The Simplest Oscillon and its Sphaleron

TL;DR

This paper explores oscillons in a 1D scalar field theory with a cubic potential, linking them to sphalerons, and develops approximations for different amplitude regimes.

Contribution

It introduces a novel connection between oscillons and sphalerons in a simple scalar field model, providing explicit approximations for various amplitudes.

Findings

Small-amplitude oscillon approximated using asymptotic expansion

Larger amplitudes modeled with sphaleron deformation modes

Explicit construction of oscillon solutions in the given theory

Abstract

Oscillons in a simple, 1-dimensional scalar field theory with a cubic potential are discussed. The theory has a classical sphaleron, whose decay generates a version of the oscillon. A good approximation to the small-amplitude oscillon is constructed explicitly using the asymptotic expansion of Fodor et al., but for larger amplitudes a better approximation uses the discrete, unstable and stable deformation modes of the sphaleron.