Conservation laws for strings in the Abelian Sandpile Model

Details Conservation laws for strings in the Abelian Sandpile Model Conservation laws for strings in the Abelian Sandpile Model

2010-02-21

arxiv.org/abs/1002.3974v1

EPL 90 (2010) 60003

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures in color

Scientific paper

10.1209/0295-5075/90/60003

The Abelian Sandpile generates complex and beautiful patterns and seems to display allometry. On the plane, beyond patches, patterns periodic in both dimensions, we remark the presence of structures periodic in one dimension, that we call strings. We classify completely their constituents in terms of their principal periodic vector k, that we call momentum. We derive a simple relation between the momentum of a string and its density of particles, E, which is reminiscent of a dispersion relation, E=k^2. Strings interact: they can merge and split and within these processes momentum is conserved. We reveal the role of the modular group SL(2,Z) behind these laws.

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