Neutron matter, neutron pairing, and neutron drops based on chiral effective field theory interactions

The physics of neutron-rich systems is of great interest in nuclear and astrophysics. Precise knowledge of the properties of neutron-rich nuclei is crucial for understanding the synthesis of heavy elements. Infinite neutron matter determines properties of neutron stars, a final stage of heavy stars after a core-collapse supernova. It also provides a unique theoretical laboratory for nuclear forces. Strong interactions are determined by quantum chromodynamics (QCD). However, QCD is non-perturbative at low energies and one presently cannot directly calculate nuclear forces from it. Chiral effective field theory circumvents these problems and connects the symmetries of QCD to nuclear interactions. It naturally and systematically includes many-nucleon forces and gives access to uncertainty estimates. We use chiral interactions throughout all calculation in this thesis. Neutron stars are very extreme objects. The densities in their interior greatly exceed those in nuclei. The exact composition and properties of neutron stars is still unclear but they consist mainly of neutrons. One can explore neutron stars theoretically with calculations of neutron matter. In the inner core of neutron stars exist very high densities and thus maybe exotic phases of matter. To investigate whether there exists a phase transition to such phases even at moderate densities we study the chiral condensate in neutron matter, the order parameter of chiral symmetry breaking, and find no evidence for a phase transition at nuclear densities. We also calculate the more extreme system of spin-polarised neutron matter. With this we address the question whether there exists such a polarised phase in neutron stars and also provide a benchmark system for lattice QCD. We find spin-polarised neutron matter to be an almost non-interacting Fermi gas. To understand the cooling of neutron stars neutron pairing is of great importance. Due to the high densities especially triplet pairing is of interest. We calculate the pairing gaps in neutron matter and provide uncertainty estimates. The formation of heavy elements in the early universe proceeds through the rapid neutron-capture process. This process requires precise knowledge of the properties of very neutron-rich nuclei, which are unstable and at present not accessible in experiments. Thus, one can explore their properties only with theoretical calculations. Currently the only approach to the properties of all nuclei are energy-density functionals (EDFs). All EDFs used today are based on phenomenological models and fits to stable nuclei, which makes their predictive power for unknown (neutron-rich) nuclei unclear. Deriving an ab initio EDF directly from the nuclear forces is an important goal of nuclear theory. A promising approach is the optimised effective potential (OEP) method. We take a step into that direction and calculate neutron drops within the OEP formalism. In addition to the exact-exchange approximation we study for the first time the effect of second-order contributions and compare to quantum Monte Carlo and other results

Many-Body Perturbation Theory Approach to Raman Spectroscopy and Its Application to 2D Materials

Raman spectroscopy has become one of the most important techniques for the characterization of materials, as it allows the simultaneous probing of several properties, such as electronic and vibrational excitations, at once. This versatility, however, makes its theoretical description very challenging and, up to now, no fully satisfactory and general way for the calculation of Raman spectra from first principles exists. In this thesis, we aim to fill this gap and present a coherent theory of Raman scattering within the framework of many-body perturbation theory. We develop a novel and general, correlation function-based approach for the calculation of Raman scattering rates that can potentially also be applied to ultra-fast Raman spectroscopy out of equilibrium. Besides these theoretical developments, we present concrete computational recipes for the calculation of Raman intensities that allow the inclusion of both excitonic effects and non-adiabatic effects of lattice vibrations. The latter has so far not been possible with state-of-the-art methods, which can only take into account one of the two effects. As a first test case, we apply our theory to graphene, for which we use it to study the laser frequency and Fermi energy dependence of the Raman G-peak intensity. The flexibility of our approach also allows us to demonstrate that non-resonant processes and quantum mechanical interference effects play a significant role in Raman scattering. This applies not only to graphene but also to other two-dimensional materials of current interest, such as MoTe2 and MoS2. In addition to the development of a consistent and comprehensive description of Raman scattering, we derive a novel approach for the calculation of phonon frequencies and the screened electron-phonon coupling. It can be applied also to strongly correlated systems, for which the currently used methods are not entirely satisfactory or insufficient. Our new method goes beyond the limitations of the methods currently in use and will permit the computation of phonon-related quantities also in systems with strong correlation effects such as Kohn anomalies (e.g., graphene) or Peierls instabilities. Lastly, we present work on the application of (magneto-)Raman spectroscopy as a probe for many-body effects in graphene. Here we focus on the description of the phenomenon of magneto-phonon resonances and how it can be used to probe electronic excitation energies and to extract electron and phonon lifetimes.Raman-Spektroskopie ist zu einer der bedeutendsten Methoden zur Materialcharakterisierung geworden, da sie die gleichzeitige Untersuchung von mehreren Eigenschaften, wie z. B. elektronische Anregungen und Gitterschwingungen, erlaubt. Diese Vielseitigkeit macht ihre theoretische Beschreibung jedoch sehr herausfordernd, sodass bis heute kein allgemeiner ab initio Zugang existiert. Mit dieser Arbeit versuchen wir diese Lücke zu schließen und stellen eine kohärente Theorie der Raman-Streuung im Rahmen der Vielteilchenstörungstheorie vor. Wir entwickeln einen neuartigen Zugang für die Berechnung von Raman-Streuraten, der potenziell auch auf ultra-schnelle Raman-Streuung außerhalb des Gleichgewichts angewandt werden kann. Neben dieser theoretischen Arbeit präsentieren wir auch konkrete Ausdrücke für die computergestützte Berechnung von Raman-Intensitäten, die es erlauben, sowohl exzitonische Effekte als auch dynamisch behandelte Gitterschwingungen in die Rechnung miteinzubeziehen. Die gleichzeitige Berücksichtigung letzterer Aspekte ist mit bisherigen Methoden nicht möglich gewesen. Als ersten Test wenden wir unsere Theorie auf Graphen an und untersuchen die Abhängigkeit der Intensität der Raman G-Linie von der Laser- und Fermi-Energie. Unser flexibler Zugang erlaubt es uns außerdem zu zeigen, dass nicht-resonante Prozesse und Quanteninterferenzeffekte eine wesentliche Rolle im Raman-Streuprozess spielen. Dies trifft auch auf andere zweidimensionale Materialien zu, wie z. B. MoTe2 und MoS2, die im Fokus der aktuellen Forschung stehen. Zusätzlich zur Entwicklung einer umfassenden Beschreibung der Raman-Streuung leiten wir einen neuartigen Ansatz zur Berechnung von Phononenfrequenzen und der abgeschirmten Elektron-Phonon-Kopplung her. Dieser kann auch auf stark korrelierte Systeme angewandt werden, für die die bis- lang benutzten Methoden nicht zufrieden stellend sind. Unsere neue Methode erlaubt es, die Einschränkungen aktueller Methoden zu überwinden, auch in Systemen mit starken Korrelationseffekten wie z. B. Kohn-Anomalien (wie z. B. in Graphen) oder Peierls-Instabilitäten. Zum Abschluss untersuchen wir Vielteicheneffekte in Graphen mittels (Magneto-)Raman-Spektroskopie. Hierbei liegt der Schwerpunkt auf Magneto-Phonon-Resonanzen und wie diese dazu genutzt werden können, um elektronische Anregungsenergien und die Lebenszeiten von Elektronen und Phononen zu untersuchen

