Search Results (41 total)

This investigation follows up the suggestion that the equation of state for superconducting cosmic strings provided by Witten’s prototype biscalar field model can be well represented by an effective Lagrangian of simple logarithmic form depending on only 3 independent parameters. The numerical work described here confirms the validity of this approximation and initiates the evaluation of the 3 required parameters, as functions of the masses and other parameters specifying the underlying U(1)×U(1) scalar field model in the limit for which the relevant gauge coupling constants are small. In this limit, subject to calibration of the relevant length and mass scales, the scalar field model is characterized by just 3 dimensionless ratios which (in order to provide conducting strings) must be subject to three inequalities (of which two have obvious analytic expressions). It is found here that when all three of these inequalities are satisfied by a reasonably large margin, there is a simple empirical formula that can be used to provide a fairly accurate prescription for the algebraic dependence on these 3 dimensionless ratios of the 3 parameters required for the logarithmic equation of state.

We study the thermodynamic and gravitational stability of Kerr anti-de Sitter black holes in five and higher dimensions. We show, in the case of equal rotation parameters, a_i=a, that the Kerr-AdS background metrics become stable, both thermodynamically and gravitationally, when the rotation parameters a_i take values comparable to the AdS curvature radius. In turn, a Kerr-AdS black hole can be in thermal equilibrium with the thermal radiation around it only when the rotation parameters become not significantly smaller than the AdS curvature radius. We also find with equal rotation parameters that a Kerr-AdS black hole is thermodynamically favored against the existence of a thermal AdS space, while the opposite behavior is observed in the case of a single nonzero rotation parameter. The five-dimensional case is however different and also special in that there is no high temperature thermal AdS phase regardless of the choice of rotation parameters. We also verify that at fixed entropy, the temperature of a rotating black hole is always bounded above by that of a nonrotating black hole, in four and five dimensions, but not in six and more dimensions (especially, when the entropy approaches zero or the minimum of entropy does not correspond to the minimum of temperature). In this last context, the six-dimensional case is marginal.

The large scale dynamics of the universe appears to be dominated by a “dark energy” constituent with negative pressure to density ratio w=P/ρ, which could be stable if sufficiently rigid, but not if purely fluid. It was suggested by Bucher and Spergel that such a cosmological solid might be constituted by a cold (static) distribution of cosmic strings with w=-1/3, or membranes with the observationally more favored value w=-2/3, but it was not shown that the rigidity actually would be sufficient for stability. For cases in which the defect lattice is formed from even junctions, it is found that the rigidity to density ratio will be given by μ/ρ=4/15 in both the string and membrane cases, and it is confirmed that this is indeed sufficient for stabilisation with respect to sufficiently small perturbations.

We compute the regularized force density and renormalized action due to fields of external origin coupled to a brane of arbitrary dimension in a spacetime of any dimension. Specifically, we consider forces generated by gravitational, dilatonic, and generalized antisymmetric form-fields. The force density is regularized using a recently developed gradient operator. For the case of a Nambu-Goto brane, we show that the regularization leads to a renormalization of the tension, which is seen to be the same in both approaches. We discuss the specific couplings which lead to cancellation of the self-force in this case.

This article is based on the covariant canonical formalism and corresponding symplectic structure on phase space developed by Witten, Zuckerman, and others in the context of field theory. After recalling the basic principles of this procedure, we construct the conserved bilinear symplectic current for generic elastic string models. These models describe current carrying cosmic strings evolving in an arbitrary curved background spacetime. Particular attention is paid to the special case of the chiral string for which the worldsheet current is null. Different formulations of the chiral string action are discussed in detail, and as a result the integrability property of the chiral string is clarified.

