Author： Dhar Deepak
Publisher： IOP Publishing
E-ISSN： 1751-8121|48|17|175001-175010
ISSN： 1751-8121
Source： Journal of Physics A: Mathematical and Theoretical, Vol.48, Iss.17, 2015-05, pp. : 175001-175010
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Abstract
We consider a model of the fragmentation of a sheet by cracks that move with a velocity in a preferred direction but which undergo random transverse displacements as they move. There is a non-zero probability of crack-splitting and the split cracks move independently. If two cracks meet, they merge, and move as a single crack. In the steady state, there is non-zero density of cracks and the sheet left behind by the moving cracks is broken into a large number of fragments of different sizes. The evolution operator for this model reduces to the Hamiltonian of a quantum XY spin chain, which is exactly integrable. This allows us to determine the steady state and to also determine the distribution of the sizes of the fragments.
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