Exact solution of two-species ballistic annihilation with general pair-reaction probability |
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Authors: | M J E Richardson |
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Institution: | (1) Department of Theoretical Physics, University of Oxford, OX1 3NP Oxford, UK |
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Abstract: | The reaction processA + B → ∅ is modeled for ballistic reactants on an infinite line with particle velocitiesυ
A
=c andυ
B
= -c and initially segregated conditions, i.e., allA particles to the left and allB particles to the right of the origin. Previous models of ballistic annihilation have particles that always react on contact,
i.e., pair-reaction probabilityp = 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< 1, allowing particles to pass through
each other without necessarily reacting. In this way, theA andB particle domains overlap to form a fluctuating, finitesized reaction zone where the product ∅ is created. Fluctuations are
also included in the currents ofA andB 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 theintrinsic reaction rate, seen in a single system, and theextrinsic 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 |
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Keywords: | Ballistic annihilation reaction process reaction zone nonequilibrium Statistical mechanics exactly solved model |
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