Energy levels, radiative rates and electron impact excitation rates for transitions in C III

We report energy levels, radiative rates (A-values) and lifetimes for the astrophysically important Be-like ion C III. For the calculations, 166 levels belonging to the n ≤ 5 configurations are considered and the GRASP (General-purpose Relativistic Atomic Structure Package) is adopted. Einstein A-coefficients are provided for all E1, E2, M1 and M2 transitions, while lifetimes are compared with available measurements as well as theoretical results, and no large discrepancies noted. Our energy levels are assessed to be accurate to better than 1 per cent for a majority of levels, and A-values to better than 20 per cent for most transitions. Collision strengths are also calculated, for which the Dirac Atomic R-matrix Code (DARC) is used. A wide energy range, up to 21 Ryd, is considered and resonances resolved in a fine energy mesh in the thresholds region. The collision strengths are subsequently averaged over a Maxwellian velocity distribution to determine effective collision strengths up to a temperature of 8.0 ×10[5]K, sufficient for most astrophysical applications. Our data are compared with the recent R-matrix calculations of Fernández-Menchero et al., and significant differences (up to over an order of magnitude) are noted for several transitions over the complete temperature range of the results.

Electron impact excitation of Be-like ions: a comparison of DARC and ICFT results

Emission lines of Be-like ions are frequently observed in astrophysical plasmas, and many are useful for density and temperature diagnostics. However, accurate atomic data for energy levels, radiative rates (A-values) and effective electron excitation collision strengths ($\Upsilon$) are required for reliable plasma modelling. In general it is reasonably straightforward to calculate energy levels and A- values to a high level of accuracy. By contrast, considerable effort is required to calculate $\Upsilon$, and hence it is not always possible to assess the accuracy of available data. Recently, two independent calculations (adopting the $R$-matrix method) but with different approaches (DARC and ICFT) have appeared for a range of Be-like ions. Therefore, in this work we compare the two sets of $\Upsilon$, highlight the large discrepancies for a significant number of transitions and suggest possible reasons for these.

Photoionization of Co+ and electron-impact excitation of Co2 + using the Dirac R-matrix method

Modelling of massive stars and supernovae (SNe) plays a crucial role in understanding galaxies. From this modelling we can derive fundamental constraints on stellar evolution, mass-loss processes, mixing, and the products of nucleosynthesis. Proper account must be taken of all important processes that populate and depopulate the levels (collisional excitation, de-excitation, ionization, recombination, photoionization, bound–bound processes). For the analysis of Type Ia SNe and core collapse SNe (Types Ib, Ic and II) Fe group elements are particularly important. Unfortunately little data is currently available and most noticeably absent are the photoionization cross-sections for the Fe-peaks which have high abundances in SNe. Important interactions for both photoionization and electron-impact excitation are calculated using the relativistic Dirac atomic R-matrix codes (DARC) for low-ionization stages of Cobalt. All results are calculated up to photon energies of 45 eV and electron energies up to 20 eV. The wavefunction representation of Co III has been generated using GRASP0 by including the dominant 3d⁷, 3d⁶[4s, 4p], 3p⁴3d⁹ and 3p⁶3d⁹ configurations, resulting in 292 fine structure levels. Electron-impact collision strengths and Maxwellian averaged effective collision strengths across a wide range of astrophysically relevant temperatures are computed for Co III. In addition, statistically weighted level-resolved ground and metastable photoionization cross-sections are presented for Co II and compared directly with existing work.

Atom Lithography

We review the two kinds of forces that near-resonant light exerts on atoms the spontaneous force that is used for laser cooling, and the stimulated force that is used for coherent manipulation of atoms. We will discuss an experiment where laser cooling is used to collimate an atomic beam of sodium atoms, and the stimulated force within one period of a one-dimensional standing wave is used as a lens to focus the atoms to a narrow line about 20 nm wide. This kind of atom lithography is an example of the general field of atom optics in which light is used to manipulate atoms.

Topics in gravitational-wave science : macroscopic quantum mechanics and black hole physics

The theories of relativity and quantum mechanics, the two most important physics discoveries of the 20th century, not only revolutionized our understanding of the nature of space-time and the way matter exists and interacts, but also became the building blocks of what we currently know as modern physics. My thesis studies both subjects in great depths --- this intersection takes place in gravitational-wave physics.

Gravitational waves are "ripples of space-time", long predicted by general relativity. Although indirect evidence of gravitational waves has been discovered from observations of binary pulsars, direct detection of these waves is still actively being pursued. An international array of laser interferometer gravitational-wave detectors has been constructed in the past decade, and a first generation of these detectors has taken several years of data without a discovery. At this moment, these detectors are being upgraded into second-generation configurations, which will have ten times better sensitivity. Kilogram-scale test masses of these detectors, highly isolated from the environment, are probed continuously by photons. The sensitivity of such a quantum measurement can often be limited by the Heisenberg Uncertainty Principle, and during such a measurement, the test masses can be viewed as evolving through a sequence of nearly pure quantum states.

