Seminar
| Parent Program: | -- |
|---|---|
| Location: | SLMath: Eisenbud Auditorium |
We study the dynamics of charged particles in the interior of a compact
manifold M under the influence of a magnetic field. We consider a class of fields which
diverge to infinity at the boundary and are controlled by a 1-form σ defined on ∂M.
We show that in this case particles can only escape the region through the zero locus
of σ. When the 1-form is nowhere vanishing we conclude that charged particles become
confined to the interior for all time. We describe a topological characterization of such
manifolds and discuss various examples such as bounded regions in the plane, different
examples of solid tori in 3-space, tubular neighborhoods of loops, principal circle bundles
over manifolds with boundary and log-symplectic manifolds. If time permits we discuss
relations to the quantum mechanics of these systems and quantum tunneling phenomena.