We present a method for extracting the persistence exponent ? for the diffusion equation, based on the distribution P of "sign times." With the aid of a numerically verified ansatz for P, we derive an analytic formula for ? (in arbitrary spatial dimension d) which we conjecture to be the exact result. Our results are in excellent agreement with previous numerical studies. Furthermore, our results indicate a qualitative change in P above d = 36, signaling the existence of a sharp change in the ergodic properties of the diffusion field.
|Number of pages||4|
|Journal||Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics|
|Publication status||Published - 1 Sep 1998|
Newman, T. J., & Toroczkai, Z. (1998). Diffusive persistence and the "sign-time" distribution. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 58(3 ), R2685-R2688. https://doi.org/10.1103/PhysRevE.58.R2685