Exciting the Domain Wall Soliton

Abstract

Many solitonic configurations in field theory have localized bound states in their spectrum of linear perturbations. This opens up the possibility of having long lived excitations of these solitons that could affect their dynamics. We start the study of these effects in the simplest configuration of a domain wall kink solution in the $\lambda {\varphi }^4$ theory in $1+1$ dimensions. We show that this solution has a single bound state and numerically study its slow decay rate in flat space. We then investigate the amplitude of this excitation by simulating a cosmological phase transition that leads to the formation of these kinks in an expanding universe. We find that kinks get formed with a $20\%$ excess of energy with respect to their lowest energy configuration. We also explore the kink solution interacting with a thermal bath and extract the amplitude of the localized excitation as a function of temperature. We note that this amplitude increases with temperature but again the extra energy in the kink never goes over the $20\%$ level. Finally, we argue that this extra energy may have important consequences in the subsequent evolution of defects in numerical simulations.

arXiv comment49 pages, 17 figures; typos corrected

References in corpus (12)

• Pseudo-Stable Bubbles
• Probing the gravitational wave background from cosmic strings with LISA
• New limits on cosmic strings from gravitational wave observation
• Numerical simulations of string networks in the Abelian-Higgs model
• Phase Transitions at Preheating
• Scaling from gauge and scalar radiation in Abelian Higgs string networks
• Decay of Cosmic String Loops Due to Particle Radiation
• Emergence of Oscillons in an Expanding Background
• Field theory simulation of Abelian-Higgs cosmic string cusps
• phi^4 Kinks - Gradient Flow and Dynamics
• Radiation from cosmic string standing waves
• Evolution of Topological Defects During Inflation

Cited by in corpus (11)

• Loop decay in Abelian-Higgs string networks
• Nambu-Goto Dynamics of Field Theory Cosmic String Loops
• The dynamics of Domain Wall Strings
• Spontaneous Emission from Excited Quantum Kinks
• Oscillon spectroscopy
• Wobbling kinks in a two-component scalar field theory: Interaction between shape modes
• Inclusion of radiation in the CCM approach of the ${\varphi }^4$ model
• Asymmetric scattering between kinks and wobblers
• Parametric Resonances in Axionic Cosmic Strings
• Dimensional deformation of sine-Gordon breathers into oscillons
• Internal Excitations of Global Vortices