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.

Investigation of a superthermal ultracold neutron source based on a solid deuterium converter for the TRIGA Mainz reactor

Research in fundamental physics with the free neutron is one of the key tools for testing the Standard Model at low energies. Most prominent goals in this field are the search for a neutron electric dipole moment (EDM) and the measurement of the neutron lifetime. Significant improvements of the experimental performance using ultracold neutrons (UCN) require reduction of both systematic and statistical errors.rnThe development and construction of new UCN sources based on the superthermal concept is therefore an important step for the success of future fundamental physics with ultracold neutrons. rnSignificant enhancement of today available UCN densities strongly correlates with an efficient use of an UCN converter material. The UCN converter here is to be understood as a medium which reduces the velocity of cold neutrons (CN, velocity of about 600 m/s) to the velocity of UCN (velocity of about 6 m/s).rnSeveral big research centers around the world are presently planning or constructing new superthermal UCN sources, which are mainly based on the use of either solid deuterium or superfluid helium as UCN converter.rnThanks to the idea of Yu.Pokotilovsky, there exists the opportunity to build competitive UCN sources also at small research reactors of the TRIGA type. Of course these smaller facilities don't promise high UCN densities of several 1000 UCN/cm³, but they are able to provide densities around 100 UCN/cm³ for experiments.rnIn the context of this thesis, it was possible to demonstrate succesfully the feasibility of a superthermal UCN source at the tangential beamport C of the research reactor TRIGA Mainz. Based on a prototype for the future UCN source at the Forschungs-Neutronenquelle Heinz Maier-Leibnitz (FRMII) in munich, which was planned and built in collaboration with the Technical University of Munich, further investigations and improvements were done and are presented in this thesis. rnIn parallel, a second UCN source for the radial beamport D was designed and built. The comissioning of this new source is foreseen in spring 2010.rnAt beamport D with its higher thermal neutron flux, it should be possible to increase the available UCN densities of 4 UCN/cm³ by minimum one order of magnitude.