111,988 research outputs found
On a Conjecture of Givental
These brief notes record our puzzles and findings surrounding Givental's
recent conjecture which expresses higher genus Gromov-Witten invariants in
terms of the genus-0 data. We limit our considerations to the case of a
projective line, whose Gromov-Witten invariants are well-known and easy to
compute. We make some simple checks supporting his conjecture.Comment: 13 pages, no figures; v.2: new title, minor change
Wave packet transmission of Bloch electron manipulated by magnetic field
We study the phenomenon of wave packet revivals of Bloch electrons and
explore how to control them by a magnetic field for quantum information
transfer. It is showed that the single electron system can be modulated into a
linear dispersion regime by the "quantized" flux and then an electronic wave
packet with the components localized in this regime can be transferred without
spreading. This feature can be utilized to perform the high-fidelity transfer
of quantum information encoded in the polarization of the spin. Beyond the
linear approximation, the re-localization and self-interference occur as the
novel phenomena of quantum coherence.Comment: 6 pages, 5 figures, new content adde
Open string instantons and relative stable morphisms
We show how topological open string theory amplitudes can be computed by
using relative stable morphisms in the algebraic category. We achieve our goal
by explicitly working through an example which has been previously considered
by Ooguri and Vafa from the point of view of physics. By using the method of
virtual localization, we successfully reproduce their results for multiple
covers of a holomorphic disc, whose boundary lies in a Lagrangian submanifold
of a Calabi-Yau 3-fold, by Riemann surfaces with arbitrary genera and number of
boundary components. In particular we show that in the case we consider there
are no open string instantons with more than one boundary component ending on
the Lagrangian submanifold.Comment: This is the version published by Geometry & Topology Monographs on 22
April 200
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