Effective Field Equations Research Articles

Chaotic symmetry breaking and dissipative two-field dynamics

The dynamical symmetry breaking in a two-field model is studied by numerically solving the coupled effective field equations. These are dissipative equations of motion that can exhibit strong chaotic dynamics. By choosing very general model parameters leading to symmetry breaking along one of the field directions, the symmetry broken vacua make the role of transitory strange attractors and the field trajectories in phase space are strongly chaotic. Chaos is quantified by means of the determination of the fractal dimension, which gives an invariant measure for chaotic behavior. Discussions concerning chaos and dissipation in the model and possible applications to related problems are given.

Spherically Symmetric Solutions and Dark Matter on the Brane

It has recently been suggested that our universe is a three-brane embedded in a higher dimensional spacetime. In this paper I examine static, spherically symmetric solutions that satisfy the effective Einstein field equations on a brane embedded in a five dimensional spacetime. The field equations involve a term depending on the five dimensional Weyl tensor, so that the solutions will not be Schwarzschild in general. This Weyl term is traceless so that any solution of $^{(4)}R=0$ is a possible four dimensional spacetime. Different solutions correspond to different five dimensional spacetimes and to different induced energy-momentum tensors on the brane. One interesting possibility is that the Weyl term could be responsible for the observed dark matter in the universe.

Dynamical evolution of the scalar condensate in heavy ion collisions

We derive the effective coarse-grained field equation for the scalar condensate of the linear sigma model in a simple and straightforward manner using linear response theory. The dissipative coefficient is calculated consistently at tree level on the basis of the physical processes of sigma-meson decay and of thermal sigma mesons and pions knocking sigma mesons out of the condensate. The field equation is solved for hot matter undergoing either one- or three-dimensional expansion and cooling in the aftermath of a high energy nuclear collision. The results show that the time constant for returning the scalar condensate to thermal equilibrium is of order $2\mathrm{fm}/c.$

Event-by-event fluid dynamcis

Coarse grained Langevin-type effective field equations may provide some guidance for the analysis of mesoscopic or microscopic molecular systems exhibiting fluctuations, or for systems of hundreds to thousands of atomic or subatomic particles produced in atomic or high-energy nuclear collisions. Suggestions for consistent realization of random fluctuations in discretized fluid dynamics will be presented.

Nonperturbative Models for the Quantum Gravitational Back-Reaction on Inflation

We consider a universe in which inflation commences because of a positive cosmological constant, the effect of which is progressively screened by the interaction between virtual gravitons that become trapped in the expansion of spacetime. Perturbative calculations have shown that screening becomes nonperturbatively large at late times. In this paper we consider effective field equations which can be evolved numerically to provide a non-perturbative description of the process. The induced stress tensor is that of an effective scalar field which is a non-local functional of the metric. We use the known perturbative result, constrained by general principles and guided by a physical description of the screening mechanism, to formulate a class of ansätze for this functional. A scheme is given for numerically evolving the field equations which result from a simple ansatz, from the beginning of inflation past the time when it ends. We find that inflation comes to a sudden end, producing a system whose equation of state rapidly approaches that of radiation. Explicit numerical results are presented.

Fluctuation and dissipation in classical many-particle systems

Coarse-grained Langevin-type effective field equations are derived for classical systems of particles. These equations include the effects of thermal fluctuation and dissipation which may arise from coupling to an external bath, as in the Brownian motion of a single particle, or which may arise from statistical fluctuations in small parts of an isolated many-particle system, as in sound waves. These equations may provide some guidance for the analysis of mesoscopic or microscopic molecular systems, or for systems of hundreds to thousands of subatomic particles produced in high energy nuclear collisions.

Mixed (open/closed) N = (2, 2) string theory as an integrable deformation of self-duality

The exact effective field equations of motion, corresponding to the perturbative mixed theory of open and closed (2,2) world-sheet supersymmetric strings, are investigated. It is shown that they are only integrable in the case of an abelian gauge group. The gravitational equations are then stationary with respect to the Born-Infeld-type effective action.

