Persistence in non-equilibrium systems: a study on spatial correlations

Abstract

Some aspects of coarsening and the associated notion of persistence in a few well-known non-equilibrium processes are studied in this thesis. This thesis consists of 5 chapters. Apart from the introduction chapter, 2nd and 3rd chapters comprises of the first part of the thesis, which studies the time evolution of the spatial structure of the persistent region in several standard models of coarsening in different spatial dimensions. The most important result is the formation of a scale-invariant pattern in the distribution of persistent regions in space. A detailed study of the problem in d=1 Ising model which coarsens only at T=0 is made. This study is extended to higher dimensions and non-zero temperatures and some other relevant models, emphasising the universality of the phenomenon. It is investigated to find 'whether a fluctuating interface may be viewed as a coarsening system evolving towards a phase separated steady state'. This assertion is found to be true but the phase separation is found to be different in several ways from that found in more conventional systems.