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Hamiltonian Postdoc Workshop: Magnetic Confinement from a Dynamical Perspective November 12, 2018 (02:05 PM PST - 03:00 PM PST)
Parent Program: --
Location: MSRI: Simons Auditorium
Speaker(s) Gabriel Martins (University of California, Santa Cruz)
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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.

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