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Segregation in diffusion-limited multispecies pair annihilation. (English) Zbl 1064.82031

Summary: The kinetics of the \(q\) species pair annihilation reaction (\(A_i + A_j \to \emptyset\) for \(1 \leq i < j \leq q\)) in \(d\) dimensions is studied by means of analytical considerations and Monte Carlo simulations. In the long-time regime the total particle density decays as \(\rho(t) \sim t^{-\alpha}\). For \(d = 1\) the system segregates into single-species domains, yielding a different value of \(\alpha\) for each \(q\); for a simplified version of the model in one dimension we derive \(\alpha(q) = (q - 1)/(2q)\). Within mean-field theory, applicable in \(d \geq 2\), segregation occurs only for \(q < 1 + (4/d)\). The only physical realization of this scenario is the two-species process (\(q = 2\)) in \(d = 2\) and \(d = 3\), governed by an extra local conservation law. For \(d \geq 2\) and \(q \geq 1 + (4/d)\) the system remains disordered and its density is shown to decay universally with the mean-field power law (\(\alpha = 1\)) that also characterizes the single-species annihilation process \(A + A \to \emptyset\).

MSC:

82C40 Kinetic theory of gases in time-dependent statistical mechanics
82C80 Numerical methods of time-dependent statistical mechanics (MSC2010)
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