Novel simulation methods for Coulomb and hydrodynamic interactions

This thesis presents new methods to simulate systems with hydrodynamic and electrostatic interactions. Part 1 is devoted to computer simulations of Brownian particles with hydrodynamic interactions. The main influence of the solvent on the dynamics of Brownian particles is that it mediates hydrodynamic interactions. In the method, this is simulated by numerical solution of the Navier--Stokes equation on a lattice. To this end, the Lattice--Boltzmann method is used, namely its D3Q19 version. This model is capable to simulate compressible flow. It gives us the advantage to treat dense systems, in particular away from thermal equilibrium. The Lattice--Boltzmann equation is coupled to the particles via a friction force. In addition to this force, acting on {it point} particles, we construct another coupling force, which comes from the pressure tensor. The coupling is purely local, i.~e. the algorithm scales linearly with the total number of particles. In order to be able to map the physical properties of the Lattice--Boltzmann fluid onto a Molecular Dynamics (MD) fluid, the case of an almost incompressible flow is considered. The Fluctuation--Dissipation theorem for the hybrid coupling is analyzed, and a geometric interpretation of the friction coefficient in terms of a Stokes radius is given. Part 2 is devoted to the simulation of charged particles. We present a novel method for obtaining Coulomb interactions as the potential of mean force between charges which are dynamically coupled to a local electromagnetic field. This algorithm scales linearly, too. We focus on the Molecular Dynamics version of the method and show that it is intimately related to the Car--Parrinello approach, while being equivalent to solving Maxwell's equations with freely adjustable speed of light. The Lagrangian formulation of the coupled particles--fields system is derived. The quasi--Hamiltonian dynamics of the system is studied in great detail. For implementation on the computer, the equations of motion are discretized with respect to both space and time. The discretization of the electromagnetic fields on a lattice, as well as the interpolation of the particle charges on the lattice is given. The algorithm is as local as possible: Only nearest neighbors sites of the lattice are interacting with a charged particle. Unphysical self--energies arise as a result of the lattice interpolation of charges, and are corrected by a subtraction scheme based on the exact lattice Green's function. The method allows easy parallelization using standard domain decomposition. Some benchmarking results of the algorithm are presented and discussed.

108 Sn studied with intermediate-energy Coulomb excitation

In dieser Arbeit wurde der instabile, Neutronenarme Kern 108Sn mit Hilfe der Coulomb-Anregung bei intermediaeren Energien in inverser Kinematik studiert. Diese Methode wurde bisher zur Untersuchung der ersten angeregten 2+ Zustaende und deren E2 Zerfallsraten in Kernen mit Kernladungszahl Z< 30 angewendet. 108Sn ist somit der Kern mit der groeßten Kernladungszahl, bei dem diese Studien bisher stattfanden. Das Ziel dieses Experiments war die Messung der unbekannten reduzierten Uebergangswahrscheinlichkeit B(E2,0+ -> 2+). Der B(E2)-Wert von 0.230(57) e2b2 wurde relativ zu dem bekannten Wert des Isotops 112Sn bestimmt. Das Experiment wurde an der GSI Darmstadt mit Hilfe des RISING Detektors und des Fragmentseperators (FRS) durchgefuehrt. Sekundaere Strahlen (108Sn, 112Sn) mit einer Energie von ca. 150 MeV pro Nukleon wurden auf ein 386 mg/cm2 dickes 197Au Target geschossen. Die Projektilfragmente wurden mit Hilfe des Fragmentseparators selektiert und identifiziert. Zur Selektion des Reaktionskanals und zur Bestimmung des Winkels der gestreuten Fragmente wurde das Teilchenteleskop CATE, das sich hinter dem Target befand, verwendet. Gammastrahlung, die in Koinzidenz mit den Projektilrestkernen emittiert wurde, wurde in den Germanium-Cluster Detektoren des RISING Detektors nachgewiesen. Der gemessene B(E2,0+ -> 2+)-Wert von 108Sn ist in Uebereinstimmung mit neueren Schalenmodellrechnungen, die auf realistischen effektiven Wechselwirkungen basieren und im Rahmen eines verallgemeinerten Seniorit¨ats-Schemas erklaert werden.

