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

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.

5d superconformal field theories and graphs

We propose graphs, the Combined Fiber Diagrams (CFD), to characterize all 5d superconformal field theories (SCFTs) that arise as S1-reductions of 6d SCFTs. Transitions between CFDs encode mass deformations that trigger RG-flows between SCFTs. They provide a combinatorial classification of all such 5d SCFTs and encode physical information about the strongly coupled theories, like the superconformal flavor symmetry and BPS states. We consistently reproduce known results, but more importantly predict new theories and strong coupling effects in 5d SCFTs

Nonequilibrium perturbation theory for spin-1/2 fields

A partial resummation of perturbation theory is described for field theories containing spin-1/2 particles in states that may be far from thermal equilibrium. This allows the nonequilibrium state to be characterized in terms of quasiparticles that approximate its true elementary excitations. In particular, the quasiparticles have dispersion relations that differ from those of free particles, finite thermal widths and occupation numbers which, in contrast to those of standard perturbation theory evolve with the changing nonequilibrium environment. A description of this kind is essential for estimating the evolution of the system over extended periods of time. In contrast to the corresponding description of scalar particles, the structure of nonequilibrium fermion propagators exhibits features which have no counterpart in the equilibrium theory.Comment: 16 pages; no figures; submitted to Phys. Rev.

Component masses of young, wide, non-magnetic white dwarf binaries in the SDSS DR7

We present a spectroscopic component analysis of 18 candidate young, wide, non-magnetic, double-degenerate binaries identified from a search of the Sloan Digital Sky Survey Data Release 7 (DR7). All but two pairings are likely to be physical systems. We show SDSS J084952.47+471247.7 + SDSS J084952.87+471249.4 to be a wide DA+DB binary, only the second identified to date. Combining our measurements for the components of 16 new binaries with results for three similar, previously known systems within the DR7, we have constructed a mass distribution for the largest sample to date (38) of white dwarfs in young, wide, non-magnetic, double-degenerate pairings. This is broadly similar in form to that of the isolated field population with a substantial peak around M~0.6 Msun. We identify an excess of ultra-massive white dwarfs and attribute this to the primordial separation distribution of their progenitor systems peaking at relatively larger values and the greater expansion of their binary orbits during the final stages of stellar evolution. We exploit this mass distribution to probe the origins of unusual types of degenerates, confirming a mild preference for the progenitor systems of high-field-magnetic white dwarfs, at least within these binaries, to be associated with early-type stars. Additionally, we consider the 19 systems in the context of the stellar initial mass-final mass relation. None appear to be strongly discordant with current understanding of this relationship.Comment: 20 pages, 5 Tables, 7 figures. accepted for publication in MNRA

Binary Reactive Adsorbate on a Random Catalytic Substrate

We study the equilibrium properties of a model for a binary mixture of catalytically-reactive monomers adsorbed on a two-dimensional substrate decorated by randomly placed catalytic bonds. The interacting $A$ and $B$ monomer species undergo continuous exchanges with particle reservoirs and react ($A + B \to \emptyset$) as soon as a pair of unlike particles appears on sites connected by a catalytic bond. For the case of annealed disorder in the placement of the catalytic bonds this model can be mapped onto a classical spin model with spin values $S = -1,0,+1$, with effective couplings dependent on the temperature and on the mean density $q$ of catalytic bonds. This allows us to exploit the mean-field theory developed for the latter to determine the phase diagram as a function of $q$ in the (symmetric) case in which the chemical potentials of the particle reservoirs, as well as the $A-A$ and $B-B$ interactions are equal.Comment: 12 pages, 4 figure

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