1996/05/22 by Satya N. Majumdar, Clement Sire, Alan J. Bray +1 · 1 citation
Physics and Astronomy · #cond-mat
paper · pdf · doi:10.1103/physrevlett.77.2867
published as Phys. Rev. Lett. 77 (1996) 2867 · Minor typos corrected, affecting table of exponents. 4 pages, REVTEX, 1 eps figure. Uses epsf.sty and multicol.sty
arxiv created 1996/05/22 · arxiv updated 2009/11/30
The diffusion equation ∂tϕ= ∇2ϕis considered, with initial condition ϕ( x_ ,0) a gaussian random variable with zero mean. Using a simple approximate theory we show that the probability pn(t1,t2) that ϕ( x_ ,t) [for a given space point x_ ] changes sign n times between t1 and t2 has the asymptotic form pn(t1,t2) ∼ [ln(t2/t1)]n(t1/t2)-θ. The exponent θhas predicted values 0.1203, 0.1862, 0.2358 in dimensions d=1,2,3, in remarkably good agreement with simulation results.