A novel functional renormalization group framework for gauge theories and gravity

In this thesis we develop further the functional renormalization group (RG) approach to quantum field theory (QFT) based on the effective average action (EAA) and on the exact flow equation that it satisfies. The EAA is a generalization of the standard effective action that interpolates smoothly between the bare action for krightarrowinfty and the standard effective action rnfor krightarrow0. In this way, the problem of performing the functional integral is converted into the problem of integrating the exact flow of the EAA from the UV to the IR. The EAA formalism deals naturally with several different aspects of a QFT. One aspect is related to the discovery of non-Gaussian fixed points of the RG flow that can be used to construct continuum limits. In particular, the EAA framework is a useful setting to search for Asymptotically Safe theories, i.e. theories valid up to arbitrarily high energies. A second aspect in which the EAA reveals its usefulness are non-perturbative calculations. In fact, the exact flow that it satisfies is a valuable starting point for devising new approximation schemes. In the first part of this thesis we review and extend the formalism, in particular we derive the exact RG flow equation for the EAA and the related hierarchy of coupled flow equations for the proper-vertices. We show how standard perturbation theory emerges as a particular way to iteratively solve the flow equation, if the starting point is the bare action. Next, we explore both technical and conceptual issues by means of three different applications of the formalism, to QED, to general non-linear sigma models (NLsigmaM) and to matter fields on curved spacetimes. In the main part of this thesis we construct the EAA for non-abelian gauge theories and for quantum Einstein gravity (QEG), using the background field method to implement the coarse-graining procedure in a gauge invariant way. We propose a new truncation scheme where the EAA is expanded in powers of the curvature or field strength. Crucial to the practical use of this expansion is the development of new techniques to manage functional traces such as the algorithm proposed in this thesis. This allows to project the flow of all terms in the EAA which are analytic in the fields. As an application we show how the low energy effective action for quantum gravity emerges as the result of integrating the RG flow. In any treatment of theories with local symmetries that introduces a reference scale, the question of preserving gauge invariance along the flow emerges as predominant. In the EAA framework this problem is dealt with the use of the background field formalism. This comes at the cost of enlarging the theory space where the EAA lives to the space of functionals of both fluctuation and background fields. In this thesis, we study how the identities dictated by the symmetries are modified by the introduction of the cutoff and we study so called bimetric truncations of the EAA that contain both fluctuation and background couplings. In particular, we confirm the existence of a non-Gaussian fixed point for QEG, that is at the heart of the Asymptotic Safety scenario in quantum gravity; in the enlarged bimetric theory space where the running of the cosmological constant and of Newton's constant is influenced by fluctuation couplings.

Measurement of the ZZ production cross section and limits to the anomalous triple gauge couplings with forward electrons with the ATLAS detector

Measurements of the self coupling between bosons are important to test the electroweak sector of the Standard Model (SM). The production of pairs of Z bosons through the s-channel is forbidden in the SM. The presence of physics, beyond the SM, could lead to a deviation of the expected production cross section of pairs of Z bosons due to the so called anomalous Triple Gauge Couplings (aTGC). Proton-proton data collisions at the Large Hadron Collider (LHC) recorded by the ATLAS detector at a center of mass energy of 8 TeV were analyzed corresponding to an integrated luminosity of 20.3 fb-1. Pairs of Z bosons decaying into two electron-positron pairs are searched for in the data sample. The effect of the inclusion of detector regions corresponding to high values of the pseudorapidity was studied to enlarge the phase space available for the measurement of the ZZ production. The number of ZZ candidates was determined and the ZZ production cross section was measured to be: rn7.3±1.0(Stat.)±0.4(Sys.)±0.2(lumi.)pb, which is consistent with the SM expectation value of 7.2±0.3pb. Limits on the aTGCs were derived using the observed yield, which are twice as stringent as previous limits obtained by ATLAS at a center of mass energy of 7 TeV.