EXACT SOLUTION OF TWO-SPECIES BALLISTIC ANNIHILATION WITH GENERAL PAIR-REACTION PROBABILITY

摘要

The reaction process A + B --> is modelled for ballistic reactants on an infinite line with particle velocities upsilon(A) = c and upsilon(B) = -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 evolutions of such systems are wholly determined by the initial distributions of particles and therefore do not have a stochastic dynamics. However, in this paper the generalization is made to p less than or equal to 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 rate, seen in a single system, and the extrinsic reaction rate, seen in an average over many systems. The intrinsic and extrinsic behaviors are examined and compared to the case of isotropically diffusing reactants. [References: 29]