Cold, warm, and composite (cool) cosmic string models

The dynamical behaviour of a cosmic string is strongly affected by any reduction of the effective string tension $T$ below the constant value $T=m^2$ say that characterizes the simple, longitudinally Lorentz invariant, Goto Nambu string model in terms of a fixed mass scale $m$ whose magnitude depends on that of the Higgs field responsible for the existence of the string. Such a reduction occurs in the standard "hot" cosmic string model in which the effect of thermal perturbations of a simple Goto Nambu model is expressed by the formula $T^2=m^2(m^2-2\pi\Theta^2/3)$, where $\Theta$ is the string temperature. A qualitatively similar though analytically more complicated tension reduction phenomenon occurs in "cold" conducting cosmic string models where the role of the temperature is played by an effective chemical potential $\mu$ that is constructed as the magnitude of the phase $\phi$ of a bosonic condensate of the kind whose existence was first proposed by Witten. The present article describes the construction and essential mechanical properties of a category of "warm" cosmic string models that are intermediate between these "hot" and "cold" extremes. These "warm" models are the string analogues of the standard Landau model for a 2-constituent finite temperature superfluid, and as such involve two independent currents interpretable as that of the entropy on one hand and that of the bosonic condensate on the other. It is surmised that the stationary (in particular ring) equilibrium states of such "warm" cosmic strings may be of cosmological significance.Comment: 31 pages, Tex preprint version of manuscript subsequently published (with editorial modifications) in Nuclear Physics

Relativistic models for Superconducting-Superfluid Mixtures

The material below the crust of a neutron star is understood to be describable in terms of three principal independently moving constituents, identifiable as neutrons, protons, and electrons, of which the first two are believed to form mutually coupled bosonic condensates. The large scale comportment of such a system will be that of a positively charged superconducting superfluid in a negatively charged ``normal'' fluid background. As a contribution to the development of the theory of such a system, the present work shows how, subject to neglect of dissipative effects, it is possible to set up an elegant category of simplified but fully relativistic three-constituent superconducting superfluid models whose purpose is to provide realistic approximations for cases in which a strictly conservative treatment is sufficient. A "mesoscopic" model, describing the fluid between the vortices, is constructed, as well as a "macroscopic" model taking into account the average effect of quantised vortices.Comment: 28 pages, LaTeX, no figure; to appear in Nuclear Physics

Fields in nonaffine bundles. III. Effective symmetries and conserved currents in strings and higher branes

The principles of a previously developed formalism for the covariant treatment of multi-scalar fields for which (as in a nonlinear sigma model) the relevant target space is not of affine type -- but curved -- are recapitulated. Their application is extended from ordinary harmonic models to a more general category of "harmonious" field models, with emphasis on cases in which the field is confined to a string or higher brane worldsheet, and for which the relevant internal symmetry group is non Abelian, so that the conditions for conservation of the corresponding charge currents become rather delicate, particularly when the symmetry is gauged. Attention is also given to the conditions for conservation of currents of a different kind -- representing surface fluxes of generalised momentum or energy -- associated with symmetries not of the internal target space but of the underlying spacetime background structure, including the metric and any relevant gauge field. For the corresponding current to be conserved the latter need not be manifestly invariant: preservation modulo a gauge adjustment will suffice. The simplest case is that of "strong" symmetry, meaning invariance under the action of an effective Lie derivative (an appropriately gauge adjusted modification of an ordinary Lie derivative). When the effective symmetry is of the more general "weak" kind, the kinetic part of the current is not conserved by itself but only after being supplemented by a suitable contribution from the background.Comment: 27 pages Latex (color

EDITOR\u27S CORNER

1980 - Explorations begins a new decade. Surprise! In terms of the longevity of professional and scholarly journals, and statistically, the journal should have folded. Instead, Explorations moves ahead with optimism and starts the new decade with a sense of pride and accomplishment. If Explorations survives until January, 1990, we will know that Ethnic Studies has survived

Triple linking numbers and triple point numbers of certain T2T^2-links

The triple linking number of an oriented surface link was defined as an analogical notion of the linking number of a classical link. We consider a certain $m$-component $T^2$-link ($m \geq 3$) determined from two commutative pure $m$-braids $a$ and $b$. We present the triple linking number of such a $T^2$-link, by using the linking numbers of the closures of $a$ and $b$. This gives a lower bound of the triple point number. In some cases, we can determine the triple point numbers, each of which is a multiple of four.Comment: 15 pages, 4 figures, minor modification

