Curl forces and beyond

TYPETheor./Math. Physics Seminar
Speaker:Professor Sir Michael Berry
Affiliation:Bristol University
Location:Lewiner Seminar Room (412)
Abstract:Forces depending on position but which are not derivable from a potential, that is,
forces with non-zero curl, give rise to dynamics that is not Hamiltonian or
Lagrangian, while also being non-dissipative. Noether’s theorem does not apply, so
the link between symmetries and conservation laws is broken. The physical existence
of curl forces has been controversial and the subject of intense debate among
engineers. But an example is familiar in optics: force on a dielectric particle in an
optical field. Motion under curl forces near optical vortices can be understood in
detail, and the full series of ‘superadiabatic’ correction forces derived, leading to an
exact slow manifold in which fast (internal) and slow (external) motion of the particle
is separated.