Domain-size statistics in the time-dependent Ginzburg-Landau equation driven by a dichotomous Markov noise

Abstract

The domain dynamics of magnetization obeying the time-dependent Ginzburg-Landau equation driven by a dichotomous Markov noise is discussed. The system with various domain sizes in the early stage temporally evolves following an annihilation of neighboring domain walls, where each domain wall moves diffusively. Three statistics on the domain size, i.e., average domain size, the ensemble average of the domain size distribution function, and the spatial power spectrum of the magnetization, are evaluated to characterize the domain wall annihilation process. A phenomenological evolution equation for the domain-size distribution function is constructed by simplifying the annihilation process of the domain wall appropriately, and the underlying mechanism of those statistics is investigated.