Magnetic properties of a mixed spin-1/2 and spin-3/2 transverse Ising model

A theoretical study of a mixed spin-1/2 and spin-3/2 Ising system with independent transverse fields is presented using an effective field method within the framework of a single-site cluster theory. In this approach the effective field equations are derived using a probability distribution method based on the use of generalized van der Waerden identities accounting exactly for the single-site kinematic relations. The effect of the transverse fields on the critical behaviour is studied. The thermal dependence of the longitudinal and transverse components of the magnetization and its higher moments is also studied.

Phase diagrams of the spin‐3/2 transverse ising model with random interactions

AbstractThe transverse spin‐3/2 Ising model with random interactions is studied using an effective field method within the framework of a single‐site cluster theory. The effective field equations are derived using a probability distribution method based on the use of generalized Van der Waerden identities, that account exactly for the single‐site kinematic relations. A model is adopted in which the nearest‐neighbour exchange couplings are described by the probability distribution law: P(Jij) = p δ(Jij‐J) + (1‐p) δ(Jij‐aJ). The critical temperature at which the longitudinal magnetization vanishes is studied as a function of p and the transverse field strength. The thermal variation of the longitudinal and transverse magnetizations and higher‐order magnetization moments are also studied.

Theoretical study of the quenched diluted spin 2 ising ferromagnet in a transverse field

A theoretical study of the spin 2 Ising ferromagnet with site dilution in a transverse field is presented using an effective field method within the framework of a single site cluster theory. The effective field equations are derived using a probability distribution method based on the use of generalised Van der Waerden identities, that account exactly for the single-site kinematic relations. Correlations between the site disorder and the local configurational-dependent thermal averages of the spin variables are included. The dependence of the transition temperature for longitudinal ordering is studied both as a function of the transverse field strength and the dilution. The thermal dependence of the longitudinal and transverse magnetizations, and higher order magnetization moments, are also studied.

Phase Diagram and Magnetization Moments of the Spin‐5/2 Diluted Ising Ferromagnet in a Transverse Field

AbstractThe phase diagram and the magnetization moments of the spin‐5/2 diluted Ising ferromagnet in a transverse field is studied by an effective field method within a single‐site cluster theory. The effective field equations are derived using a probability distribution obtained with the aid of generalized van der Waerden identities that account for the single‐site spin kinematic relations. Correlations between the site disorder and the local configurational‐dependent thermal averages of the spin variable are included. The dependence of the transition temperature for longitudinal ordering is studied both as a function of the transverse field strength and the site dilution. Selected results for the thermal dependence of the longitudinal and transverse components of the magnetization and their higher moments are also presented.

On the theory of the transverse Ising model with arbitrary spin

A theoretical study of the transverse Ising model with arbitrary spin is presented using an extension of an effective field theory that has recently been inroduced for studying general spin S Ising models. In the theory, the effective field equations are derived using a probability distribution method, and the single site kinematic relations are accounted for by the use of the generalised Van der Waerden identities of Tucker. The dependence of the transition temperature for longitudinal ordering is studied as a function of the transverse field strength for all spin values from S = 1 2 to S = 5 2 . Selected results for the thermal dependence of the longitudinal and transverse components of the magnetization and its higher moments are also presented.

A study of the quenched diluted spin [formula omitted] transverse Ising model

A theoretical study of the site-diluted spin 3 2 transverse Ising model is presented using an effective field method within the framework of a single-site cluster theory. The effective field equations are derived using a probability distribution method based on the use of generalized Van der Waerden identities, that account exactly for the single-site kinematic relations. Correlations between the site disorder and the local configurational-dependent thermal averages of the spin variables are included. The critical temperature at which the longitudinal magnetization vanishes is studied both as a function of dilution and as a function of the transverse field strength. The thermal dependence of the longitudinal and transverse magnetizations, and higher-order magnetization moments, are also studied.

