Information-Entropic for Travelling Solitons in Lorentz and CPT Breaking Systems

TL;DR

This paper introduces a configurational entropy measure for travelling solitons in Lorentz and CPT breaking models, revealing how symmetry-breaking parameters influence energy distribution and providing a new tool to analyze such systems.

Contribution

It constructs a novel travelling configurational entropy measure for solitons in Lorentz-breaking scenarios and analyzes its implications for energy distribution and parameter selection.

Findings

TCE peaks when energy density is symmetric around the origin.

Exact solutions for double and single-kink configurations are obtained.

TCE can identify optimal symmetry-breaking parameters.

Abstract

In this work we group three research topics apparently disconnected, namely solitons, Lorentz symmetry breaking and entropy. Following a recent work [Phys. Lett. B 713 (2012) 304], we show that it is possible to construct in the context of travelling wave solutions a configurational entropy measure in functional space, from the field configurations. Thus, we investigate the existence and properties of travelling solitons in Lorentz and CPT breaking scenarios for a class of models with two interacting scalar fields. Here, we obtain a complete set of exact solutions for the model studied which display both double and single-kink configurations. In fact, such models are very important in applications that include Bloch branes, Skyrmions, Yang-Mills, Q-balls, oscillons and various superstring-motivated theories. We find that the so-called Configurational Entropy (CE) for travelling solitons, which we name as travelling Configurational Entropy (TCE), shows that the best value of parameter responsible to break the Lorentz symmetry is one where the energy density is distributed equally around the origin. In this way, the information-theoretical measure of travelling solitons in Lorentz symmetry violation scenarios opens a new window to probe situations where the parameters responsible for breaking the symmetries are random. In this case, the TCE selects the best value.