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We consider a model of fragmentation of sheet by cracks that move with a velocity in preferred direction, but 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 quantum XY spin chain, which is exactly integrable. This allows us to determine the steady state, and also the distribution of sizes of fragments.
We examine statistical properties of a laser beam propagating in a turbulent medium. We prove that the intensity fluctuations at large propagation distances possess Gaussian probability density function and establish quantitative criteria for realizi
The Coulomb phase, with its dipolar correlations and pinch-point-scattering patterns, is central to discussions of geometrically frustrated systems, from water ice to binary and mixed-valence alloys, as well as numerous examples of frustrated magnets
We study the phenomenon of Hilbert space fragmentation in isolated Hamiltonian and Floquet quantum systems using the language of commutant algebras, the algebra of all operators that commute with each term of the Hamiltonian or each gate of the circu
Bernoulli random walks, a simple avalanche model, and a special branching process are essesntially identical. The identity gives alternative insights into the properties of these basic model sytems.
We derive exact statistical properties of a class of recursive fragmentation processes. We show that introducing a fragmentation probability 0<p<1 leads to a purely algebraic size distribution in one dimension, P(x) ~ x^{-2p}. In d dimensions, the vo