The first part of this thesis (Chapter 2) concerns how to minimize the adverse effect of thermal fluctuations on the sensitivity of advanced gravitational detectors, thereby making them closer to being quantum-limited. My colleagues and I present a detailed analysis of coating thermal noise in advanced gravitational-wave detectors, which is the dominant noise source of Advanced LIGO in the middle of the detection frequency band. We identified the two elastic loss angles, clarified the different components of the coating Brownian noise, and obtained their cross spectral densities.

The second part of this thesis (Chapters 3-7) concerns formulating experimental concepts and analyzing experimental results that demonstrate the quantum mechanical behavior of macroscopic objects - as well as developing theoretical tools for analyzing quantum measurement processes. In Chapter 3, we study the open quantum dynamics of optomechanical experiments in which a single photon strongly influences the quantum state of a mechanical object. We also explain how to engineer the mechanical oscillator's quantum state by modifying the single photon's wave function.

In Chapters 4-5, we build theoretical tools for analyzing the so-called "non-Markovian" quantum measurement processes. Chapter 4 establishes a mathematical formalism that describes the evolution of a quantum system (the plant), which is coupled to a non-Markovian bath (i.e., one with a memory) while at the same time being under continuous quantum measurement (by the probe field). This aims at providing a general framework for analyzing a large class of non-Markovian measurement processes. Chapter 5 develops a way of characterizing the non-Markovianity of a bath (i.e.,whether and to what extent the bath remembers information about the plant) by perturbing the plant and watching for changes in the its subsequent evolution. Chapter 6 re-analyzes a recent measurement of a mechanical oscillator's zero-point fluctuations, revealing nontrivial correlation between the measurement device's sensing noise and the quantum rack-action noise.

Chapter 7 describes a model in which gravity is classical and matter motions are quantized, elaborating how the quantum motions of matter are affected by the fact that gravity is classical. It offers an experimentally plausible way to test this model (hence the nature of gravity) by measuring the center-of-mass motion of a macroscopic object.

The most promising gravitational waves for direct detection are those emitted from highly energetic astrophysical processes, sometimes involving black holes - a type of object predicted by general relativity whose properties depend highly on the strong-field regime of the theory. Although black holes have been inferred to exist at centers of galaxies and in certain so-called X-ray binary objects, detecting gravitational waves emitted by systems containing black holes will offer a much more direct way of observing black holes, providing unprecedented details of space-time geometry in the black-holes' strong-field region.

The third part of this thesis (Chapters 8-11) studies black-hole physics in connection with gravitational-wave detection.

Chapter 8 applies black hole perturbation theory to model the dynamics of a light compact object orbiting around a massive central Schwarzschild black hole. In this chapter, we present a Hamiltonian formalism in which the low-mass object and the metric perturbations of the background spacetime are jointly evolved. Chapter 9 uses WKB techniques to analyze oscillation modes (quasi-normal modes or QNMs) of spinning black holes. We obtain analytical approximations to the spectrum of the weakly-damped QNMs, with relative error O(1/L^2), and connect these frequencies to geometrical features of spherical photon orbits in Kerr spacetime. Chapter 11 focuses mainly on near-extremal Kerr black holes, we discuss a bifurcation in their QNM spectra for certain ranges of (l,m) (the angular quantum numbers) as a/M → 1. With tools prepared in Chapter 9 and 10, in Chapter 11 we obtain an analytical approximate for the scalar Green function in Kerr spacetime.

Tests of a Roman Pot Prototype for the TOTEM Experiment

The TOTEM collaboration has developed and tested the first prototype of its Roman Pots to be operated in the LHC. TOTEM Roman Pots contain stacks of 10 silicon detectors with strips oriented in two orthogonal directions. To measure proton scattering angles of a few microradians, the detectors will approach the beam centre to a distance of 10 sigma + 0.5 mm (= 1.3 mm). Dead space near the detector edge is minimised by using two novel "edgeless" detector technologies. The silicon detectors are used both for precise track reconstruction and for triggering. The first full-sized prototypes of both detector technologies as well as their read-out electronics have been developed, built and operated. The tests took place first in a fixed-target muon beam at CERN's SPS, and then in the proton beam-line of the SPS accelerator ring. We present the test beam results demonstrating the successful functionality of the system despite slight technical shortcomings to be improved in the near future.

