Muon stopping sites in magnetic systems from density functional theory

This thesis concerns the use of density functional theory (DFT) to determine muon stopping sites in crystalline solids. New tools for carrying out these calculations are introduced and these techniques are demonstrated through the results of calculations on the skyrmion-hosting semiconductors GaV$_4$S$_8$ and GaV$_4$S$_8$ and the heavy-fermion metals URu$_2$Si$_2$ and CeRu$_2$Si$_2$. The results of three studies on significantly different magnetic systems are presented, where in each case the interpretation of the results of muon-spin spectroscopy ($\mu^+$SR) experiments is aided by knowledge of the muon site. The results of $\mu^+$SR measurements on the iron-pnictide compound FeCrAs are presented and indicate a magnetically ordered phase throughout the material below $T_\mathrm{N}$ =105(5) K. There are signs of fluctuating magnetism in a narrow range of temperatures above $T_\mathrm{N}$ involving low-energy excitations, while at temperatures well below $T_\mathrm{N}$ a characteristic freezing of dynamics is observed. Using DFT, a distinct muon stopping site is proposed for this system. The results of transverse-field (TF) $\mu^{+}$SR measurements on the molecular spin ladder compound (Hpip)$_{2}$CuBr$_4$, [Hpip=(C$_{5}$H$_{12}$N)] are reported. Characteristic behaviour in each of the regions of the phase diagram is identified in the TF $\mu^+$SR spectra. Analysis of the muon stopping sites, calculated using DFT, suggests that the muon plus its local distortion can lead to a local probe unit with good sensitivity to the magnetic state. Finally, the results of $\mu^+$SR measurements on the charge density wave system 1T-TaS$_2$ are presented, which show three distinct phases versus temperature. The critical exponents for each of these phases are compared with the predictions of quantum spin liquid models. Using DFT, a quantum delocalised state for the muon between the TaS$_2$ layers is proposed, which is used in conjunction with its associated hyperfine interactions to determine the coupling of the muon to the diffusing spinons

Unitarity-based Methods for Muon-Electron Scattering in Quantum Electrodynamics

In this thesis we elaborate on the modern techniques for the evaluation of Scattering Amplitudes in Quantum Field Theory, and apply them to the calculation of at one loop in Quantum Electrodynamics, within the Dimensional Regularization scheme. The corresponding Feynman diagrams contribute to the so called real-virtual term of the Next-to-Next-to-Leading-Order corrections to scattering. Their calculation is crucial for a novel estimation of the leading Hadronic corrections to the muon’s anomalous magnetic moment, which is the goal of the MUonE experiment, recently proposed at CERN. First, we review the theoretical background behind the contributions to the muon’s magnetic moment and the connection with scattering. Then, we elaborate on the algorithimic steps required by the evaluation of multi-loop Feynman amplitudes, from the form-factor decomposition, to the reduction onto a basis of Master Integrals, and, finally, to the calculation of the latter by means of the Differential Equations method. We outline the modern frameworks based on Unitarity of the S-matrix, which employ amplitude cuts to construct a decomposition onto Master Integrals in the Generalised Unitarity framework. This includes Integrand-level Decomposition methods which take advantage of the polynomial properties of Feynman amplitude integrands and offer a higher level of automation for the calculation of complex amplitudes. Specifically we detail the more recent Adaptive Integrand Decomposition and its automated code implementation AIDA used to carry out the calculations presented. We illustrate the Momentum Twistor parametrisation for particle kinematics used by AIDA, and introduce four and five-point twistor parametrisations suitable for our goals. We present our results on the Master Integral decompositions of and at one-loop, both considering massive and massless electrons, and finally we review the evaluation of the Master Integrals for in the limit with Differential Equations.ope

GSI Scientific Report 2009 [GSI Report 2010-1]

Displacement design response spectrum is an essential component for the currently-developing displacement-based seismic design and assessment procedures. This paper proposes a new and simple method for constructing displacement design response spectra on soft soil sites. The method takes into account modifications of the seismic waves by the soil layers, giving due considerations to factors such as the level of bedrock shaking, material non-linearity, seismic impedance contrast at the interface between soil and bedrock, and plasticity of the soil layers. The model is particularly suited to applications in regions with a paucity of recorded strong ground motion data, from which empirical models cannot be reliably developed

Growth and characterisation of uranium nanostructures

Uranium is the only element in the periodic table to exhibit a charge-density wave and superconductivity at ambient pressure. The competition between these effects in technologically important high-temperature superconducting systems has come under increasing scrutiny, and uranium offers a model system in which to study the CDW. However, the element is difficult to grow in single-crystals in the bulk. We describe the growth by magnetron sputtering and characterisation of single-crystal epitaxial thin- films of alpha-uranium in the (110) orientation on the Nb(110)/A-plane sapphire buffer layer/substrate system. We use X-ray scattering methods to determine the influence of the thickness of the component layers of the samples on the microstructure, and find that there is a non-trivial dependence of the microstructural state of the uranium layers on both the thickness of the uranium layers themselves and the thickness of the niobium buffer layers upon which they are grown. In particular, the widths of the uranium peaks decrease when the uranium layer thickness is increased, but increase when the buffer layer thickness is increased. An extensive review of the methods for characterisation of thin- film microstructures using X-ray diffraction is given, and several widely used models and interpretations are critically discussed, in particular those given in the many instances in which two-component line shapes are seen in transverse scans from thin- films. We also use X-ray diffraction from high-intensity synchrotron sources to characterise the charge-density wave state in these samples, and discuss the effect of uranium-layer thickness on its characteristics as a function of temperature. Important differences between the CDW seen in bulk uranium and in thin- films are seen and discussed in terms of the microstructure of the films. In particular, no incommensurate{commensurate transition is seen in the films, and a large intensity asymmetry is seen between the 2+2+1± and 2+2-1± CDW satellites. Furthermore, the correlation-length of the CDW is limited in the plane of the film, and dependent on the thickness of the uranium layers

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