Figure 8. Validation of the quantization rule equation (4). Shown are the relations between wavenumber k and magnetic flux α, for (a) the period-4 scar in figure 6(a), and (b) the period-3 scar in figure 6(c). The orange up-triangles indicate scars with a counterclockwise flow, and the blue down-triangles are those with a clockwise flow. The gray squares mark the scars whose flow orientations cannot be identified, which typically occur close to the cross points of the two orientation cases. The solid lines are theoretical predictions of equation (4). Vertical lines indicate the position of α = π/2. The step in the variation of α is 0.01. Adapted from [569] with permission.
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