# Field Theory Simulations for Kinks

#### Kink Soliton excitations

The following movies correspond to some of the simulations performed for the paper:

- “
**Exciting the Domain Wall Soliton**” (Jose J. Blanco-Pillado, Daniel Jiménez-Aguilar, Jon Urrestilla, e-Print: arXiv:2006.13255 [hep-th]).

**Evolution of an excited kink**

In the following video we show the evolution of a kink initially excited with a bound state of amplitude A(t=0)=0.6 . The four figures represent:

- The field scalar field evolution of a kink in an excited state.
- The perturbation of the field around the kink solution.
- The radiation field produced from this excited state.
- The evolution of the instantaneous amplitude of the bound state as a function of time.

We use absorbing boundary conditions throughout this simulation. (See the paper for further details).

**Large amplitude excitation**

In this video we show the evolution of a large amplitude perturbation on a kink solution. The amplitude is large enough (A(t=0)=1.5) for the system to eject a couple of kinks to infinity leaving behind an excited anti-kink solution.

** Formation of excited kinks in a phase transition**

In this video we show the formation of a collection of kinks and anti-kinks in a phase transition from a thermal initial condition. The evolution is performed in a (1+1) de Sitter spacetime with 1/H = 25, where the units of length are determined by the thickness of the kink. Note that the transition also leads to the formation of oscillon configurations.

We show in the following video a zoom in the region to the far right of the previous simulation where a kink is formed. We also show the amplitude of the excitation in this case as a function of time.

**A kink in a thermal bath**

In this movie we show the evolution of a kink in de Sitter space from an initial condition of the excited soliton heated at temperature Theta= 0.01 (This dimensionless constant describes the ratio between the temperature of the thermal bath and the typical energy of the kink solution) . We also show the field distribution of the perturbation and the evolution of the amplitude of the excitation.

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