Abstract
We study collisions between nearly planar domain walls including the effects of small initial nonplanar fluctuations. These perturbations represent the small fluctuations that must exist in a quantum treatment of the problem. In a previous paper, we demonstrated that at the linear level a subset of these fluctuations experience parametric amplification as a result of their coupling to the planar symmetric background. Here we study the full three-dimensional nonlinear dynamics using lattice simulations, including both the early time regime when the fluctuations are well described by linear perturbation theory as well as the subsequent stage of fully nonlinear evolution. We find that the nonplanar fluctuations have a dramatic effect on the overall evolution of the system. Specifically, once these fluctuations begin to interact nonlinearly the split into a planar symmetric part of the field and the nonplanar fluctuations loses its utility. At this point the colliding domain walls dissolve, with the endpoint of this being the creation of a population of oscillons in the collision region. The original (nearly) planar symmetry has been completely destroyed at this point and an accurate study of the system requires the full three-dimensional simulation.
Highlights
The case of interacting parallel planar walls in this class of theories has been considered by many authors, usually under the assumption that the nonlinear dynamics can be treated as exactly planar reducing the system to a single spatial dimension
As anticipated in [1] we find that accounting for these fluctuations can drastically change the collision dynamics between the walls, in the process completely invalidating the original assumption of planar symmetry
In every case involving the dynamics of a wall-antiwall pair, we find that the stage of nonlinear interactions leads to a complete breakdown of the original planar symmetry
Summary
We present the results for the full three-dimensional nonlinear field dynamics. The first slice is parallel to the collision axis, providing a view of the effective one-dimensional dynamics at early times, the production of outgoing radiation, and the rippling of the walls as the transverse fluctuations are amplified. To study the spectral content of the transverse fluctuations we include pseudocolor plots of the two-dimensional angle averaged power spectrum of ρ for the transverse wavenumbers k⊥ as a function of position along the collision axis. Our discrete Fourier transform convention is ρ2kd⊥(x ) = i e−ik⊥,n·x⊥,iρ(x⊥,i, x ) with x⊥ = (y, z) the coordinates in the directions orthogonal to the collision axis This gives us a very clear view of the spatial localization (along x ) of the amplified fluctuations as well as their typical transverse wavenumber. Details and illustrations that clarify this picture are presented below
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