Microscopic shape of shocks in a domain growth model

Considering the hydrodynamical limit of some interacting particle systems leads to hyperbolic differential equation for the conserved quantities, e.g. the inviscid Burgers equation for the simple exclusion process. The physical solutions of these partial differential equations develop discontinuities, called shocks. The microscopic structure of these shocks is of much interest and far from being well understood. We introduce a domain growth model in which we find a stationary (in time) product measure for the model, as seen from a defect tracer or second class particle, traveling with the shock. We also show that under some natural assumptions valid for a wider class of domain growth models, no other model has stationary product measure as seen from the moving defect tracer. Key-words: second class particle; shock solution. Introduction The hydrodynamical limit of the nearest neighbor asymmetric simple exclusion model leads to the inviscid Burgers equation ∂u ∂t + 1 2 ∂u ∂x = 0 which is a special case of the one-component hyperbolic conservation law ∂u ∂t + ∂J(u) ∂x = 0 (1) where u 7→ J(u) is a smooth, typically convex function. (By changing x to −x, concave J-s can be transformed to convex ones.) This equation has a shock