3 problems

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Finite-gap conjecture for a second supersymmetric partner potential
Let $a$ be an integer, and consider the periodic potential $[(a-1)a,2,(a-2)(a-1),2]$ . A potential is finite-gap if it has only finitely many spectral band gaps. Finite-gap conjectu…
Conjectureopenband-gaps periodic-potentials supersymmetric-quantum-mechanicsarXiv posted 2 days ago
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Band-edge correspondence for a PT-invariant Lamé potential
Let $a$ be an integer, and consider the associated Lamé potentials denoted by $[a(a+1),a(a+1),a(a+1),(a-1)a]$ and the Lamé potential $[2a(2a+1),0,0,0]$ . Their band edges are the sp…
Conjectureopenband-gaps periodic-potentials spectral-theoryarXiv posted 2 days ago
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High-symmetry optimality conjecture for three-dimensional photonic-crystal band gaps
A three-dimensional photonic crystal is a periodic structure whose electromagnetic spectrum may contain an omnidirectional band gap, meaning a frequency interval with no propagatin…
Conjectureopenband-gaps photonic-crystals topology-optimizationarXiv posted 2 days ago

Finite-gap conjecture for a second supersymmetric partner potential