121 research outputs found
Fermat Principle for spinning light
Mimicking the description of spinning particles in General Relativity, the
Fermat Principle is extended to spinning photons. Linearization of the
resulting Papapetrou-Souriau type equations yields the semiclassical model used
recently to derive the ``Optical Hall Effect'' (alias the ``Optical Magnus
Effect'') for polarized light.Comment: Final revised version, to appear in Phys. Rev. D (Rapid
Communication). 5 pages, no figure
Anomalous Hall Effect in non-commutative mechanics
The anomalous velocity term in the semiclassical model of a Bloch electron
deviates the trajectory from the conventional one. When the Berry curvature
(alias noncommutative parameter) is a monopole in momentum space as found
recently in some ferromagnetic semiconductors while observing the anomalous
Hall effect, we get a transverse shift, similar to that in the optical Hall
effect.Comment: 4 pages. A figure added. To be published in Phys. Lett.
Non-commutative mechanics, in mathematical & in condensed matter physics
Non-commutative structures were introduced, independently and around the same
time, in mathematical and in condensed matter physics (see Table~1). Souriau's
construction applied to the two-parameter central extension of the planar
Galilei group leads to the ``exotic'' particle, which has non-commuting
position coordinates. A Berry-phase argument applied to the Bloch electron
yields in turn a semiclassical model that has been used to explain the
anomalous/spin/optical Hall effects. The non-commutative parameter is
momentum-dependent in this case, and can take the form of a monopole in
momentum space.Comment: This is a contribution to the Proc. of the O'Raifeartaigh Symposium
on Non-Perturbative and Symmetry Methods in Field Theory (June 2006,
Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry:
Methods and Applications) at http://www.emis.de/journals/SIGMA
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