Local cohomology of logarithmic forms

Let Y be a divisor on a smooth algebraic variety X. We investigate the geometry of the Jacobian scheme of Y, homological invariants derived from logarithmic differential forms along Y, and their relationship with the property that Y is a free divisor. We consider arrangements of hyperplanes as a source of examples and counterexamples. In particular, we make a complete calculation of the local cohomology of logarithmic forms of generic hyperplane arrangements.Comment: 21 pages, minor corrections and updated bibliograph

A single ion as a shot noise limited magnetic field gradient probe

It is expected that ion trap quantum computing can be made scalable through protocols that make use of transport of ion qubits between sub-regions within the ion trap. In this scenario, any magnetic field inhomogeneity the ion experiences during the transport, may lead to dephasing and loss of fidelity. Here we demonstrate how to measure, and compensate for, magnetic field gradients inside a segmented ion trap, by transporting a single ion over variable distances. We attain a relative magnetic field sensitivity of \Delta B/B_0 ~ 5*10^{-7} over a test distance of 140 \micro m, which can be extended to the mm range, still with sub \micro m resolution. A fast experimental sequence is presented, facilitating its use as a magnetic field gradient calibration routine, and it is demonstrated that the main limitation is the quantum shot noise.Comment: 5 pages, 3 figure

Otto Hesse : Lebenslauf / in moderner Rechtschreibung neu hrsg. von Gabriele Dörflinger, Universitätsbibliothek Heidelberg

Biographie des Mathematikers Otto Hesse (1811-1874) in der 1897 von der Bayerischen Akademie der Wissenschaften herausgegebenen Werkausgabe Otto Hesses, die von Walther von Dyck (1856-1934), Sigmund Gundelfinger (1846-1910), Jakob Lüroth (1844-1910) und Max Noether (1844-1921) erarbeitet wurde. Die Originalbiographie wurde in der vor 1900 gültigen Rechtschreibung publiziert. Die Neuausgabe benutzt die aktuelle Rechtschreibung. Das in der Werkausgabe enthaltene Portrait O. Hesses ist der Biographie beigefügt

Die unzeitgemäße Zeitgenossin: Doppelrezension zu "The Subversive Simone Weil: A Life in Five Ideas" von Robert Zaretsky und "Effort and Grace: On the Spiritual Exercise of Philosophy" von Simone Kotva

Robert Zaretsky: The Subversive Simone Weil - A Life in Five Ideas. Chicago, IL: Chicago University Press 2021. 9780226549330.+++Simone Kotva: Effort and Grace - On the Spiritual Exercise of Philosophy. London/ New York: Bloomsbury Academic 2020. 978135011365

Generalized multi-photon quantum interference

Non-classical interference of photons lies at the heart of optical quantum information processing. This effect is exploited in universal quantum gates as well as in purpose-built quantum computers that solve the BosonSampling problem. Although non-classical interference is often associated with perfectly indistinguishable photons this only represents the degenerate case, hard to achieve under realistic experimental conditions. Here we exploit tunable distinguishability to reveal the full spectrum of multi-photon non-classical interference. This we investigate in theory and experiment by controlling the delay times of three photons injected into an integrated interferometric network. We derive the entire coincidence landscape and identify transition matrix immanants as ideally suited functions to describe the generalized case of input photons with arbitrary distinguishability. We introduce a compact description by utilizing a natural basis which decouples the input state from the interferometric network, thereby providing a useful tool for even larger photon numbers

Imaging the tympanic membrane oscillation ex vivo with Doppler optical coherence tomography during simulated Eustachian catarrh

Recently, optical coherence tomography (OCT) was utilized in multiple studies for structural and functional imaging of the middle ear and the tympanic membrane. Since Doppler OCT allows both, the spatially resolved measurement of the tympanic membrane oscillation and high-resolution imaging, it is regarded as a promising tool for future in vivo applications. In this study, Doppler OCT is utilized for the visualization of the tympanic membrane oscillation in temporal bones with simulated Eustachian catarrh, which was realized by generating a depression in the tympanic cavity. The transfer function, meaning the oscillation amplitude normalized to the applied sound pressure, is measured frequency resolved in the range from 0.5 kHz to 6 kHz and with a lateral spatial resolution of 0.4 mm. Typical oscillation patterns could be observed in case of ambient pressure in the tympanic cavity. Under depression the characteristic oscillation patterns were observed with widely congruent appearance but at higher frequencies