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Light Induced Hall effect in semiconductors with spin-orbit coupling
We show that optically excited electrons by a circularly polarized light in a
semiconductor with spin-orbit coupling subject to a weak electric field will
carry a Hall current transverse to the electric field. This light induced Hall
effect is a result of quantum interference of the light and the electric field,
and can be viewed as a physical consequence of the spin current induced by the
electric field. The light induced Hall conductance is calculated for the p-type
GaAs bulk material, and the n-type and p-type quantum well structures.Comment: 5 pages, 3 figure
Lipschitz continuity of harmonic maps between Alexandrov spaces
In 1997, J. Jost [27] and F. H. Lin [39], independently proved that every
energy minimizing harmonic map from an Alexandrov space with curvature bounded
from below to an Alexandrov space with non-positive curvature is locally
H\"older continuous. In [39], F. H. Lin proposed a challenge problem: Can the
H\"older continuity be improved to Lipschitz continuity? J. Jost also asked a
similar problem about Lipschitz regularity of harmonic maps between singular
spaces (see Page 38 in [28]). The main theorem of this paper gives a complete
resolution to it.Comment: We remove the assumption in the previous version that the domain
space has nonnegative generalized Ricci curvature. This solves Lin's
conjecture completely. To appear in Invent. Mat
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