Microscopic shape of shocks in a domain growth model

Abstract

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, travelling 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.

Submitted to Journal of Statistical Physics. 16 pages, 1 figure. Some minor comments were added for more clear and better understanding; a few more references are also given

References in corpus (1)

• Shock Profiles for the Asymmetric Simple Exclusion Process in One Dimension

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• Fluctuation bounds in the exponential bricklayers process
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• Universal scaling for second class particles in a one-dimensional misanthrope process
• Multi-species reaction-diffusion models admitting shock solutions