Corporate Hierarchies and the Size of Nations: Theory and Evidence

Corporate organization varies within a country and across countries with country size. The paper starts by establishing some facts about corporate organization based on unique data of 660 Austrian and German corporations. The larger country (Germany) has larger firms with flatter more decentral corporate hierarchies compared to the smaller country (Austria). Firms in the larger country change their organization less fast than firms in the smaller country. Over time firms have been introducing less hierarchical organizations by delegating power to lower levels of the corporation. We develop a theory which explains these facts and which links these features to the trade environment that countries and firms face. We introduce firms with internal hierarchies in a Krugman (1980) model of trade. We show that international trade and the toughness of competition in international markets induce a power struggle in firms which eventually leads to decentralized corporate hierarchies. We offer econometric evidence which is consistent with the models predictions

Dark-State Polaritons in Single- and Double-Λ\Lambda Media

We derive the properties of polaritons in single-$\Lambda$ and double-$\Lambda$ media using a microscopic equation-of-motion technique. In each case, the polaritonic dispersion relation and composition arise from a matrix eigenvalue problem for arbitrary control field strengths. We show that the double-$\Lambda$ medium can be used to up- or down-convert single photons while preserving quantum coherence. The existence of a dark-state polariton protects this single-photon four-wave mixing effect against incoherent decay of the excited atomic states. The efficiency of this conversion is limited mainly by the sample size and the lifetime of the metastable state.Comment: 7 pages, 6 figure

Set-based approach to passenger aircraft family design

Presented is a method for the design of passenger aircraft families. Existing point-based methods found in the literature employ sequential approaches in which a single design solution is selected early and is then iteratively modified until all requirements are satisfied. The challenge with such approaches is that the design is driven toward a solution that, although promising to the optimizer, may be infeasible due to factors not considered by the models. The proposed method generates multiple solutions at the outset. Then, the infeasible solutions are discarded gradually through constraint satisfaction and set intersection. The method has been evaluated through a notional example of a three-member aircraft family design. The conclusion is that point-based design is still seen as preferable for incremental (conventional) designs based on a wealth of validated empirical methods, whereas the proposed approach, although resource-intensive, is seen as more suited to innovative designs

Quantum Theory of a Resonant Photonic Crystal

We present a quantum model of two-level atoms localized in a 3D lattice, based on the Hopfield theory of exciton polaritons. In addition to a polaritonic gap at the exciton energy, a photonic bandgap opens up at the Brillouin zone boundary. Upon tuning the lattice period or angle of incidence to match the photonic gap with the exciton energy, one obtains a combined polaritonic and photonic gap as a generalization of Rabi splitting. For typical experimental parameters, the size of the combined gap is on the order of 25 cm^{-1}, up to 10^5 times the detuned gap size. The dispersion curve contains a branch supporting slow-light modes with vanishing exciton probability density.Comment: 4 pages, 3 figure

Weyl points and line nodes in gapless gyroid photonic crystals

Weyl points and line nodes are three-dimensional linear point- and line-degeneracies between two bands. In contrast to Dirac points, which are their two-dimensional analogues, Weyl points are stable in the momentum space and the associated surface states are predicted to be topologically non-trivial. However, Weyl points are yet to be discovered in nature. Here, we report photonic crystals, based on the double-gyroid structures, exhibiting frequency-isolated Weyl points with intricate phase diagrams. The surface states associated with the non-zero Chern numbers are demonstrated. Line nodes are also found in similar geometries; the associated surface states are shown to be flat bands. Our results are readily experimentally realizable at both microwave and optical frequencies.Comment: 6 figures and 8 pages including the supplementary informatio

Non-Abelian Generalizations of the Hofstadter model: Spin-orbit-coupled Butterfly Pairs

The Hofstadter model, well-known for its fractal butterfly spectrum, describes two-dimensional electrons under a perpendicular magnetic field, which gives rise to the integer quantum hall effect. Inspired by the real-space building blocks of non-Abelian gauge fields from a recent experiment [Science, 365, 1021 (2019)], we introduce and theoretically study two non-Abelian generalizations of the Hofstadter model. Each model describes two pairs of Hofstadter butterflies that are spin-orbit coupled. In contrast to the original Hofstadter model that can be equivalently studied in the Landau and symmetric gauges, the corresponding non-Abelian generalizations exhibit distinct spectra due to the non-commutativity of the gauge fields. We derive the genuine (necessary and sufficient) non-Abelian condition for the two models from the commutativity of their arbitrary loop operators. At zero energy, the models are gapless and host Weyl and Dirac points protected by internal and crystalline symmetries. Double (8-fold), triple (12-fold), and quadrupole (16-fold) Dirac points also emerge, especially under equal hopping phases of the non-Abelian potentials. At other fillings, the gapped phases of the models give rise to $\mathbb{Z}_2$ topological insulators. We conclude by discussing possible schemes for the experimental realizations of the models in photonic platforms

Reflection nebulae in the Galactic Center: the case for soft X-ray imaging polarimetry

The origin of irradiation and fluorescence of the 6.4 keV bright giant molecular clouds surrounding Sgr A*, the central supermassive black hole of our Galaxy, remains enigmatic. Testing the theory of a past active period of Sgr A* requires X-ray polarimetry. In this paper, we show how modern imaging polarimeters could revolutionize our understanding of the Galactic Center. Through Monte Carlo modeling, we produce a 4-8 keV polarization map of the Galactic Center, focusing on the polarimetric signature produced by Sgr B1, Sgr B2, G0.11-0.11, Bridge E, Bridge D, Bridge B2, MC2, MC1, Sgr C3, Sgr C2, and Sgr C1. We estimate the resulting polarization, include polarized flux dilution by the diffuse plasma emission detected toward the GC, and simulate the polarization map that modern polarimetric detectors would obtain assuming the performances of a mission prototype. The eleven reflection nebulae investigated in this paper present a variety of polarization signatures, ranging from nearly unpolarized to highly polarized (about 77%) fluxes. A major improvement in our simulation is the addition of a diffuse, unpolarized plasma emission that strongly impacts soft X-ray polarized fluxes. The dilution factor is in the range 50% - 70%, making the observation of the Bridge structure unlikely even in the context of modern polarimetry. The best targets are the Sgr B and Sgr C complexes, and the G0.11-0.11 cloud. An exploratory observation of a few hundred kilo-seconds of the Sgr B complex would allow a significant detection of the polarization and be sufficient to derive hints on the primary source of radiation. A more ambitious program (few Ms) of mapping the giant molecular clouds could then be carried out to probe with great precision the turbulent history of Sgr A*, and place important constraints on the composition and three-dimensional position of the surrounding gas.Comment: 7 pages, 3 figures, 2 tables, accepted for publication in A&