# Fluctuations and dissipation of collective dynamics in spin and pseudospin ferromagnets

## Abstract

In this thesis a careful study of the equilibrium and transport properties of ν = 1 quantum Hall bilayers is presented. Our approach is based on the pseudospin analogy in which the layer degree of freedom for the electrons is treated as a spin degree of freedom. This treatment reveals the many analogies between these systems and spin systems. After briefly reviewing the basic physics of the quantum Hall effect in chapter 2, in chapter 3 we introduce the quantum Hall bilayer systems and define the pseuduspin model used in the following chapters to study their properties. In chapter 4 we present our results on the equilibrium properties of quantum Hall bilayers in presence of strong disorder. In particular we calculate the critical disorder strength above which the interlayer phase coherence is lost, and the Kosterlitz-Thouless temvi perature goes to zero. In chapter 5 we develop a theory for the tunneling transport in these systems. In contrast to most previous theoretical work our theory predicts that the zero bias conductance is finite even in a perfect disorder free bilayer at zero temperature and accounts, within an order of magnitude, for the width of the anomaly observed in experiments. Also the theory correctly predicts the suppression of the tunneling conductance in presence of a magnetic field in the plane of the 2DEG. Using the results of chapter 4 the theory can also quantify the suppression of the tunneling conductance due to disorder. In chapter 6 we study the dynamics of the magnetization when coupled to a thermal bath of elastic modes. We derive explicit expressions for the memory friction kernel and the spectral density of the fluctuations starting from a realistic form of the coupling of the magnetization to the elastic modes. Finally in chapter 7 we study the dynamics of a particularly interesting class of collective modes in magnetized plasmas: tearing modes. We develop a rigorous approach to describe the evolution of these modes beyond the linear approximation. Using this approach we then consider nonlinear effects due to the coupling of the fundamental mode to higher harmonics and external perturbations.