We discuss the linearized, gravitational self-interaction of a brane of arbitrary codimension in a spacetime of arbitrary dimension. We find that in the codimension two case the gravitational self-force is exactly zero for a Nambu-Goto equation of state, generalizing a previous result for a string in four dimensions. For the case of a 3-brane, this picks out the case of a six-dimensional brane-world model as having special properties that we discuss. In particular, we see that bare tension on the brane has no effect locally, suppressing the cosmological constant problem.

We discuss various issues related to stabilized embedded strings in a thermal background. In particular, we demonstrate that such strings will generically become superconducting at moderately low temperatures, thus enhancing their stability. We then present a new class of defects—drum vortons—which arise when a small symmetry breaking term is added to the potential. We display these points within the context of the O(4) sigma model, relevant for hadrodynamics below the QCD scale. This model admits “embedded defects” (topological defect configurations of a simpler—in this case O(2) symmetric—model obtained by imposing an embedding constraint) that are unstable in the full model at zero temperature, but that can be stabilized (by electromagnetic coupling to photons) in a thermal gas at moderately high termperatures. It is shown here that below the embedded defect stabilization threshold, there will still be stabilized cosmic string defects. However, they will not be of the symmetric embedded vortex type, but of an “asymmetric” vortex type, and are automatically superconducting. In the presence of weak symmetry breaking terms, such as arise naturally when using the O(4) model for hadrodynamics, the strings become the boundary of a new kind of cosmic sigma membrane, with tension given by the pion mass. The string current would then make it possible for a loop to attain a (classically) stable equilibrium state that differs from an “ordinary” vorton state by the presence of a sigma membrane stretched across it in a drum-like configuration. Such defects will however be entirely destabilized if the symmetry breaking is too strong, as is found to be the case—due to the rather large value of the pion mass—in the hadronic application of the O(4) sigma model.

We consider a brane-world of codimension one without the reflection symmetry which is commonly imposed between the two sides of the brane. Using the coordinate-free formalism of the Gauss-Codazzi equations, we derive the effective Einstein equations by relating the local curvature to the matter on the brane in the case when its bare tension is much larger than the localized matter, and hence show that Einstein gravity is a natural consequence of such models in the weak-field limit. We find agreement with the recently derived cosmological case, which can be solved exactly, and point out that such models can be realized naturally in the case where there is a minimally coupled form field in the bulk.

This work is the sequel to a previous investigation of stationary and cylindrically symmetric vortex configurations for simple models representing an incompressible nonrelativistic superconductor in a rigidly rotating background. In the present paper, we carry out our analysis with a generalized Ginzburg-Landau description of the superconductor, which provides a prescription for the radial profile of the normal density within the vortex. Within this framework, it is shown that the Bogomol’nyi limit condition marking the boundary between type I and type II behavior is unaffected by the rotation of the background.

We carry out a systematic analytic investigation of stationary and cylindrically symmetric vortex configurations for simple models representing an incompressible nonrelativistic superconductor in a background, which is rigidly rotating with the angular velocity Ω. It is shown that although the magnetic and kinetic contributions to the energy per unit length of such a vortex are separately modified by the background angular velocity, its effect on the total energy per unit length cancels out. For a type II superconductor threaded by a parallel array of such vortices, this result implies that the conventionally defined local magnetic field strength H will not be equal to the local space average 〈B〉 of the magnetic induction B (as has previously been suggested), but instead that H will simply be equal to the London field B_L=-(2m/q)Ω (where m and q are the mass and charge of the condensate particles).

We investigate the cosmological consequences of particle physics theories that admit stable loops of current-carrying string—vortons. In particular, we consider chiral theories where a single fermion zero mode is excited in the string core, such as those arising in supersymmetric theories with a D term. The resulting vortons formed in such theories are expected to be more stable than their nonchiral cousins. General symmetry breaking schemes are considered in which strings formed at one symmetry breaking scale become current carrying at a subsequent phase transition. The vorton abundance is estimated and constraints placed on the underlying particle physics theories from cosmological observations. Our constraints on the chiral theory are considerably more stringent than the previous estimates for more general theories.

