Thors Hans Hansson

Reconstructing Nonlinearities with Intermodulation Spectroscopy

We describe a method of analysis which allows for reconstructing the nonlinear disturbance of a high Q harmonic oscillator. When the oscillator is driven with two or more frequencies, the nonlinearity causes intermodulation of the drives, resulting in a complicated spectral response. Analysis of this spectrum allows one to approximate the nonlinearity. The method, which is generally applicable to measurements based on resonant detection, increases the information content of the measurement without requiring a large detection bandwidth, and optimally uses the enhanced sensitivity near resonance to extract information and minimize error due to detector noise.

Hadronic correlators in hot QCD

Abstract We argue that the static color-singlet correlation functions (DeTar correlators) in three-dimensional QCD at high temperature are calculable in the dimensionally reduced theory. We estimate the correlation length in these correlators by solving an analogue two-dimensional Coulomb bound state problem. In the case of hot QCD in four dimensions, the method is less rigorous, but does give results consistent with recent numerical calculations.

Pfaffian quantum Hall state made simple : Multiple vacua and domain walls on a thin torus

We analyze the Moore-Read Pfaffian state on a thin torus. The known sixfold degeneracy is realized by two inequivalent crystalline states with a four- and twofold degeneracy, respectively. The fund ...

On Polyakov's spin factors

Abstract We discuss the connection between the description of spin using Grassmann variables and that using Polyakovs spin factor. The spin factor can be interpreted as a geometrical phase and expressed as a Wilson loop with the angular velocity of Thomas precession as gauge potential. We show that the non-covariant spin factor has a sign ambiguity, and is thus not suitable for use in path integrals.

Quantum Hall physics : Hierarchies and conformal field theory techniques

The fractional quantum Hall effect, being one of the most studied phenomena in condensed matter physics during the past 30 years, has generated many ground-breaking new ideas and concepts. Very ear ...

Charge and current in the quantum Hall matrix model

The fractional quantum Hall effect (FQHE), discovered in 1982 in a two-dimensional electron system, has generated a wealth of successful theory and new concepts in condensed matter physics, but is still not fully understood. The possibility of having nonabelian quasiparticle statistics has recently attracted attention on purely theoretical grounds but also because of its potential applications in topologically protected quantum computing.This thesis focuses on the quasiparticles using three different approaches. The first is an effective Chern-Simons theory description, where the noncommutativity imposed on the classical space variables captures the incompressibility. We propose a construction of the quasielectron and illustrate how many-body quantum effects are emulated by a classical noncommutative theory.The second approach involves a study of quantum Hall states on a torus where one of the periods is taken to be almost zero. Characteristic quantum Hall properties survive in this limit in which they become very simple to understand. We illustrate this by giving a simple counting argument for degeneracy 2n-1, pertinent to nonabelian statistics, in the presence of 2n quasiholes in the Moore-Read state and generalise this result to 2n-k quasiholes and k quasielectrons.In the third approach, we study the topological nature of the degeneracy 2n-1 by using a recently proposed analogy between the Moore-Read state and the two-dimensional spin-polarized p-wave BCS state. We study a version of this problem where one can use techniques developed in the context of high-Tc superconductors to turn the vortex background into an effective gauge field in a Dirac equation. Topological arguments in the form of index theory gives the degeneracy 2n-1 for 2n vortices.

A general approach to quantum Hall hierarchies

The Abelian hierarchy of quantum Hall states accounts for most of the states in the lowest Landau level, and there is evidence of a similar hierarchy of non-Abelian states emanating from the nu = 5 ...

Quantum Hall wave functions on the torus

We present explicit expressions for a large set of hierarchy wave functions on the torus. Included are the Laughlin states, the states in the positive Jain series, and recently observed states at, ...

Microscopic theory of the quantum Hall hierarchy.

We solve the quantum Hall problem exactly in a limit and show that the ground states can be organized in a fractal pattern consistent with the Haldane-Halperin hierarchy, and with the global phase diagram. We present wave functions for a large family of states, including those of Laughlin and Jain and also for states recently observed by Pan et al., and show that they coincide with the exact ones in the solvable limit. We submit that they establish an adiabatic continuation of our exact results to the experimentally accessible regime, thus providing a unified approach to the hierarchy states.

FIELD THEORY OF ANYONS IN THE LOWEST LANDAU LEVEL

Abstract We construct a field theory for anyons in the lowest Landau level starting from the N-particle description, and discuss the connection to the full field theory of anyons defined using a statistical gauge potential. The theory is transformed to free form, with the fields defined on the circle and satisfying modified commutation relations. The Fock space of the anyons is discussed, and the theory is related to that of edge excitations of an anyon droplet in a harmonic-oscillator well.