Aharonov–Bohm Effect in Resonances for Scattering by Three Solenoids at Large Separation

Mathematical study of scattering resonances

“…The introduction of randomness should be a beginning of a new development in the subject. We also do not discuss the important case of resonances for magnetic Schrödinger operators and refer to Alexandrova-Tamura [4], Bony-Bruneau-Raikov, [26] and Tamura [258,259] for 6 Small prizes are offered by the author for the first proofs of the conjectures within five years of the publication of this survey: a dinner in a restaurant for an even numbered conjecture and in a restaurant, for an odd numbered one.…”

“…The introduction of randomness should be a beginning of a new development in the subject. We also do not discuss the important case of resonances for magnetic Schrödinger operators and refer to Alexandrova-Tamura [AT14], Bony-Bruneau-Raikov, [BBR14] and Tamura [Ta15] for some recent results and pointers to the literature. We do not address issues around threshold resonances (see Jensen-Nenciu [JN01] and references given there) and their importance in dispersive estimates (see the survey by Schlag [Sc07]) and for non-linear equations (for an example of a linearly counterintuitive phenomenon, see [HZ09,Figure 6]).…”

The wave trace and resonances of the magnetic Hamiltonian with singular vector potentials

“…Our result generalizes the existence part of their result to arbitrary number of solenoids. The resonances generated by three and four solenoids with large separations were also studied by Tamura in [Tam17].…”