2,568 research outputs found
Wall crossing for symplectic vortices and quantum cohomology
We derive a wall crossing formula for the symplectic vortex invariants of
toric manifolds. As an application, we give a proof of Batyrev's formula for
the quantum cohomology of a monotone toric manifold with minimal Chern number
at least two.Comment: 45 pages, no figures, some typos remove
Floer homology and the heat flow
We study the heat flow in the loop space of a closed Riemannian manifold
as an adiabatic limit of the Floer equations in the cotangent bundle. Our main
application is a proof that the Floer homology of the cotangent bundle, for the
Hamiltonian function kinetic plus potential energy, is naturally isomorphic to
the homology of the loop space.Comment: 83 pages, 1 figure. We introduce a class of abstract perturbations in
order to achieve transversality. The argument carries over to this clas
Transmission phase of a quantum dot and statistical fluctuations of partial-width amplitudes
Experimentally, the phase of the amplitude for electron transmission through
a quantum dot (transmission phase) shows the same pattern between consecutive
resonances. Such universal behavior, found for long sequences of resonances, is
caused by correlations of the signs of the partial-width amplitudes of the
resonances. We investigate the stability of these correlations in terms of a
statistical model. For a classically chaotic dot, the resonance eigenfunctions
are assumed to be Gaussian distributed. Under this hypothesis, statistical
fluctuations are found to reduce the tendency towards universal phase
evolution. Long sequences of resonances with universal behavior only persist in
the semiclassical limit of very large electron numbers in the dot and for
specific energy intervals. Numerical calculations qualitatively agree with the
statistical model but quantitatively are closer to universality.Comment: 8 pages, 4 figure
- …