The Stability of Noncommutative Scalar Solitons

TL;DR

This paper analyzes the stability of noncommutative scalar solitons, revealing a relationship between stability and potential parameters at critical noncommutativity, with implications for understanding soliton behavior.

Contribution

It establishes stability conditions for radially symmetric noncommutative scalar solitons and links stability to the potential's cubic term at critical noncommutativity.

Findings

Level-1 solutions have nearly-vanishing eigenvalues at critical $ heta m^2$

Stability depends on the $^3$ coefficient in the potential

Higher-level solutions exhibit ambiguities in finite $ heta$ extrapolation

Abstract

We determine the stability conditions for a radially symmetric noncommutative scalar soliton at finite noncommutivity parameter $\theta$. We find an intriguing relationship between the stability and existence conditions for all level-1 solutions, in that they all have nearly-vanishing stability eigenvalues at critical $\theta m^2$. The stability or non-stability of the system may then be determined entirely by the $\phi^3$ coefficient in the potential. For higher-level solutions we find an ambiguity in extrapolating solutions to finite $\theta$ which prevents us from making any general statements. For these stability may be determined by comparing the fluctuation eigenvalues to critical values which we calculate.