Modification of the formation of high-Mach number electrostatic shock-like structures by the ion acoustic instability

The formation of unmagnetized electrostatic shock-like structures with a high Mach number is examined with one- and two-dimensional particle-in-cell (PIC) simulations. The structures are generated through the collision of two identical plasma clouds, which consist of equally hot electrons and ions with a mass ratio of 250. The Mach number of the collision speed with respect to the initial ion acoustic speed of the plasma is set to 4.6. This high Mach number delays the formation of such structures by tens of inverse ion plasma frequencies. A pair of stable shock-like structures is observed after this time in the 1D simulation, which gradually evolve into electrostatic shocks. The ion acoustic instability, which can develop in the 2D simulation but not in the 1D one, competes with the nonlinear process that gives rise to these structures. The oblique ion acoustic waves fragment their electric field. The transition layer, across which the bulk of the ions change their speed, widens and their speed change is reduced. Double layer-shock hybrid structures develop.

Temporal structure of attosecond pulses from laser-driven coherent synchrotron emission

The microscopic dynamics of laser-driven coherent synchrotron emission transmitted through thin foils are investigated using particle-in-cell simulations. For normal incidence interactions, we identify the formation of two distinct electron nanobunches from which emission takes place each half-cycle of the driving laser pulse. These emissions are separated temporally by 130 attoseconds and are dominant in different frequency ranges, which is a direct consequence of the distinct characteristics of each electron nanobunch. This may be exploited through spectral filtering to isolate these emissions, generating electromagnetic pulses of duration ~70 as.

Systematic multi-configuration calculations on structures and properties of complex atoms

Die relativistische Multikonfigurations Dirac-Fock (MCDF) Methode ist gegenwärtig eines der am häufigsten benutzten Verfahren zur Berechnung der elektronischen Struktur und der Eigenschaften freier Atome. In diesem Verfahren werden die Wellenfunktionen ausgewählter atomarer Zustände als eine Linearkombination von sogenannten Konfigurationszuständen (CSF - Configuration State Functions) konstruiert, die in einem Teilraum des N-Elektronen Hilbert-Raumes eine (Vielteilchen-)Basis aufspannen. Die konkrete Konstruktion dieser Basis entscheidet letzlich über die Güte der Wellenfunktionen, die üblicherweise mit Hilfe einer Variation des Erwartungswertes zum no-pair Dirac-Coulomb Hamiltonoperators gewonnen werden. Mit Hilfe von MCDF Wellenfunktionen können die dominanten relativistischen und Korrelationseffekte in freien Atomen allgemein recht gut erfaßt und verstanden werden. Außer der instantanen Coulombabstoßung zwischen allen Elektronenpaaren werden dabei auch die relativistischen Korrekturen zur Elektron-Elektron Wechselwirkung, d.h. die magnetischen und Retardierungsbeiträge in der Wechselwirkung der Elektronen untereinander, die Ankopplung der Elektronen an das Strahlungsfeld sowie der Einfluß eines ausgedehnten Kernmodells erfaßt. Im Vergleich mit früheren MCDF Rechnungen werden in den in dieser Arbeit diskutierten Fallstudien Wellenfunktionsentwicklungen verwendet, die um 1-2 Größenordnungen aufwendiger sind und daher systematische Untersuchungen inzwischen auch an Atomen mit offenen d- und f-Schalen erlauben. Eine spontane Emission oder Absorption von Photonen kann bei freien Atomen theoretisch am einfachsten mit Hilfe von Übergangswahrscheinlichkeiten erfaßt werden. Solche Daten werden heute in vielen Forschungsbereichen benötigt, wobei neben den traditionellen Gebieten der Fusionsforschung und Astrophysik zunehmend auch neue Forschungsrichtungen (z.B. Nanostrukturforschung und Röntgenlithographie) zunehmend ins Blickfeld rücken. Um die Zuverlässigkeit unserer theoretischen Vorhersagen zu erhöhen, wurde in dieser Arbeit insbesondere die Relaxation der gebundenen Elektronendichte, die rechentechnisch einen deutlich größeren Aufwand erfordert, detailliert untersucht. Eine Berücksichtigung dieser Relaxationseffekte führt oftmals auch zu einer deutlich besseren Übereinstimmung mit experimentellen Werten, insbesondere für dn=1 Übergänge sowie für schwache und Interkombinationslinien, die innerhalb einer Hauptschale (dn=0) vorkommen. Unsere in den vergangenen Jahren verbesserten Rechnungen zu den Wellenfunktionen und Übergangswahrscheinlichkeiten zeigen deutlich den Fortschritt bei der Behandlung komplexer Atome. Gleichzeitig kann dieses neue Herangehen künftig aber auch auf (i) kompliziertere Schalensstrukturen, (ii) die Untersuchung von Zwei-Elektronen-ein-Photon (TEOP) Übergängen sowie (iii) auf eine Reihe weiterer atomarer Eigenschaften übertragen werden, die bekanntermaßen empflindlich von der Relaxation der Elektronendichte abhängen. Dies sind bspw. Augerzerfälle, die atomare Photoionisation oder auch strahlende und dielektronische Rekombinationsprozesse, die theoretisch bisher nur selten überhaupt in der Dirac-Fock Näherung betrachtet wurden.

