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

Large-N transition temperature for superconducting films in a magnetic field

We consider the $N$-component Ginzburg-Landau model in the large $N$ limit, the system being embedded in an external constant magnetic field and confined between two parallel planes a distance $L$ apart from one another. On physical grounds, this corresponds to a material in the form of a film in the presence of an external magnetic field. Using techniques from dimensional and $zeta$-function regularization, modified by the external field and the confinement conditions, we investigate the behavior of the system as a function of the film thickness $L$. This behavior suggests the existence of a minimal critical thickness below which superconductivity is suppressed.Comment: Revtex, two column, 4 pages, 2 figure

Nonequilibrium perturbation theory for complex scalar fields

Real-time perturbation theory is formulated for complex scalar fields away from thermal equilibrium in such a way that dissipative effects arising from the absorptive parts of loop diagrams are approximately resummed into the unperturbed propagators. Low order calculations of physical quantities then involve quasiparticle occupation numbers which evolve with the changing state of the field system, in contrast to standard perturbation theory, where these occupation numbers are frozen at their initial values. The evolution equation of the occupation numbers can be cast approximately in the form of a Boltzmann equation. Particular attention is given to the effects of a non-zero chemical potential, and it is found that the thermal masses and decay widths of quasiparticle modes are different for particles and antiparticles.Comment: 15 pages using RevTeX; 2 figures in 1 Postscript file; Submitted to Phys. Rev.

An Analytic Equation of State for Ising-like Models

Using an Environmentally Friendly Renormalization we derive, from an underlying field theory representation, a formal expression for the equation of state, $y=f(x)$, that exhibits all desired asymptotic and analyticity properties in the three limits $x\to 0$, $x\to \infty$ and $x\to -1$. The only necessary inputs are the Wilson functions $\gamma_\lambda$, $\gamma_\phi$ and $\gamma_{\phi^2}$, associated with a renormalization of the transverse vertex functions. These Wilson functions exhibit a crossover between the Wilson-Fisher fixed point and the fixed point that controls the coexistence curve. Restricting to the case N=1, we derive a one-loop equation of state for $2< d<4$ naturally parameterized by a ratio of non-linear scaling fields. For $d=3$ we show that a non-parameterized analytic form can be deduced. Various asymptotic amplitudes are calculated directly from the equation of state in all three asymptotic limits of interest and comparison made with known results. By positing a scaling form for the equation of state inspired by the one-loop result, but adjusted to fit the known values of the critical exponents, we obtain better agreement with known asymptotic amplitudes.Comment: 10 pages, 2 figure

Treatment options for recurrent glioblastoma: a network meta-analysis

This is a protocol for a Cochrane Review (Intervention). The objectives are as follows:. To evaluate the effectiveness of further treatment/s for first and subsequent recurrence of glioblastoma multiforme (GBM) among people who have received the standard of care for primary treatment of the disease (chemoradiotherapy) or following development of GBM from a lower grade (radiotherapy with subsequent temozolomide at relapse); and to prepare a brief economic commentary on the available evidence

Osteoprotegerin in cardiometabolic disorders.

Osteoprotegerin (OPG), a glycoprotein traditionally implicated in bone remodelling, has been recently related to cardiovascular disease (CVD). Human studies show a positive relationship between circulating OPG, vascular damage, and CVD, and as such OPG has emerged as a potential biomarker for CVD. This review focuses on the relationship between circulating OPG and different endocrine cardiometabolic alterations such as type 1 and 2 diabetes. The association of OPG with diabetic complications (neuropathy, nephropathy, or retinopathy) as well as with atherosclerosis, coronary artery calcification, morbidity, and mortality is pointed out. Moreover, OPG modulation by different treatments is also established. Besides, other associated diseases such as obesity, hypertension, and metabolic syndrome, which are known cardiovascular risk factors, are also considered

Critical temperature for first-order phase transitions in confined systems

We consider the Euclidean $D$-dimensional $-\lambda |\phi |^4+\eta |\phi |^6$ ($\lambda ,\eta >0$) model with $d$ ($d\leq D$) compactified dimensions. Introducing temperature by means of the Ginzburg--Landau prescription in the mass term of the Hamiltonian, this model can be interpreted as describing a first-order phase transition for a system in a region of the $D$-dimensional space, limited by $d$ pairs of parallel planes, orthogonal to the coordinates axis $x_1, x_2, ..., x_d$. The planes in each pair are separated by distances $L_1, L_2, ..., L_d$. We obtain an expression for the transition temperature as a function of the size of the system, $$, $i=1, 2, ..., d$. For D=3 we particularize this formula, taking $L_1=L_2=... =L_d=L$ for the physically interesting cases $d=1$ (a film), $d=2$ (an infinitely long wire having a square cross-section), and for $d=3$ (a cube). For completeness, the corresponding formulas for second-order transitions are also presented. Comparison with experimental data for superconducting films and wires shows qualitative agreement with our theoretical expressionsComment: REVTEX, 11 pages, 3 figures; to appear in Eur. Phys. Journal

Coherent State Approach to Quantum Clocks

The ``problem of time'' has been a pressing issue in quantum gravity for some time. To help understand this problem, Rovelli proposed a model of a two harmonic oscillators system where one of the oscillators can be thought of as a ``clock'' for the other oscillator thus giving a natural time reference frame for the system. Recently, the author has constructed an explicit form for the coherent states on the reduced phase space of this system in terms of Klauder's projection operator approach. In this paper, by using coherent state representations and other tools from coherent state quantization, I investigate the construction of gauge invariant operators on this reduced phase space, and the ability to use a quantum oscillator as a ``clock.''Comment: 13 pages, Late

Photometric Variability and Rotation in Magnetic White Dwarfs

We present a search for long term (months—years) photometric variability in a sample of ten isolated magnetic white dwarfs using observations taken with the Liverpool Robotic Telescope between March 2005 and January 2007. These stars had previously been found to be photometrically stable on short (hours—one week) timescales [1]. We construct differential light curves for each target and then use CLEAN and Lomb‐Scargle periodograms to determine any periodicity that may be present. Photometric variability is detected in two of the targets during the observed timescale—G 240–72 and G 227–28. We find no variability in the remaining eight targets above the 1% level. Finally, we search for any correlations between the spin periods and intrinsic physical properties of magnetic white dwarfs, such as the magnetic field strength, temperature, mass and age

Critical properties of the topological Ginzburg-Landau model

We consider a Ginzburg-Landau model for superconductivity with a Chern-Simons term added. The flow diagram contains two charged fixed points corresponding to the tricritical and infrared stable fixed points. The topological coupling controls the fixed point structure and eventually the region of first order transitions disappears. We compute the critical exponents as a function of the topological coupling. We obtain that the value of the $\nu$ exponent does not vary very much from the XY value, $\nu_{XY}=0.67$. This shows that the Chern-Simons term does not affect considerably the XY scaling of superconductors. We discuss briefly the possible phenomenological applications of this model.Comment: RevTex, 7 pages, 8 figure