Modelling of thermomagnetoelectric effects in type-II superconductors in the mixed state

This article presents a phenomenological theory for studying thermomagnetoelectric effects in type-II superconductors in the mixed state. In the theoretical model, the anisotropic effect, the vortex dynamic effect, the flux-flow Hall effect and the thermomagnetic effects in the type-II superconductor in the mixed state are all taken into account self-consistently. It is shown that, at the London approximation, the classical first and second London equations for superconductors in the Meissner state are modified for the superconductors in the mixed state due to vortex dynamic effects, which are, in general, nonlinear. At the linear approximation, effective constitutive equations and field equations are derived to describe the thermomagnetoelectric behavior of anisotropic type-II superconductors in the mixed state. It is shown that the derived field equations are, in general, coupled due to the vortex dynamic effects. A possible solution of a plane thermomagnetic wave in the type-II superconductor in the mixed state is also studied illustratively.

Effective Boson-Fermion Dynamics for Subfermion Models

Abstract Effective composite particle dynamics can be derived by weak mapping of quantum fields. This method was already applied to derive effective boson or boson-fermion coupling theories from a nonlinear subfermion field. In this paper we present an extension of those calculations to the general group theoretical treatm ent of two-fermion bound states and their coupling to (elementary) fermions within an arbitrary nonlinear spinor-isospinor field model. The resulting effective field equations are com pared with the corresponding phenomenological expressions which for example underly the standard electroweak theory. PACS 11 .10 - Field theory. PACS 12.10 - Unified field theories and models. PACS 12.35 - Composite models of particles.

A new technique in the effective field theory of general spin S dilute Ising models

The effective field equations for diluted spin S Ising models are derived using a probability distribution method based on the use of generalized Van der Waerden identities. The approach is employed within the framework of a single-site cluster theory based on the use of exact Ising spin identities. The effective field equations for Ising models having all possible single-ion and nearest-neighbour pair interactions are reported for all spin values from S = 12 to S = 52.

Black hole evaporation in 1+1 dimensions

The formation and quantum mechanical evaporation of black holes in two spacetime dimensions can be studied using effective classical field equations, recently introduced by Callan et al. We find that gravitational collapse always leads to a curvature singularity, according to these equations, and that the region where the quantum corrections introduced by Callan et al. could be expected to dominate is on the unphysical side of the singularity. The model can be successfully applied to study the back-reaction of Hawking radiation on the geometry of large mass black holes, but the description breaks down before the evaporation is complete.

Two-loop instabilities of gauge vacua and topological symmetry breaking on R n × S 1

The general problem of symmetry breaking by nonintegrable phase factors, or Wilson loops, on a non-simply connected spacetime of the form R n × S 1 is considered. The background field method is used to compute the effective potential as a function of a constant gauge field which solves the classical field equations. We show, in a general setting, how Wilson loops may be used to reduce this problem to a vacuum energy calculation where the fields satisfy non-trivial boundary conditions. Analysis of the one-loop effective potential is inadequate in many cases to determine stability of solutions to the effective field equations. We perform an analysis of some models where the two-loop effective potential must be used. One particular example considered is N = 4 supersymmetric Yang-Mills theory. We show that the local SU(2) symmetry in this theory breaks to U(1), but that the supersymmetry is left intact.

Self-consistent cosmological perturbations from thermal field theory.

Finite-temperature field theory is used for a self-consistent and manifestly gauge-invariant derivation of the effective field equations governing the evolution of adiabatic perturbations of a homogeneous, isotropic cosmological model dominated by an ultrarelativistic plasma of weakly interacting particles in thermal equilibrium. Solutions are obtained in the form of rapidly converging power-series expansions

Stability of flat space, semiclassical gravity, and higher derivatives.

Flat space is shown to be perturbatively stable, to first order in ħ, against quantum fluctuations produced in semiclassical (or 1/N expansion) approximations to quantum gravity, despite past indications to the contrary. It is pointed out that most of the new «solutions» allowed by the semiclassical corrections do not fall within the perturbative framework, unlike the effective action and field equations which generate them.