Exact and approximate dynamics of the quantum mechanical O(N) model

We study a quantum dynamical system of N, O(N) symmetric, nonlinear oscillators as a toy model to investigate the systematics of a 1/N expansion. The closed time path (CTP) formalism melded with an expansion in 1/N is used to derive time evolution equations valid to order 1/N (next-to-leading order). The effective potential is also obtained to this order and its properties areelucidated. In order to compare theoretical predictions against numerical solutions of the time-dependent Schrodinger equation, we consider two initial conditions consistent with O(N) symmetry, one of them a quantum roll, the other a wave packet initially to one side of the potential minimum, whose center has all coordinates equal. For the case of the quantum roll we map out the domain of validity of the large-N expansion. We discuss unitarity violation in the 1/N expansion; a well-known problem faced by moment truncation techniques. The 1/N results, both static and dynamic, are also compared to those given by the Hartree variational ansatz at given values of N. We conclude that late-time behavior, where nonlinear effects are significant, is not well-described by either approximation.Comment: 16 pages, 12 figrures, revte

The Prosocial Framework: Theory, Practice and Applications Within Schools

Recent collaborations across psychological and evolutionary science have resulted in the emergence of an intervention programme for increasing the cohesion and effectiveness of human group processes. Prosocial (Atkins et al., 2019) combines Acceptance & Commitment Therapy (ACT; S. Hayes et al., 2012) and Multi-Level Selection Theory (Wilson & Sober, 1994) with Nobel Laureate Elinor Ostrom’s Core Design Principles (CDPs) for effective group-level processes (Ostrom, 2012, 2015). Ostrom’s work was ground-breaking but, being primarily descriptive in nature, did not provide a full account of the processes and procedures required to implement the CDPs. The current paper outlines the theoretical underpinnings of Prosocial and offers guidelines for its application within educational communities, providing specific examples of the wide array of ways in which the approach can be applied by professionals such as educational psychologists (EPs) to bring about positive change at the systemic level

The hbar Expansion in Quantum Field Theory

We show how expansions in powers of Planck's constant hbar = h/2\pi can give new insights into perturbative and nonperturbative properties of quantum field theories. Since hbar is a fundamental parameter, exact Lorentz invariance and gauge invariance are maintained at each order of the expansion. The physics of the hbar expansion depends on the scheme; i.e., different expansions are obtained depending on which quantities (momenta, couplings and masses) are assumed to be independent of hbar. We show that if the coupling and mass parameters appearing in the Lagrangian density are taken to be independent of hbar, then each loop in perturbation theory brings a factor of hbar. In the case of quantum electrodynamics, this scheme implies that the classical charge e, as well as the fine structure constant are linear in hbar. The connection between the number of loops and factors of hbar is more subtle for bound states since the binding energies and bound-state momenta themselves scale with hbar. The hbar expansion allows one to identify equal-time relativistic bound states in QED and QCD which are of lowest order in hbar and transform dynamically under Lorentz boosts. The possibility to use retarded propagators at the Born level gives valence-like wave-functions which implicitly describe the sea constituents of the bound states normally present in its Fock state representation.Comment: 8 pages, 1 figure. Version to be published in Phys. Rev.

Time evolution of the chiral phase transition during a spherical expansion

We examine the non-equilibrium time evolution of the hadronic plasma produced in a relativistic heavy ion collision, assuming a spherical expansion into the vacuum. We study the $O(4)$ linear sigma model to leading order in a large-$N$ expansion. Starting at a temperature above the phase transition, the system expands and cools, finally settling into the broken symmetry vacuum state. We consider the proper time evolution of the effective pion mass, the order parameter $\langle \sigma \rangle$, and the particle number distribution. We examine several different initial conditions and look for instabilities (exponentially growing long wavelength modes) which can lead to the formation of disoriented chiral condensates (DCCs). We find that instabilities exist for proper times which are less than 3 fm/c. We also show that an experimental signature of domain growth is an increase in the low momentum spectrum of outgoing pions when compared to an expansion in thermal equilibrium. In comparison to particle production during a longitudinal expansion, we find that in a spherical expansion the system reaches the ``out'' regime much faster and more particles get produced. However the size of the unstable region, which is related to the domain size of DCCs, is not enhanced.Comment: REVTex, 20 pages, 8 postscript figures embedded with eps

Tooth Decay in Alcohol Abusers Compared to Alcohol and Drug Abusers

Alcohol and drug abuse are detrimental to general and oral health. Though we know the effects of these harmful habits on oral mucosa, their independent and combined effect on the dental caries experience is unknown and worthy of investigation. We compared 363 “alcohol only” abusers to 300 “alcohol and drug” abusers to test the hypothesis that various components of their dental caries experience are significantly different due to plausible sociobiological explanations. After controlling for the potential confounders, we observe that the “alcohol and drug” group had a 38% higher risk of having decayed teeth compared to the “alcohol only” group (P < .05). As expected, those who belonged to a higher social class (OR = 1.98; 95%  CI = 1.43–2.75) and drank wine (OR = 1.85; 95%  CI = 1.16–2.96) had a higher risk of having more filled teeth. We conclude that the risk of tooth decay among “alcohol only” abusers is significantly lower compared to “alcohol and drug” abusers

Variation in the organization and subunit composition of the mammalian pyruvate dehydrogenase complex E2/E3BP core assembly

