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 pp-brane with chargeless 0-brane as black pp-brane

Unlike BPS $p$-brane, non-supersymmetric (non-susy) $p$-brane could be either charged or chargeless. As envisaged in [hep-th/0503007], we construct an intersecting non-susy $p$-brane with chargeless non-susy $q$-brane by taking T-dualities along the delocalized directions of the non-susy $q$-brane solution delocalized in $(p-q)$ transverse directions (where $p\geq q$). In general these solutions are characterized by four independent parameters. We show that when $q=0$ the intersecting charged as well as chargeless non-susy $p$-brane with chargeless 0-brane can be mapped by a coordinate transformation to black $p$-brane when two of the four parameters characterizing the solution take some special values. For definiteness we restrict our discussion to space-time dimensions $d=10$. 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