3 problems

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Bessis–Zinn-Justin and Bender–Boettcher reality conjectures for PT-symmetric polynomial oscillators
Bessis–Zinn-Justin and Bender–Boettcher conjectures. In the first case, all eigenvalues are real and positive; in the second case, all eigenvalues are real and positive.
Conjectureopenpolynomial-potentials pt-symmetry spectral-theoryarXiv posted 2 days ago
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Non-integrability conjecture for generic polynomial potentials in the relativistic model
Non-integrability conjecture. There are no other integer solutions of the displayed relation with $\lambda_i\in {\mathscr J}_+\cup {\mathscr J}_-$ for $i=1,\ldots,k$ beyond the one…
Conjectureopenintegrability polynomial-potentials relativistic-dynamicsarXiv posted 2 days ago
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Disconnected-support conjecture for stationary densities in semi-confining polynomial potentials
Consider invariant ensembles associated with polynomial potentials $V(x)$ of arbitrary odd degree, possibly with multiple wells, in semi-confining regimes. Let $\rho$ denote a stat…
Conjectureopenpolynomial-potentials random-matrices spectral-densityarXiv posted 2 days ago

Bessis–Zinn-Justin and Bender–Boettcher reality conjectures for PT-symmetric polynomial oscillators