Resonant States in Negative Ions

Resonant states are multiply excited states in atoms and ions that have enough energy to decay by emitting an electron. The ability to emit an electron and the strong electron correlation (which is extra strong in negative ions) makes these states both interesting and challenging from a theoretical point of view. The main contribution in this thesis is a method, which combines the use of B splines and complex rotation, to solve the three-electron Schrödinger equation treating all three electrons equally. It is used to calculate doubly excited and triply excited states of 4S symmetry with even parity in He-. For the doubly excited states there are experimental and theoretical data to compare with. For the triply excited states there is only theoretical data available and only for one of the resonances. The agreement is in general good. For the triply excited state there is a significant and interesting difference in the width between our calculation and another method. A cause for this deviation is suggested. The method is also used to find a resonant state of 4S symmetry with odd parity in H2-. This state, in this extremely negative system, has been predicted by two earlier calculations but is highly controversial. Several other studies presented here focus on two-electron systems. In one, the effect of the splitting of the degenerate H(n=2) thresholds in H-, on the resonant states converging to this threshold, is studied. If a completely degenerate threshold is assumed an infinite series of states is expected to converge to the threshold. Here states of 1P symmetry and odd parity are examined, and it is found that the relativistic and radiative splitting of the threshold causes the series to end after only three resonant states. Since the independent particle model completely fails for doubly excited states, several schemes of alternative quantum numbers have been suggested. We investigate the so called DESB (Doubly Excited Symmetry Basis) quantum numbers in several calculations. For the doubly excited states of He- mentioned above we investigate one resonance and find that it cannot be assigned DESB quantum numbers unambiguously. We also investigate these quantum numbers for states of 1S even parity in He. We find two types of mixing of DESB states in the doubly excited states calculated. We also show that the amount of mixing of DESB quantum numbers can be inferred from the value of the cosine of the inter-electronic angle. In a study on Li- the calculated cosine values are used to identify doubly excited states measured in a photodetachment experiment. In particular a resonant state that violates a propensity rule is found.

Spatial network surrogates for disentangling complex system structure from spatial embedding of nodes

ACKNOWLEDGMENTS MW and RVD have been supported by the German Federal Ministry for Education and Research (BMBF) via the Young Investigators Group CoSy-CC2 (grant no. 01LN1306A). JFD thanks the Stordalen Foundation and BMBF (project GLUES) for financial support. JK acknowledges the IRTG 1740 funded by DFG and FAPESP. MT Gastner is acknowledged for providing his data on the airline, interstate, and Internet network. P Menck thankfully provided his data on the Scandinavian power grid. We thank S Willner on behalf of the entire zeean team for providing the data on the world trade network. All computations have been performed using the Python package pyunicorn [41] that is available at https://github.com/pik-copan/pyunicorn.

Evaluation of selected recurrence measures in discriminating pre-ictal and inter-ictal periods from epileptic EEG data

7 pages, 4 figures Acknowledgement We are grateful to M. Riedl and G. Ansmann for fruitful discussions and critical comments on earlier versions of the manuscript. This work was supported by the Volkswagen Foundation (Grant Nos. 88461, 88462, 88463, 85390, 85391 and 85392).

Scientific case for avoiding dangerous climate change to protect young people and nature

28 pages, 6 figures; version submitted to Proceedings of the National Academy of Sciences

Hierarchical structures in Northern Hemispheric extratropical winter ocean-atmosphere interactions

Acknowledgements MW and RVD have been supported by the German Federal Ministry for Education and Research via the BMBF Young Investigators Group CoSy-CC2 (grant 18 Marc Wiedermann et al. no. 01LN1306A). JFD thanks the Stordalen Foundation and BMBF (project GLUES) for financial support. JK acknowledges the IRTG 1740 funded by DFG and FAPESP. Coupled climate network analysis has been performed using the Python package pyunicorn (Donges et al, 2015a) that is available at https://github.com/pik-copan/pyunicorn.

Scientific case for avoiding dangerous climate change to protect young people and nature

28 pages, 6 figures; version submitted to Proceedings of the National Academy of Sciences