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In general, the two solutions can both correspond to a positive Δ, both to a negative Δ, or one to a positive and the other to a negative Δ.
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The study of the stability of the two solutions is beyond the scope of the present article. This issue has been addressed in Ref. [24].
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By further approximating n2(d) squ;n0 we get δΦsol=2arccos(j/ √gn03/m). Since n0 is a monotonically decreasing function of j, the argument of arccos increases for increasing current. Therefore, starting from π at j=0, δΦsol decreases monotonically with j.
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Close to the critical point (δΦc,jc), and for every current-phase relation, the lower branch always has a phase decreasing with increasing current, up to the critical point itself, at which it meets the upper branch. In particular, for reentrant diagrams, this means that the dispersive part of the flow always dominates over the hydrodynamic part sufficiently close to the critical point.
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