Recent de Haas-van Alphen (dHvA) experiments on high-Tc compounds have been interpreted using Lifshitz-Kosevich (LK) theory, which ignores many-body effects. However in quasi-2d systems, interactions plus Landau level quantization give strong singularities in the self-energy $\Sigma$ and the thermodynamic potential $\Omega$. These are rapidly suppressed as one increases the c-axis tunneling amplitude $t_\perp$ and/or impurity scattering. We show that 2d-3d crossover and interaction effects should show up in these experiments, and that they can lead to strong deviations from LK behaviour. Moreover, dHvA experiments in quasi-2d systems should clearly distinguish between Fermi liquid and non-Fermi liquid states, for sufficiently weak impurity scattering.

We present calculations of de Haas van Alphen (dHvA) oscillations for strongly interacting systems, for (1) systems near a quantum phase transition (QPT); and/or (2) 2D and quasi-2D systems. The standard Lifshitz- Kosevich (LK) results are then inapplicable. Near a QPT, the electronic interaction scale goes to zero, giving strong corrections to LK. In 2D, LK breaks down entirely in the presence of interactions. Recently, dHvA oscillations in high Tc systems have been measured, but their form does not yet rule out non-Fermi liquid behaviour. We calculate the expected magnetization response assuming various Fermi reconstruction scenarios. The response depends crucially on the inter-plane couplings, and we find deviations from LK if the reconstruction is interaction- driven.

In classical hydrodynamics, a Magnus force exists between a vortex and the hosting fluid acting transverse to their relative motion. There is a quantum Magnus force acting on vortices in superfluids and superconductors and an analogous force acting on magnetic vortices excited in spin systems. Couplings with the system quasiparticles can modify this to an effective Magnus force by introducing transverse damping forces. The existence and magnitude of transverse damping forces are highly controversial and have not been settled by experiment. We derive the various damping forces on a vortex in a magnetic system, in particular, damping forces acting longitudinally and transversely to current and past motion (memory effects). In a magnetic system, we expect experiments can more accurately study vortex motion for comparison with theory. Despite the simplicity of the spin system, the results are general and should reveal quantitative behaviour for the superfluid/superconductor systems.

Quantized vortices exist in systems ranging from low-T magnets, to superfluids and superconductors; however, their dynamics remain controversial. Even the existence of a force acting transverse to the motion (like a Lorentz force) relative to thermal quasiparticles has been widely debated. Quite remarkably, it remains unresolved just what forces act on a quantum vortex.
From an influence functional calculation, we show that the expected log divergent mass generalizes to a frequency dependent mass and damping, which, in time, manifest as memory dependent damping forces, acting both longitudinal and transverse to current motion.
Because topological properties are involved, our results apply equally to quantum vortices in many different systems. For instance for vortices in insulating magnets, we are able to find the various forces, including those resulting from vortex-magnon interactions, and derive their dynamics. In contrast to superfluids and superconductors, an experimental test in insulating magnets should be possible using existing methods.

In this thesis, we consider the dynamics of vortices in the easy plane insulating ferromagnet in two dimensions. In addition to the quasiparticle excitations, here spin waves or magnons, this magnetic system admits a family of vortex solutions carrying two topological invariants, the winding number or vorticity, and the polarization.
A vortex is approximately described as a particle moving about the system, endowed with an effective mass and acted upon by a variety of forces. Classically, the vortex has an inter-vortex potential energy giving a Coulomb- like force (attractive or repulsive depending on the relative vortex vorticity), and a gyrotropic force, behaving as a self-induced Lorentz force, whose direction depends on both topological indices.
Expanding semiclassically about a many-vortex solution, the vortices are quantized by considering the scattered magnon states, giving a zero point energy correction and a many-vortex mass tensor. The vortices cannot be described as independent particles -- that is, there are off-diagonal mass terms, such as 1 /2 Mij vi vj , that are non-negligible.
This thesis examines the full vortex dynamics in further detail by evaluating the Feynman-Vernon influence functional, which describes the evolution of the vortex density matrix after the magnon modes have been traced out. In addition to the set of forces already known, we find new damping forces acting both longitudinally and transversely to the vortex motion. The vortex motion within a collective cannot be entirely separated: there are damping forces acting on one vortex due to the motion of another. The effective damping forces have memory effects: they depend not only on the current motion of the vortex collection but also on the motion history.

A 2.5-meter drift length TPC in a 3 Tesla magnetic field has been proposed as the main tracking detector for the TESLA linear collider. Using the gas electron multiplier (GEM) for the TPC readout could improve the overall detector performance over that obtainable with conventional wire/pad system. For the GEM/TPC, simulations and measurements indicate that the spatial resolution may be better determined using induced pad voltage signals rather than induced pad current signals used generally in reading out the GEM. The present status of work in designing a GEM read-out system for the TPC is described.