9 problems

Let $\hat{H}$ be the edge Hamiltonian for an integer quantum Hall effect (IQHE) system, and let $\Delta$ be the mobility-gap energy interval. Absolutely continuous edge-spectrum co…

Microlocal propagation conjecture. There exists $\beta<3/4$ such that, uniformly for $\varepsilon\in(0,1]$ and $t>0$,

Transit conjecture. General initial data semiclassically localized along $\mathcal{C}$ transit to the state $$ .

For an armchair-type edge with $delta\ne0$, let the splitting denote the separation between the two perturbed eigenvalue curves of $H^\delta$ near $k_{\parallel}=0$. Analytic calcu…

For each integer $n\ge 3$, let $(\alpha_1,\ldots,\alpha_n,\beta_1,\ldots,\beta_n)$ be the parameters used in the paper's construction of PPT states in $M_n\otimes M_n$, and let the…

Let $n\ge 3$. Consider the PPT states constructed in the paper, with parameters chosen suitably, having bi-rank $(n^2-1,n^2-2n+3)$ in the $n\otimes n$ system. Conjecture. With a su…

Consider an edge direction for which the no-fold condition fails. In this setting, the edge problem may exhibit long-lived resonant states rather than genuine eigenvalue edge state…

Let ${\mathscr{P}}_\delta[\zeta]:H^2[\zeta]\to L^2[\zeta]$ be the family of edge operators, with Dirac points $(\xi_\star^A,E_\star)$ and $(\xi_\star^B,E_\star)$ satisfying…

Consider the edge-state eigenvalue problem for $H^{(\varepsilon,\delta)}$ in Case (2), where $\varepsilon V_{1,1}<0$ and the small-parameter condition eref{small-eps-delta} holds.…