Nonlinear focusing of Terahertz laser beam using layered superconductor

We theoretically study the propagation of a Terahertz (THz) Gaussian beam through a thin sample of layered superconductor. We consider the beam axis and the superconducting layers to be perpendicular to the sample interface, while the electric field in the beam is perpendicular to the layers. We show that, in such a geometry, the Josephson current between the superconducting layers supports lensing of the beam instead of divergence on the Rayleigh range. Moreover, due to the nonlinearity, the focal length and waist of the transmitted beam depend on the incident beam intensity. These dependences demonstrate nontrivial hysteresis behavior that can be observed in experiments with THz lasers

Hamiltonian 2-forms in Kahler geometry, III Extremal metrics and stability

This paper concerns the explicit construction of extremal Kaehler metrics on total spaces of projective bundles, which have been studied in many places. We present a unified approach, motivated by the theory of hamiltonian 2-forms (as introduced and studied in previous papers in the series) but this paper is largely independent of that theory. We obtain a characterization, on a large family of projective bundles, of those `admissible' Kaehler classes (i.e., the ones compatible with the bundle structure in a way we make precise) which contain an extremal Kaehler metric. In many cases, such as on geometrically ruled surfaces, every Kaehler class is admissible. In particular, our results complete the classification of extremal Kaehler metrics on geometrically ruled surfaces, answering several long-standing questions. We also find that our characterization agrees with a notion of K-stability for admissible Kaehler classes. Our examples and nonexistence results therefore provide a fertile testing ground for the rapidly developing theory of stability for projective varieties, and we discuss some of the ramifications. In particular we obtain examples of projective varieties which are destabilized by a non-algebraic degeneration.Comment: 40 pages, sequel to math.DG/0401320 and math.DG/0202280, but largely self-contained; partially replaces and extends math.DG/050151

Modeling Framework for Integrated, Model-based Development of Product-Service Systems

Product-service systems (PSS) are seen as the 21st-century solution for direct delivery of value to customers under the requirements of high availability, quality, and reduced risks. With mutual benefits for customers, manufacturers, service providers and often the environment, PSS represent a promising approach to sustainable development. This paper addresses the integrated development of product-service systems consisting of physical products/systems and services and proposes an integrated modeling framework that utilizes the Systems Modeling Language. A use case from Lenze, a German automation company, demonstrates the applicability of the integrated modeling framework in practice

K\"ahlerian Twistor Spinors

On a K\"ahler spin manifold K\"ahlerian twistor spinors are a natural analogue of twistor spinors on Riemannian spin manifolds. They are defined as sections in the kernel of a first order differential operator adapted to the K\"ahler structure, called K\"ahlerian twistor (Penrose) operator. We study K\"ahlerian twistor spinors and give a complete description of compact K\"ahler manifolds of constant scalar curvature admitting such spinors. As in the Riemannian case, the existence of K\"ahlerian twistor spinors is related to the lower bound of the spectrum of the Dirac operator.Comment: shorter version; to appear in Math.

Toric G_2 and Spin(7) holonomy spaces from gravitational instantons and other examples

Non-compact G_2 holonomy metrics that arise from a T^2 bundle over a hyper-Kahler space are discussed. These are one parameter deformations of the metrics studied by Gibbons, Lu, Pope and Stelle in hep-th/0108191. Seven-dimensional spaces with G_2 holonomy fibered over the Taub-Nut and the Eguchi-Hanson gravitational instantons are found, together with other examples. By considering the Apostolov-Salamon theorem math.DG/0303197, we construct a new example that, still being a T^2 bundle over hyper-Kahler, represents a non trivial two parameter deformation of the metrics studied in hep-th/0108191. We then review the Spin(7) metrics arising from a T^3 bundle over a hyper-Kahler and we find two parameter deformation of such spaces as well. We show that if the hyper-Kahler base satisfies certain properties, a non trivial three parameter deformations is also possible. The relation between these spaces with the half-flat structures and almost G_2 holonomy spaces is briefly discussed.Comment: 27 pages. Typos corrected. Accepted for publication in Commun.Math.Phy

Memory functions and Correlations in Additive Binary Markov Chains

A theory of additive Markov chains with long-range memory, proposed earlier in Phys. Rev. E 68, 06117 (2003), is developed and used to describe statistical properties of long-range correlated systems. The convenient characteristics of such systems, a memory function, and its relation to the correlation properties of the systems are examined. Various methods for finding the memory function via the correlation function are proposed. The inverse problem (calculation of the correlation function by means of the prescribed memory function) is also solved. This is demonstrated for the analytically solvable model of the system with a step-wise memory function.Comment: 11 pages, 5 figure

Stable bundles on hypercomplex surfaces

A hypercomplex manifold is a manifold equipped with three complex structures I, J, K satisfying the quaternionic relations. Let M be a 4-dimensional compact smooth manifold equipped with a hypercomplex structure, and E be a vector bundle on M. We show that the moduli space of anti-self-dual connections on E is also hypercomplex, and admits a strong HKT metric. We also study manifolds with (4,4)-supersymmetry, that is, Riemannian manifolds equipped with a pair of strong HKT-structures that have opposite torsion. In the language of Hitchin's and Gualtieri's generalized complex geometry, (4,4)-manifolds are called ``generalized hyperkaehler manifolds''. We show that the moduli space of anti-self-dual connections on M is a (4,4)-manifold if M is equipped with a (4,4)-structure.Comment: 17 pages. Version 3.0: reference adde

Symmetries of supergravity black holes

We investigate Killing tensors for various black hole solutions of supergravity theories. Rotating black holes of an ungauged theory, toroidally compactified heterotic supergravity, with NUT parameters and two U(1) gauge fields are constructed. If both charges are set equal, then the solutions simplify, and then there are concise expressions for rank-2 conformal Killing-Stackel tensors. These are induced by rank-2 Killing-Stackel tensors of a conformally related metric that possesses a separability structure. We directly verify the separation of the Hamilton-Jacobi equation on this conformally related metric, and of the null Hamilton-Jacobi and massless Klein-Gordon equations on the "physical" metric. Similar results are found for more general solutions; we mainly focus on those with certain charge combinations equal in gauged supergravity, but also consider some other solutions.Comment: 36 pages; v2: minor changes; v3: slightly shorte

M-theory moduli spaces and torsion-free structures

Motivated by the description of $\mathcal{N}=1$ M-theory compactifications to four-dimensions given by Exceptional Generalized Geometry, we propose a way to geometrize the M-theory fluxes by appropriately relating the compactification space to a higher-dimensional manifold equipped with a torsion-free structure. As a non-trivial example of this proposal, we construct a bijection from the set of $Spin(7)$-structures on an eight-dimensional $S^{1}$-bundle to the set of $G_{2}$-structures on the base space, fully characterizing the $G_{2}$-torsion clases when the total space is equipped with a torsion-free $Spin(7)$-structure. Finally, we elaborate on how the higher-dimensional manifold and its moduli space of torsion-free structures can be used to obtain information about the moduli space of M-theory compactifications.Comment: 24 pages. Typos fixed. Minor clarifications adde