It is shown that for any elastic string model with energy density U and tension T the divergent contribution from gravitational self-interaction can be allowed for by an action renormalization proportional to (U-T)². This formula is applied to the important special case of a bare model of the transonic type (characterized by a constant value of the product UT) that represents the macroscopically averaged effect of short-wavelength wiggles on an underlying microscopic model of the Nambu-Goto type (characterized by U=T).

The binding of bipyridyl-(ethylenediamine)platinum(II) to calf-thymus DNA has been studied in solution via isothermal titration calorimetry and in unoriented films via midinfrared spectroscopy. The calorimetric data reveal that the ligand binds to DNA at two different sites with the first binding site being filled by about one ligand for every five base pairs. The binding is entropically driven: +25 cal/mol K for the first site and +22 cal/mol K for the second site. Midinfrared absorption data (400–1800 cm^-1) from unoriented films show no dependence on the ligand content at relative humidities of 23% and 80%.

Irrotational relativistic vortex configurations in uniform subsonic motion with respect to a surrounding perfect fluid are analyzed for the purpose of application to superfluid layers in neutron stars. Asymptotic solutions are found by asymptotically expanding the flow equation at large distances from the vortex core and then by solving it order by order. The asymptotic effective tension and energy density that are needed for an averaged macroscopic description are thus obtained as functions of the vortex velocity, the vortex circulation, the asymptotic chemical potential, and of parameters depending on the equation of state.

Earlier attempts to calculate the nonlinear dynamical evolution of Witten-type superconducting vacuum vortex defects relied on the use of approximate conducting string models that were too simple to take proper account of the effect of current saturation. This effect is however allowed for adequately in a newly developed class of rather more complicated, though still conveniently analytic, conducting string models. These more realistic models have recently been employed by Larsen and Axenides for investigating the collapse of circular string loops in the case for which angular momentum is absent. The present work extends this investigation to the generic case of circular string loops for which angular momentum is present, so that there will be a centrifugal potential barrier. This barrier will prevent collapse unless the initial conditions are such that the relevant current saturation limit is attained, in which case the string description of the vortex defect will break down, so that its subsequent fate is hard to foresee. On the other hand if saturation is avoided one would expect that the loop will eventually radiate away its excess energy and settle down into a vorton-type equilibrium state.

We investigate the cosmological consequences of particle physics theories that admit stable loops of superconducting cosmic string—vortons. General symmetry-breaking schemes are considered, in which strings are formed at one energy scale and subsequently become superconducting in a secondary phase transition at what may be a considerably lower energy scale. We estimate the abundances of the ensuing vortons, and thereby derive constraints on the relevant particle physics models from cosmological observations. For a range of values of the dimensionless parameters in the analysis, these constraints significantly restrict the category of admissible grand unified theories. However, we demonstrate that the constraints are quite compatible with recently proposed effects whereby superconducting strings may have been formed close to the electroweak phase transition.

We give a class of explicit solutions for the stationary and cylindrically symmetric vortex configurations for a ‘‘cool’’ two-component superfluid (i.e., superfluid with an ideal gas of phonons). Each solution is characterized only by a set of (true) constants of integration. We then compute the effective asymptotic contribution of the vortex to the stress-energy tensor by comparison with a uniform reference state without vortex.

Explicit cosmic string models of a new kind specified by two independent mass parameters are introduced for the purpose of providing a realistic representation of the macroscopic dynamical behavior of Witten-type (superconducting) vortex defects of the vacuum. Unlike the self-dual single mass parameter models previously used for this purpose, the new models successfully represent the effects of both spacelike and timelike current saturation and the feature that, for plausible parameter values, wiggle propagation is supersonic unless the current is strong and timelike.

