Study of the dynamics of driven periodic systems: Charge -density waves and superconducting rings

We study the dynamics of two closely related periodic systems, superconducting rings and charge-density waves, using an approach based on pattern formation.;In the first part of the thesis, we concentrate on the onset of instability in a thin superconducting ring. A periodic instability appears when current is driven by an applied external voltage to the point of instability at temperatures below the critical temperature. The main contribution of this study is to investigate how the new state is selected when the system reaches the point of instability. That is, how the selection process is affected by different factors, such as the rate at which the system is driven. In addition, the generation of Ohmic resistance due to the dissipative phase slip state at the point of instability is studied. The problem of state selection at the onset of instability is a generic problem in pattern formation systems. Our results show that the onset of dissipation leads to strong non-linear effects in the state selection process.;In the second part of this thesis, we study the nonequilibrium behavior of driven charge-density waves in random media in two spatial dimensions. We propose a novel model for charge-density wave dynamics based on the Swift-Hohenberg equation. The advantage of our model is that it includes both amplitude and phase fluctuations of the condensate. We derive the model and show its formal relation to the almost universally used elastic models for charge-density waves. We demonstrate that phase slips proliferate close to the depinning transition thereby rendering a phase-only description invalid. Finally, using our model, we explain two recent experiments that cannot be captured by the traditional elastic approximation; the dynamical x-ray scattering experiments by Ringland et al. [99b], and low temperature transport experiments by Lemay et al. [99].