The final version of this article is available at the link below.Crucial to glucose homoeostasis in humans, the hPDC (human pyruvate dehydrogenase complex) is a massive molecular machine comprising multiple copies of three distinct enzymes (E1–E3) and an accessory subunit, E3BP (E3-binding protein). Its icosahedral E2/E3BP 60-meric ‘core’ provides the central structural and mechanistic framework ensuring favourable E1 and E3 positioning and enzyme co-operativity. Current core models indicate either a 48E2+12E3BP or a 40E2+20E3BP subunit composition. In the present study, we demonstrate clear differences in subunit content and organization between the recombinant hPDC core (rhPDC; 40E2+20E3BP), generated under defined conditions where E3BP is produced in excess, and its native bovine (48E2+12E3BP) counterpart. The results of the present study provide a rational basis for resolving apparent differences between previous models, both obtained using rhE2/E3BP core assemblies where no account was taken of relative E2 and E3BP expression levels. Mathematical modelling predicts that an ‘average’ 48E2+12E3BP core arrangement allows maximum flexibility in assembly, while providing the appropriate balance of bound E1 and E3 enzymes for optimal catalytic efficiency and regulatory fine-tuning. We also show that the rhE2/E3BP and bovine E2/E3BP cores bind E3s with a 2:1 stoichiometry, and propose that mammalian PDC comprises a heterogeneous population of assemblies incorporating a network of E3 (and possibly E1) cross-bridges above the core surface.This work was partly supported by EPSRC (under grants GR/R99393/01 and EP/C015452/1)

Dental attendance, restoration and extractions in adults with intellectual disabilities compared with the general population: a record linkage study

Background: Oral health may be poorer in adults with intellectual disabilities (IDs) who rely on carer support and medications with increased dental risks. Methods: Record linkage study of dental outcomes, and associations with anticholinergic (e.g. antipsychotics) and sugar‐containing liquid medication, in adults with IDs compared with age–sex–neighbourhood deprivation‐matched general population controls. Results: A total of 2933/4305 (68.1%) with IDs and 7761/12 915 (60.1%) without IDs attended dental care: odds ratio (OR) = 1.42 [1.32, 1.53]; 1359 (31.6%) with IDs versus 5233 (40.5%) without IDs had restorations: OR = 0.68 [0.63, 0.73]; and 567 (13.2%) with IDs versus 2048 (15.9%) without IDs had dental extractions: OR = 0.80 [0.73, 0.89]. Group differences for attendance were greatest in younger ages, and restoration/extractions differences were greatest in older ages. Adults with IDs were more likely prescribed with anticholinergics (2493 (57.9%) vs. 6235 (48.3%): OR = 1.49 [1.39, 1.59]) and sugar‐containing liquids (1641 (38.1%) vs. 2315 (17.9%): OR = 2.89 [2.67, 3.12]). Conclusion: Carers support dental appointments, but dentists may be less likely to restore teeth, possibly extracting multiple teeth at individual appointments instead

Universal scaling functions for bond percolation on planar random and square lattices with multiple percolating clusters

Percolation models with multiple percolating clusters have attracted much attention in recent years. Here we use Monte Carlo simulations to study bond percolation on $L_{1}\times L_{2}$ planar random lattices, duals of random lattices, and square lattices with free and periodic boundary conditions, in vertical and horizontal directions, respectively, and with various aspect ratio $L_{1}/L_{2}$. We calculate the probability for the appearance of $n$ percolating clusters, $W_{n},$ the percolating probabilities, $P$, the average fraction of lattice bonds (sites) in the percolating clusters, $_{n}$ ($_{n}$), and the probability distribution function for the fraction $c$ of lattice bonds (sites), in percolating clusters of subgraphs with $n$ percolating clusters, $f_{n}(c^{b})$ ($f_{n}(c^{s})$). Using a small number of nonuniversal metric factors, we find that $W_{n}$, $P$, $_{n}$ ($_{n}$), and $f_{n}(c^{b})$ ($f_{n}(c^{s})$) for random lattices, duals of random lattices, and square lattices have the same universal finite-size scaling functions. We also find that nonuniversal metric factors are independent of boundary conditions and aspect ratios.Comment: 15 pages, 11 figure

Nonequilibrium Quantum Dynamics Of Disoriented Chiral Condensates

The nonequilibrium dynamics of the chiral phase transition expected during the expansion of the quark-qluon plasma produced in a high energy hadron or heavy ion collision is studied in the O(4) linear sigma model to leading order in a large $N$ expansion. Starting from an approximate equilibrium configuration at an initial proper time $\tau$ in the disordered phase we study the transition to the ordered broken symmetry phase as the system expands and cools. We give results for the proper time evolution of the effective pion mass, the order parameter $$ as well as for the pion two point correlation function expressed in terms of a time dependent phase space number density and pair correlation density. We determine the phase space of initial conditions that lead to instabilities (exponentially growing long wave length modes) as the system evolves in time. These instabilities are what eventually lead to disoriented chiral condensates. In our simulations,we found that instabilities that are formed during the initial phases of the expansion exist for proper times that are at most $3 fm/c$ and lead to condensate regions that do not contain large numbers of particles. The damping of instabilities is a consequence of strong coupling.Comment: 49 pages, figures available by reques