Exact Solution of Two-species Ballistic Annihilation with General Pair-reaction Probability

The reaction process A + B → ∅ is modelled for ballistic reactants on an infinite line with particle velocities vA = c and vB = −c and initially segregated conditions, i.e. all A particles to the left and all B particles to the right of the origin. Previous models of ballistic annihilation have particles that always react on contact, i.e. pair-reaction probability p = 1. The evolution of such systems are wholly determined by the initial distribution of particles and therefore do not have a stochastic dynamics. However, in this paper the generalisation is made to p ≤ 1, allowing particles to pass through each other without necessarily reacting. In this way, the A and B particle domains overlap to form a fluctuating, finite-sized reaction zone where the product ∅ is created. Fluctuations are also included in the currents of A and B particles entering the overlap region, thereby inducing a stochastic motion of the reaction zone as a whole. These two types of fluctuations, in the reactions and particle currents, are characterised by the intrinsic reaction zone, seen in a single system, and the extrinsic reaction zone, seen in an average over many systems. The intrinsic and extrinsic behaviours are examined and compared to the case of isotropically diffusing reactants. Date: February 29, 2008 To be submitted to J. Stat. Phys.