7 problems

Cantor spectrum conjecture. In general, $\sigma(H_{\theta}^{g})$ should be a Cantor set.

Let ${\mathbf a}_1,{mathbf a}_2:= (\sqrt{3}/2, \pm1/2)$ generate the triangular lattice ${\mathbb L}_2$, and let ${\mathbb L}_6$ be the triangular sublattice defining a six-atom gr…

Let $\mathcal{E}$ be the energy of the distorted graphene model, and let $0 < \mu_c \leq \mu_c' < \infty$ be the critical parameters such that sufficiently small $\mu$ gives strict…

Let the spinless, valleyless FBI Hamiltonian be at half filling, and consider its single Slater determinant ground states without restricting to uniformly half-filled, translation-…

In a tight-binding model of graphene, consider a graphene flake with several holes as in the cited work, and adiabatically increase the magnetic flux through the holes. Partial spe…

In graphene, charge carriers move in a planar hexagonal lattice of carbon atoms, and this motion may generate an effective internal magnetic field. Quimbay and Strange's conjecture…

Non-local nonlinear correction conjecture. In graphene, there is a non-local nonlinear correction term to the massless Dirac equation which breaks Poincaré covariance.