The positivity conjecture for constrictions

A constriction (B0,A0)(B_0,A_0) is called positive when a punctured vertical neighborhood of it lies entirely in the interior of a phase-lock area. Consider constrictions in the first quadrant

(B,A)R0×R+.(B,A)\in\mathbb R_{\geq0}\times\mathbb R_+.

For the corresponding transition matrix QQ, let bb and cc be the two triangular terms referred to in the source.

The positivity conjecture. Every constriction is positive.

The paper proves that the relevant ratio is real and gives a criterion implying positivity when c/b>0c/b>0, but the universal positivity assertion is not resolved in the supplied text.

Sources & referencesView supporting material

Primary source

Alexey Glutsyuk, “On constrictions of phase-lock areas in model of overdamped Josephson effect and transition matrix of double confluent Heun equation”, arXiv:1805.02624 (2018).

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