Chaotic symmetry breaking and dissipative two-field dynamics

Abstract

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.

Fine-tuning solution for hybrid inflation in dissipative chaotic dynamics

“…[27], while the full effective equations of motion in Minkowski spacetime were studied by Ramos and Navarro in Ref. [28]. In Ref.…”

“…In Ref. [28] the general form expected for the equations of motion for the fields, for potentials of the form of Eq. (2.1), was derived and a detailed account for the dissipative terms appearing in those equations was given.…”

“…The usual form expected for the coupled effective equations of motion for φ and σ are complicated non-local equations of motion with typical non-Markovian dissipative kernels. In [28] we have shown that at high temperature and in the large N χ , N ψ limit for the (thermal) bath fields we can find an approximate Markovian limit for the kernels, from which we can express the equations of motion for the fields in terms of dissipative local equations. In Ref.…”

“…[21] show that we can evade the assumption of an initial high temperature thermal bath as used in Ref. [28] to derive the local equations of motion for the fields and makes it, therefore, more appropriate to the application we intend for here, which is the study of the initial conditions problem for the onset of inflation in hybrid inflation models characterized by potentials like Eq. (2.1).…”

“…In fact the magnitude of the dissipation terms may be controlled by these couplings, as shown in Refs. [15,21,28].…”