Scale-invariant universal crossing probability in one-dimensional diffusion-limited coalescence

Details Scale-invariant universal crossing probability in one-dimensional diffusion-limited coalescence Scale-invariant universal crossing probability in one-dimensional diffusion-limited coalescence

2002-12-17

arxiv.org/abs/cond-mat/0212407v1

J. Phys. A 36 (2003) 3995--4005

Physics

Condensed Matter

Statistical Mechanics

12 pages, 2 figures

Scientific paper

10.1088/0305-4470/36/14/305

The crossing probability in the time direction is defined for an off-equilibrium reaction-diffusion system as the probability that the system of size L is still active at time t, in the finite-size scaling limit. Exact results are obtained for the diffusion-limited coalescence problem in 1+1 dimensions with periodic and free boundary conditions using empty interval methods. The crossing probability is a scale-invariant universal function of an effective aspect ratio, L^2/Dt, which is the natural scaling variable for this strongly anisotropic system.

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