6 problems

Solenoid-limit conjecture. In some well-defined limit, largely independent of the details of the approximating potentials, the limiting situation should be described by a singular…

Aharonov–Bohm Hardy conjecture. If $\beta\notin\mathbb{Z}$, then there exists a constant $\lambda(p)>\left(\frac{2-p}{p}\right)^p$ such that

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…

Atomic many-body Hamiltonians are operators describing systems of several interacting electrons in the field of a nucleus with a specified charge. A spectral transition is an abrup…

In a time-dependent non-Abelian gauge field configuration, let the Aharonov–Bohm phase be evaluated using the non-Abelian field strengths over a contour's associated surface, with…

Let a domain be equipped with its Laplacian, and consider spectral partitions of the domain. Allow a number of Aharonov–Bohm flux lines, with both their number and positions subjec…