The natural relativistic generalization of Landau’s two-constituent superfluid theory can be formulated in terms of a Lagrangian scrL that is given as a function of the entropy current four-vector s^ρ and the gradient ∇_ρcphi 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 scrL{s→,∇cphi} is given by an expression of the form scrL=P-3ψ where P represents the pressure as a function just of ∇_ρcphi in the (isotropic) cold limit. The entropy current-dependent contribution ψ represents the generalized pressure of the (nonisotropic) 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.

The most usual procedure for deriving curvature corrections to effective actions for topological defects is subjected to a critical reappraisal. A logically unjustified step (leading to overdetermination) is identified and rectified, taking the standard domain wall case as an illustrative example. Using the appropriately corrected procedure, we obtain a new exact (analytic) expression for the corresponding effective action contribution of quadratic order in the wall width, in terms of the intrinsic Ricci scalar R and the extrinsic curvature scalar K. The result is proportional to cK²-R with the coefficient given by c≃2. The resulting form of the ensuing dynamical equations is obtained in terms of the second fundamental form and the Dalembertian of its trace, K. It is argued that this does not invalidate the physical conclusions obtained from the ‘‘zero rigidity’’ ansatz c=0 used in previous work.

The hitherto controversial proposition that a “wiggly” Goto-Nambu cosmic string can be effectively represented by an elastic string model of permanently transonic type (with energy density U inversely proportional to its tension T) is shown to have a firm mathematical basis.

Some of the essential general principles governing cosmic string mechanics in a conformally expanding blackbody radiation background are described. It is shown that the effect of dissipative drag damping may be given a strictly conservative (i.e., variational) representation in which the usual Goto-Nambu action is simply multiplied by an appropriate cosmological temperature-dependent conformal factor. A simplified thermodynamic description is used to investigate approximately stationary equilibrium states such as may occasionally be produced as the long term outcome of large scale damping in the case of a cosmic string loop for which the (thermal or more general) distribution of surviving microscopic wiggles on an isolated cosmic string loop is characterized by a strong preponderance of ‘‘right movers’’ over ‘‘left movers’’ (or vice versa). For nonsuperconducting strings, such states can be represented very simply using the nondispersive ‘‘warm’’ cosmic string model whose dynamics is characterized by a pair of ‘‘left’’- and ‘‘right’’-moving characteristic surface currents that will be independently conserved so long as the effective heat loss to the environment is negligible. It is predicted that one of these currents will still remain conserved in the long run when account is taken of radiative energy loss from the approximately stationary equilibrium state, which will evolve with negative specific heat, monotonically increasing its effective temperature as it contracts.

It is shown how to set up a concise and fully covariant formalism, in terms of an appropriate (geodesically defined) displacement vector ξ^μ, in such a way that the corresponding second order perturbation of the Dirac-Goto-Nambu action itself provides the action for a convenient secondary variation principle governing the linearized dynamics of first order perturbations of the relevant membrane and string models in an arbitrarily curved background, as well as determining the corresponding conserved symplectic current associated with any pair of distinct solutions ξ^μ and ξ`^μ on the world sheet.

The relativistically covariant theory of two-constituent superfluid dynamics that was derived by the convective variational approach (a specialization of the formalism developed for the covariant treatment of elastic media) is found to agree precisely, in the nondissipative limit, with the theory that was derived independently using a potential variational principle (a generalization of the classical Clebsch formalism).

It is argued that, independently of the detailed (thermal or more general) noise spectrum of the microscopic extrinsic excitations that can be expected on an ordinary cosmic string, their effect can be taken into account at a macroscopic level by replacing the standard isotropic Goto-Nambu-type string model by the nondegenerate string model characterized by an equation of state of the nondispersive "fixed determinant" type, with the effective surface stress-energy tensor satisfying (T^ν_ν)²-T^μ_νT^ν_μ=2T₀², where T₀ is a constant representing the null-state limit of the string tension T, whose product with the energy density U of the string is thereby held fixed: TU=T₀². It is shown that this equation of state has the special property of giving rise (in a flat background) to explicitly integrable dynamical equations.