111,437 research outputs found
Quantization in geometric pluripotential theory
The space of K\"ahler metrics can, on the one hand, be approximated by
subspaces of algebraic metrics, while, on the other hand, can be enlarged to
finite-energy spaces arising in pluripotential theory. The latter spaces are
realized as metric completions of Finsler structures on the space of K\"ahler
metrics. The former spaces are the finite-dimensional spaces of Fubini--Study
metrics of K\"ahler quantization. The goal of this article is to draw a
connection between the two. We show that the Finsler structures on the space of
K\"ahler potentials can be quantized. More precisely, given a K\"ahler manifold
polarized by an ample line bundle we endow the space of Hermitian metrics on
powers of that line bundle with Finsler structures and show that the resulting
path length metric spaces recover the corresponding metric completions of the
Finsler structures on the space of K\"ahler potentials. This has a number of
applications, among them a new approach to the rooftop envelopes and
Pythagorean formulas of K\"ahler geometry, a new Lidskii type inequality on the
space of K\"ahler metrics, and approximation of finite energy potentials, as
well as geodesic segments by the corresponding smooth algebraic objects
Quantum Corrals, Eigenmodes and Quantum Mirages in s-wave Superconductors
We study the electronic structure of magnetic and non-magnetic quantum
corrals embedded in s-wave superconductors. We demonstrate that a quantum
mirage of an impurity bound state peak can be projected from the occupied into
the empty focus of a non-magnetic quantum corral via the excitation of the
corral's eigenmodes. We observe an enhanced coupling between magnetic
impurities inside the corral, which can be varied through oscillations in the
corral's impurity potential. Finally, we discuss the form of eigenmodes in
magnetic quantum corrals.Comment: 4 pages, 4 figure
The Poisson geometry of SU(1,1)
We study the natural Poisson structure on the Lie group SU(1,1) and related
questions. In particular, we give an explicit description of the
Ginzburg-Weinstein isomorphism for the sets of admissible elements. We also
establish an analogue of Thompson's conjecture for this group.Comment: 11 pages, minor correction
Intersecting non-SUSY -brane with chargeless 0-brane as black -brane
Unlike BPS -brane, non-supersymmetric (non-susy) -brane could be either
charged or chargeless. As envisaged in [hep-th/0503007], we construct an
intersecting non-susy -brane with chargeless non-susy -brane by taking
T-dualities along the delocalized directions of the non-susy -brane solution
delocalized in transverse directions (where ). In general
these solutions are characterized by four independent parameters. We show that
when the intersecting charged as well as chargeless non-susy -brane
with chargeless 0-brane can be mapped by a coordinate transformation to black
-brane when two of the four parameters characterizing the solution take some
special values. For definiteness we restrict our discussion to space-time
dimensions . We observe that parameters characterizing the black brane
and the related dynamics are in general in a different branch of the parameter
space from those describing the brane-antibrane annihilation process. We
demonstrate this in the two examples, namely, the non-susy D0-brane and the
intersecting non-susy D4 and D0-branes, where the solutions with the explicit
microscopic descriptions are known.Comment: 25 page
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