Dynamics of spinodal decomposition in finite-lifetime systems

Abstract

We present a statistical theory of the phase-separation dynamics in many-particle systems with a finite lifetime. Temporal evolution of the spinodal decomposition is traced with the single-point distribution function and the dynamical structure factor under the situation where the mean particle number is constant by balancing between decay and creation of the particles. The finite lifetime prevents phase separation and order formation; hence the lower critical wave number ${k}_{\mathrm{c}}^{(1)}(t)$ appears; domains of larger size than $[{k}_{\mathrm{c}}^{(1)}(t){]}^{\ensuremath{-}1}$ cannot grow. Differences between the infinite- and finite-lifetime cases are clarified in terms of this critical wave number. A universal relation between the lifetime and the asymptotic $(\stackrel{\ensuremath{\rightarrow}}{t}\ensuremath{\infty})$ critical wave number is confirmed numerically. Comparison with the nucleation process is also made.