Information-Entropic Measure of Energy-Degenerate Kinks in Two-Field Models

TL;DR

This paper explores kink solutions in two-field models, demonstrating how Configurational Entropy can differentiate between energy-degenerate configurations, offering a novel information-theoretic approach to analyzing spatial complexity.

Contribution

It introduces the use of Configurational Entropy to distinguish between energy-degenerate kink solutions in two-field models, providing a new analytical tool.

Findings

CE can distinguish between degenerate kink configurations

Analytical solutions are obtained using BPS bounds

The approach offers a new perspective on spatial complexity

Abstract

We investigate the existence and properties of kink-like solitons in a class of models with two interacting scalar fields. In particular, we focus on models that display both double and single-kink solutions, treatable analytically using the Bogomol'nyi--Prasad--Sommerfield bound (BPS). Such models are of interest in applications that include Skyrmions and various superstring-motivated theories. Exploring a region of parameter space where the energy for very different spatially-bound configurations is degenerate, we show that a newly-proposed momentum-space entropic measure called Configurational Entropy (CE) can distinguish between such energy-degenerate spatial profiles. This information-theoretic measure of spatial complexity provides a complementary perspective to situations where strictly energy-based arguments are inconclusive.