Friction in inflaton equations of motion

The possibility of a friction term in the equation of motion for a scalar field is investigated in non-equilibrium field theory. The results obtained differ greatly from existing estimates based on linear response theory, and suggest that dissipation is not well represented by a term of the form $\eta\dot{\phi}$.Comment: 4 pages, 2 figures, RevTex4. An obscurity in the original version has been clarifie

Numerical investigation of friction in inflaton equations of motion

The equation of motion for the expectation value of a scalar quantum field does not have the local form that is commonly assumed in studies of inflationary cosmology. We have recently argued that the true, temporally non-local equation of motion does not possess a time-derivative expansion and that the conversion of inflaton energy into particles is not, in principle, described by the friction term estimated from linear response theory. Here, we use numerical methods to investigate whether this obstacle to deriving a local equation of motion is purely formal, or of some quantitative importance. Using a simple scalar-field model, we find that, although the non-equilibrium evolution can exhibit significant damping, this damping is not well described by the local equation of motion obtained from linear response theory. It is possible that linear response theory does not apply to the situation we study only because thermalization turns out to be slow, but we argue that that the large discrepancies we observe indicate a failure of the local approximation at a more fundamental level.Comment: 13 pages, 7 figure

Perturbative nonequilibrium dynamics of phase transitions in an expanding universe

A complete set of Feynman rules is derived, which permits a perturbative description of the nonequilibrium dynamics of a symmetry-breaking phase transition in $\lambda\phi^4$ theory in an expanding universe. In contrast to a naive expansion in powers of the coupling constant, this approximation scheme provides for (a) a description of the nonequilibrium state in terms of its own finite-width quasiparticle excitations, thus correctly incorporating dissipative effects in low-order calculations, and (b) the emergence from a symmetric initial state of a final state exhibiting the properties of spontaneous symmetry breaking, while maintaining the constraint $\equiv 0$. Earlier work on dissipative perturbation theory and spontaneous symmetry breaking in Minkowski spacetime is reviewed. The central problem addressed is the construction of a perturbative approximation scheme which treats the initial symmetric state in terms of the field $\phi$, while the state that emerges at later times is treated in terms of a field $\zeta$, linearly related to $\phi^2$. The connection between early and late times involves an infinite sequence of composite propagators. Explicit one-loop calculations are given of the gap equations that determine quasiparticle masses and of the equation of motion for $$ and the renormalization of these equations is described. The perturbation series needed to describe the symmetric and broken-symmetry states are not equivalent, and this leads to ambiguities intrinsic to any perturbative approach. These ambiguities are discussed in detail and a systematic procedure for matching the two approximations is described.Comment: 22 pages, using RevTeX. 6 figures. Submitted to Physical Review

Dissipation in equations of motion of scalar fields

The methods of non-equilibrium quantum field theory are used to investigate the possibility of representing dissipation in the equation of motion for the expectation value of a scalar field by a friction term, such as is commonly included in phenomenological inflaton equations of motion. A sequence of approximations is exhibited which reduces the non-equilibrium theory to a set of local evolution equations. However, the adiabatic solution to these evolution equations which is needed to obtain a local equation of motion for the expectation value is not well defined; nor, therefore, is the friction coefficient. Thus, a non-equilibrium treatment is essential, even for a system that remains close to thermal equilibrium, and the formalism developed here provides one means of achieving this numerically.Comment: 17 pages, 5 figure

Scaling in high-temperature superconductors

A Hartree approximation is used to study the interplay of two kinds of scaling which arise in high-temperature superconductors, namely critical-point scaling and that due to the confinement of electron pairs to their lowest Landau level in the presence of an applied magnetic field. In the neighbourhood of the zero-field critical point, thermodynamic functions scale with the scaling variable $(T-T_{c2}(B))/B^{1/2\nu}$, which differs from the variable $(T - T_c(0))/B^{1/2\nu}$ suggested by the gaussian approximation. Lowest-Landau-level (LLL) scaling occurs in a region of high field surrounding the upper critical field line but not in the vicinity of the zero-field transition. For YBaCuO in particular, a field of at least 10 T is needed to observe LLL scaling. These results are consistent with a range of recent experimental measurements of the magnetization, transport properties and, especially, the specific heat of high-$T_c$ materials.Comment: 22 pages + 1 figure appended as postscript fil

Inequalities in the dental health needs and access to dental services among looked after children in Scotland: a population data linkage study

Background: There is limited evidence on the health needs and service access among children and young people who are looked after by the state. The aim of this study was to compare dental treatment needs and access to dental services (as an exemplar of wider health and well-being concerns) among children and young people who are looked after with the general child population. Methods: Population data linkage study utilising national datasets of social work referrals for ‘looked after’ placements, the Scottish census of children in local authority schools, and national health service’s dental health and service datasets. Results: 633 204 children in publicly funded schools in Scotland during the academic year 2011/2012, of whom 10 927 (1.7%) were known to be looked after during that or a previous year (from 2007–2008). The children in the looked after children (LAC) group were more likely to have urgent dental treatment need at 5 years of age: 23%vs10% (n=209/16533), adjusted (for age, sex and area socioeconomic deprivation) OR 2.65 (95% CI 2.30 to 3.05); were less likely to attend a dentist regularly: 51%vs63% (n=5519/388934), 0.55 (0.53 to 0.58) and more likely to have teeth extracted under general anaesthesia: 9%vs5% (n=967/30253), 1.91 (1.78 to 2.04). Conclusions: LAC are more likely to have dental treatment needs and less likely to access dental services even when accounting for sociodemographic factors. Greater efforts are required to integrate child social and healthcare for LAC and to develop preventive care pathways on entering and throughout their time in the care system

Critical-point scaling function for the specific heat of a Ginzburg-Landau superconductor

If the zero-field transition in high temperature superconductors such as YBa_2Cu_3O_7-\delta is a critical point in the universality class of the 3-dimensional XY model, then the general theory of critical phenomena predicts the existence of a critical region in which thermodynamic functions have a characteristic scaling form. We report the first attempt to calculate the universal scaling function associated with the specific heat, for which experimental data have become available in recent years. Scaling behaviour is extracted from a renormalization-group analysis, and the 1/N expansion is adopted as a means of approximation. The estimated scaling function is qualitatively similar to that observed experimentally, and also to the lowest-Landau-level scaling function used by some authors to provide an alternative interpretation of the same data. Unfortunately, the 1/N expansion is not sufficiently reliable at small values of N for a quantitative fit to be feasible.Comment: 20 pages; 4 figure

Renormalization group and 1/N expansion for 3-dimensional Ginzburg-Landau-Wilson models

A renormalization-group scheme is developed for the 3-dimensional O($2N$)-symmetric Ginzburg-Landau-Wilson model, which is consistent with the use of a 1/N expansion as a systematic method of approximation. It is motivated by an application to the critical properties of superconductors, reported in a separate paper. Within this scheme, the infrared stable fixed point controlling critical behaviour appears at $z=0$, where $z=\lambda^{-1}$ is the inverse of the quartic coupling constant, and an efficient renormalization procedure consists in the minimal subtraction of ultraviolet divergences at $z=0$. This scheme is implemented at next-to-leading order, and the standard results for critical exponents calculated by other means are recovered. An apparently novel result of this non-perturbative method of approximation is that corrections to scaling (or confluent singularities) do not, as in perturbative analyses, appear as simple power series in the variable $y=zt^{\omega\nu}$. At least in three dimensions, the power series are modified by powers of $\ln y$.Comment: 20 pages; 5 figure