Fig. 5: Simulated skyrmion number under perturbations.
From: Skyrmions based on optical anisotropy for topological encoding
The mean skyrmion number \({N}_{{\rm{sk}}}^{{\prime} }\) (solid red line) and the standard deviation \({\sigma }_{{N}_{{\rm{sk}}}^{{\prime} }}\) (shaded region) are plotted against the standard deviation \(\sigma\) of the added noise \({\delta }_{x}\). For \(\sigma \le 0.30\pi\), \({N}_{{\rm{sk}}}^{{\prime} }\approx 1\) and \({\sigma }_{{N}_{{\rm{sk}}}^{{\prime} }}\) is negligible, confirming the predicted topological protection of the AGB skyrmion. In the range of \(0.30\pi < \sigma \le 0.40\pi\), the AGB skyrmion retains its stability, although the mean skyrmion number decreases slightly. As \(\sigma\) increases further, \({N}_{{\rm{sk}}}^{{\prime} }\) progressively decreases, whereas \({\sigma }_{{N}_{{\rm{sk}}}^{{\prime} }}\) continues to grow, indicating a loss of topological information
