Persistent currents in quantum rings

In this thesis, three different types of quantum rings arestudied. These are quantum rings with diamagnetic,paramagnetic or spontaneous persistent currents. It turns out that the main observable to characterizequantum rings is the Drude weight. Playing a key role inthis thesis, it will be used to distinguish betweendiamagnetic (positive Drude weight) and paramagnetic(negative Drude weight) ring currents. In most models, theDrude weight is positive. Especially in the thermodynamiclimit, it is positive semi-definite. In certain modelshowever, intuitivelysurprising, a negative Drude weight is found. This rareeffect occurs, e.g., in one-dimensional models with adegenerate ground state in conjunction with the possibilityof Umklapp scattering. One aim of this thesis is to examineone-dimensional quantum rings for the occurrence of anegative Drude weight. It is found, that the sign of theDrude weight can also be negative, if the band structurelacks particle-hole symmetry. The second aim of this thesis is the modeling of quantumrings intrinsically showing a spontaneous persistentcurrent. The construction of the model starts from theextended Hubbard model on a ring threaded by anAharonov-Bohm flux. A feedback term through which thecurrent in the ring can generate magnetic flux is added.Another extension of the Hamiltonian describes the energystored in the internally generated field. This model isevaluated using exact diagonalization and an iterativescheme to find the minima of the free energy. The quantumrings must satisfy two conditions to exhibit a spontaneousorbital magnetic moment: a negative Drude weight and aninductivity above the critical level. The magneticproperties of cyclic conjugated hydrocarbons likebenzene due to electron delocalization [magnetic anisotropy,magnetic susceptibility exaltation, nucleus-independent chemical shift (NICS)]---that have become important criteriafor aromaticity---can be examined using this model. Corrections to the presented calculations are discussed. Themost substantial simplification made in this thesis is theneglect of the Zeeman interaction of the electron spins withthe magnetic field. If a single flux tube threads a quantumring, the Zeeman interaction is zero, but in mostexperiments, this situation is difficult to realize. In themore realistic situation of a homogeneous field, the Zeemaninteraction has to be included, if the electrons have atotal spin component in the direction of the magnetic field,or if the magnetic field is strong.

Measurement of the forward-backward asymmetry of Z boson decays in electron-positron pairs with the ATLAS detector in proton-proton collisions at root out s = 7TeV at the LHC

In this thesis the measurement of the effective weak mixing angle wma in proton-proton collisions is described. The results are extracted from the forward-backward asymmetry (AFB) in electron-positron final states at the ATLAS experiment at the LHC. The AFB is defined upon the distribution of the polar angle between the incoming quark and outgoing lepton. The signal process used in this study is the reaction pp to zgamma + X to ee + X taking a total integrated luminosity of 4.8\,fb^(-1) of data into account. The data was recorded at a proton-proton center-of-mass energy of sqrt(s)=7TeV. The weak mixing angle is a central parameter of the electroweak theory of the Standard Model (SM) and relates the neutral current interactions of electromagnetism and weak force. The higher order corrections on wma are related to other SM parameters like the mass of the Higgs boson.rnrnBecause of the symmetric initial state constellation of colliding protons, there is no favoured forward or backward direction in the experimental setup. The reference axis used in the definition of the polar angle is therefore chosen with respect to the longitudinal boost of the electron-positron final state. This leads to events with low absolute rapidity have a higher chance of being assigned to the opposite direction of the reference axis. This effect called dilution is reduced when events at higher rapidities are used. It can be studied including electrons and positrons in the forward regions of the ATLAS calorimeters. Electrons and positrons are further referred to as electrons. To include the electrons from the forward region, the energy calibration for the forward calorimeters had to be redone. This calibration is performed by inter-calibrating the forward electron energy scale using pairs of a central and a forward electron and the previously derived central electron energy calibration. The uncertainty is shown to be dominated by the systematic variations.rnrnThe extraction of wma is performed using chi^2 tests, comparing the measured distribution of AFB in data to a set of template distributions with varied values of wma. The templates are built in a forward folding technique using modified generator level samples and the official fully simulated signal sample with full detector simulation and particle reconstruction and identification. The analysis is performed in two different channels: pairs of central electrons or one central and one forward electron. The results of the two channels are in good agreement and are the first measurements of wma at the Z resonance using electron final states at proton-proton collisions at sqrt(s)=7TeV. The precision of the measurement is already systematically limited mostly by the uncertainties resulting from the knowledge of the parton distribution functions (PDF) and the systematic uncertainties of the energy calibration.rnrnThe extracted results of wma are combined and yield a value of wma_comb = 0.2288 +- 0.0004 (stat.) +- 0.0009 (syst.) = 0.2288 +- 0.0010 (tot.). The measurements are compared to the results of previous measurements at the Z boson resonance. The deviation with respect to the combined result provided by the LEP and SLC experiments is up to 2.7 standard deviations.