The pair annihilation reaction D + D --> 0 in disordered media and conformal invariance

TL;DR

This paper models a reaction D + D --> 0 within a fluctuating interface framework, revealing conformal invariance and providing exact results through quantum chain connections.

Contribution

It introduces a generalized interface model with defects that captures the D + D annihilation reaction and demonstrates conformal invariance with exact analytical results.

Findings

Defects annihilate in the stationary state.

The model exhibits conformal invariance.

Exact results are obtained via quantum chain connection.

Abstract

The raise and peel model describes the stochastic model of a fluctuating interface separating a substrate covered with clusters of matter of different sizes, and a rarefied gas of tiles. The stationary state is obtained when adsorption compensates the desorption of tiles. This model is generalized to an interface with defects (D). The defects are either adjacent or separated by a cluster. If a tile hits the end of a cluster with a defect nearby, the defect hops at the other end of the cluster changing its shape. If a tile hits two adjacent defects, the defect annihilate and are replaced by a small cluster. There are no defects in the stationary state. This model can be seen as describing the reaction D + D -->0, in which the particles (defects) D hop at long distances changing the medium and annihilate. Between the hops the medium also changes (tiles hit clusters changing their shapes). Several properties of this model are presented and some exact results are obtained using the connection of our model with a conformal invariant quantum chain.