Nonhermitian transport effects in coupled-resonator optical waveguides

Coupled-resonator optical waveguides (CROWs) are known to have interesting and useful dispersion properties. Here, we study the transport in these waveguides in the general case where each resonator is open and asymmetric, i.e., is leaky and possesses no mirror-reflection symmetry. Each individual resonator then exhibits asymmetric backscattering between clockwise and counterclockwise propagating waves, which in combination with the losses induces non-orthogonal eigenmodes. In a chain of such resonators, the coupling between the resonators induces an additional source of non-hermiticity, and a complex band structure arises. We show that in this situation the group velocity of wave packets differs from the velocity associated with the probability density flux, with the difference arising from a non-hermitian correction to the Hellmann-Feynman theorem. Exploring these features numerically in a realistic scenario, we find that the complex band structure comprises almost-real branches and complex branches, which are joined by exceptional points, i.e., nonhermitian degeneracies at which not only the frequencies and decay rates coalesce but also the eigenmodes themselves. The non-hermitian corrections to the group velocity are largest in the regions around the exceptional points.Comment: 11 pages, 9 figure

Integration of Car-2-Car Communication as a Virtual Sensor in Automotive Sensor Fusion for Advanced Driver Assistance Systems

Advanced driver assistance systems (ADAS) require a comprehensive and accurate situation model. Often in-vehicle sensors do not provide sufficient quality and quantity of information to fulfill the demanding requirements. Car-2-Car communication can be seen as an adaptive sensor that provides additional information regularly but also on demand. Due to the fact that Car-2-Car communication strongly depends on the penetration rate, we argue for a seamless integration of Car-2-Car communication as an additional sensor in automotive sensor fusion. With increasing penetration rate the sensor fusion will significantly benefit and eventually unfold its full potential. Due to the fundamentally different measuring principles of in-vehicle sensors and information provided by Car-2-Car communication, redundancy and complementarity can be leveraged to a great extent, thus, increasing accuracy, reliability and robustness of the situation assessment. In addition to a detailed description of the fusion algorithm this paper outlines DLR’s system architecture for ADAS and an enhanced ACC as an application example to show the potential of our approach

The conformal current algebra on supergroups with applications to the spectrum and integrability

We compute the algebra of left and right currents for a principal chiral model with arbitrary Wess-Zumino term on supergroups with zero Killing form. We define primary fields for the current algebra that match the affine primaries at the Wess-Zumino-Witten points. The Maurer-Cartan equation together with current conservation tightly constrain the current-current and current-primary operator product expansions. The Hilbert space of the theory is generated by acting with the currents on primary fields. We compute the conformal dimensions of a subset of these states in the large radius limit. The current algebra is shown to be consistent with the quantum integrability of these models to several orders in perturbation theory.Comment: 45 pages. Minor correction

Massless particles on supergroups and AdS3 x S3 supergravity

Firstly, we study the state space of a massless particle on a supergroup with a reparameterization invariant action. After gauge fixing the reparameterization invariance, we compute the physical state space through the BRST cohomology and show that the quadratic Casimir Hamiltonian becomes diagonalizable in cohomology. We illustrate the general mechanism in detail in the example of a supergroup target GL(1|1). The space of physical states remains an indecomposable infinite dimensional representation of the space-time supersymmetry algebra. Secondly, we show how the full string BRST cohomology in the particle limit of string theory on AdS3 x S3 renders the quadratic Casimir diagonalizable, and reduces the Hilbert space to finite dimensional representations of the space-time supersymmetry algebra (after analytic continuation). Our analysis provides an efficient way to calculate the Kaluza-Klein spectrum for supergravity on AdS3 x S3. It may also be a step towards the identification of an interesting and simpler subsector of logarithmic supergroup conformal field theories, relevant to string theory.Comment: 16 pages, 10 figure

A pseudointegrable Andreev billiard

A circular Andreev billiard in a uniform magnetic field is studied. It is demonstrated that the classical dynamics is pseudointegrable in the same sense as for rational polygonal billiards. The relation to a specific polygon, the asymmetric barrier billiard, is discussed. Numerical evidence is presented indicating that the Poincare map is typically weak mixing on the invariant sets. This link between these different classes of dynamical systems throws some light on the proximity effect in chaotic Andreev billiards.Comment: 5 pages, 5 figures, to appear in PR

Topological Cigar and the c=1 String : Open and Closed

We clarify some aspects of the map between the c=1 string theory at self-dual radius and the topologically twisted cigar at level one. We map the ZZ and FZZT D-branes in the c=1 string theory at self dual radius to the localized and extended branes in the topological theory on the cigar. We show that the open string spectrum on the branes in the two theories are in correspondence with each other, and their two point correlators are equal. We also find a representation of an extended N=2 algebra on the worldsheet which incorporates higher spin currents in terms of asymptotic variables on the cigar.Comment: 37 pages, 2 figures, corrections to section 3.1, references adde

Open strings in Lie groups and associative products

Firstly, we generalize a semi-classical limit of open strings on D-branes in group manifolds. The limit gives rise to rigid open strings, whose dynamics can efficiently be described in terms of a matrix algebra. Alternatively, the dynamics is coded in group theory coefficients whose properties are translated in a diagrammatical language. In the case of compact groups, it is a simplified version of rational boundary conformal field theories, while for non-compact groups, the construction gives rise to new associative products. Secondly, we argue that the intuitive formalism that we provide for the semi-classical limit, extends to the case of quantum groups. The associative product we construct in this way is directly related to the boundary vertex operator algebra of open strings on symmetry preserving branes in WZW models, and generalizations thereof, e.g. to non-compact groups. We treat the groups SU(2) and SL(2,R) explicitly. We also discuss the precise relation of the semi-classical open string dynamics to Berezin quantization and to star product theory.Comment: 47 pages, 14 figure

Towards Highly Automated Driving: Intermediate report on the HAVEit-Joint System

International audienceThis overview article describes the goals, concepts and very preliminary results of the subproject Joint System within the EU-project HAVEit. The goal of HAVEit is to develop and investigate vehicle automation beyond ADAS systems, especially highly automated driving, where the automation is doing a high percentage of the driving, while the driver is still meaningfully involved in the driving task. In HAVEit, an overarching architecture and several prototypes will be built up over time by manufacturers and suppliers. As a trail blazer, a Joint System prototype is under development by an interdisciplinary team of several European research institutes in order to investigate and demonstrate the basic principles of highly automated driving, which will then be gradually applied to vehicles closer to serial production. Starting with sensor data fusion, the Co-System part of the Joint Systems plans manoeuvres and trajectories, which are then used to control active interfaces and, taking into account the results of an online driver assessment, joined with the actions of the driver. While many aspects of this research undertaking are still under investigation, the concept, a first prototype and first results from a simulator evaluation will be sketched