithmic singularity. The properties of the insulating (Mott) phase depend on the character of the short-wavelength screening of the Coulomb forces. For a sufficiently short screening length the characteristics of the charge excitations in the insulating phase are totally determined by the Coulomb interaction and these quasipartic les can be described as quasiclassical Coulomb solitons.Comment: 14 pages, LaTeX, G{\"o}teborg preprint APR 94-3