The Equation of State for Cool Relativistic Two-Constituent Superfluid Dynamics

The natural relativistic generalisation of Landau's two constituent superfluid theory can be formulated in terms of a Lagrangian $L$ that is given as a function of the entropy current 4-vector $s^\rho$ and the gradient $\nabla\varphi$ of the superfluid phase scalar. It is shown that in the ``cool" regime, for which the entropy is attributable just to phonons (not rotons), the Lagrangian function $L(\vec s, \nabla\varphi)$ is given by an expression of the form $L=P-3\psi$ where $P$ represents the pressure as a function just of $\nabla\varphi$ in the (isotropic) cold limit. The entropy current dependent contribution $\psi$ represents the generalised pressure of the (non-isotropic) phonon gas, which is obtained as the negative of the corresponding grand potential energy per unit volume, whose explicit form has a simple algebraic dependence on the sound or ``phonon" speed $c_P$ that is determined by the cold pressure function $P$.Comment: 26 pages, RevTeX, no figures, published in Phys. Rev. D. 15 May 199

Instanton-Induced Interactions in Finite Density QCD

We consider the finite density, zero-temperature behaviour of quark matter in the instanton picture. Since the instanton-induced interactions are attractive in both $\bar{q}q$ and $qq$ channels, a competition ensues between phases of matter with condensation in either or both. It results in chiral symmetry restoration due to the onset of diquark condensation, a `colour superconductor', at finite density.Comment: 4 pages, 5 figures, uses espcrc1.sty. To appear in Proceedings of Quark Matter 99 (10-14 May 1999, Torino, Italy) and PANIC 99 (10-16 June 1999, Uppsala, Sweden

Poly-essential and general Hyperelastic World (brane) models

This article provides a unified treatment of an extensive category of non-linear classical field models whereby the universe is represented (perhaps as a brane in a higher dimensional background) in terms of a structure of a mathematically convenient type describable as hyperelastic, for which a complete set of equations of motion is provided just by the energy-momentum conservation law. Particular cases include those of a perfect fluid in quintessential backgrounds of various kinds, as well as models of the elastic solid kind that has been proposed to account for cosmic acceleration. It is shown how an appropriately generalised Hadamard operator can be used to construct a symplectic structure that controles the evolution of small perturbations, and that provides a characteristic equation governing the propagation of weak discontinuities of diverse (extrinsic and extrinsic) kinds. The special case of a poly-essential model - the k-essential analogue of an ordinary polytropic fluid - is examined and shown to be well behaved (like the fluid) only if the pressure to density ratio $w$ is positive.Comment: 16 pages Latex, Contrib. to 10th Peyresq Pysics Meeting, June 2005: Micro and Macro Structures of Spacetim

Recent developments in Vorton Theory

This article provides a concise overview of recent theoretical results concerning the theory of vortons, which are defined to be (centrifugally supported) equilibrium configurations of (current carrying) cosmic string loops. Following a presentation of the results of work on the dynamical evolution of small circular string loops, whose minimum energy states are the simplest examples of vortons, recent order of magnitude estimates of the cosmological density of vortons produced in various kinds of theoretical scenario are briefly summarised.Comment: 6 pages Latex. Contribution to 1996 Cosmology Meeting, Peyresq, Franc

The Secular Bar-Mode Instability in Rapidly Rotating Stars Revisited

Uniformly rotating, homogeneous, incompressible Maclaurin spheroids that spin sufficiently rapidly are secularly unstable to nonaxisymmetric, bar-mode perturbations when viscosity is present. The intuitive explanation is that energy dissipation by viscosity can drive an unstable spheroid to a stable, triaxial configuration of lower energy - a Jacobi ellipsoid. But what about rapidly rotating compressible stars? Unlike incompressible stars, which contain no internal energy and therefore immediately liberate all the energy dissipated by viscosity, compressible stars have internal energy and can retain the dissipated energy as internal heat. Now compressible stars that rotate sufficiently rapidly and also manage to liberate this dissipated energy very quickly are known to be unstable to bar-mode perturbations, like their incompressible counterparts. But what is the situation for rapidly rotating compressible stars that have very long cooling timescales, so that all the energy dissipated by viscosity is retained as heat, whereby the total energy of the star remains constant on a secular (viscous) evolution timescale? Are such stars also unstable to the nonlinear growth of bar modes, or is the viscous heating sufficient to cause them to expand, drive down the ratio of rotational kinetic to gravitational potential energy T/|W| ~ 1/R, where R is the equatorial radius, and turn off the instability before it gets underway? If the instability still arises in such stars, at what rotation rate do they become unstable, and to what final state do they evolve? We provide answers to these questions in the context of the compressible ellipsoid model for rotating stars. The results should serve as useful guides for numerical simulations in 3+1 dimensions for rotating stars containing viscosity.Comment: Accepted for publication in ApJ 613, 1213-1220, 200