Quantum criticality and non-equilibrium dynamics in correlated electron systems

In this thesis, several cases of non-equilibrium phenomena and quantum phase transitions in strongly correlated electron systems are analyzed. The unconventional critical behavior near magnetic quantum phase transitions in various heavy-fermion metals has triggered proposals on the breakdown of the Kondo effect at the critical point. In part I, we investigate, within one specific scenario, the fate of such a zero-temperature transition upon coupling of the electronic to lattice degrees of freedom. We study a Kondo-Heisenberg model with volume-dependent Kondo coupling � this model displays both Kondo volume collapse and Kondo-breakdown transitions. Within a large-N treatment, we find that the Kondo breakdown transition remains of second order except for very soft lattices. Finally, we relate our findings to current heavy-fermion experiments. Using non-equilibrium Green�s functions, we derive transport equations for the degrees of freedom participating in the quantum critical region of the Kondo breakdown transition. We discuss conditions under which the transport of electrical charge is described by the independent motion of conduction electrons and auxiliary bosons. Under these conditions, we derive a semiclassical transport equation for the bosons and quantitatively discuss the electrical conductivity of the whole system. Motivated by pressure experiments on FeAs-122 superconductors, in part II we propose a scenario based on local-moment physics to explain salient features at the magnetic phase boundary of CaFe2As2. In this scenario, the low-pressure magnetic phase derives from Fe moments, which become screened in the paramagnetic high-pressure phase. The quantum phase transition can be described as an orbital-selective Mott transition, which is rendered first order by coupling to the lattice. These ideas are illustrated by a suitable mean-field analysis of an Anderson lattice model. An analytical description of non-equilibrium phenomena in interacting quantum systems is rarely possible. In part III we present one example where such a description can be achieved, namely the ferromagnetic Kondo model. In equilibrium, this model is tractable via perturbative renormalization-group techniques. We employ a recently developed extension of the flow-equation method to calculate the non-equilibrium decay of the local magnetization at zero temperature. The flow equations admit analytical solutions which become exact at short and long times, in the latter case revealing that the system always retains a memory of its initial state. Finally, in part IV we analyze the Nernst effect resulting from normal state quasiparticles in the cuprates in presence of various types of translational symmetry breaking. In the electron-doped cuprates, the Nernst signal resulting from a reconstruction of the Fermi surface due to spin density wave order is discussed. An order parameter consistent with the reconstruction of the Fermi surface detected in electron-doped materials is shown to sharply enhance the Nernst signal close to optimal doping. Within a semiclassical treatment, the obtained magnitude and position of the enhanced Nernst signal agrees with Nernst measurements in electron-doped cuprates. In the hole-doped cuprates, we discuss relations between the normal-state Nernst effect and stripe order. We find that Fermi pockets caused by translational symmetry breaking lead to a strongly enhanced Nernst signal with a sign depending on the modulation period of the ordered state and other details of the Fermi surface. This implies differences between antiferromagnetic and charge-only stripes. We compare our findings with recent data from La1.6−xNd0.4SrxCuO4 and YBa2Cu3Oy

Influence of Phonons on Semiconductor Quantum Emission

A microscopic theory of interacting charge carriers, lattice vibrations, and light modes in semiconductor systems is presented. The theory is applied to study quantum dots and phonon-assisted luminescence in bulk semiconductors and hetero structures

Space programs summary no. 37-49, volume 3 for the period December 1, 1967 to January 30, 1968. Supporting research and advanced development

Space program research projects on systems analysis and engineering, telecommunications, guidance and control, propulsion, and data system

The Fifteenth Marcel Grossmann Meeting

The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity

The Fifteenth Marcel Grossmann Meeting

The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described