Year: 1996
Type: article
Abstract: We study the following one-dimensional (1D) two-species reaction-diffusion model: there is a small concentration of B particles with diffusion constant ${\mathit{D}}_{\mathit{B}}$ in an homogenous background of W particles with diffusion constant ${\mathit{D}}_{\mathit{W}}$; two W particles of the majority species either coagulate (W+W\ensuremath{\rightarrow}W) or annihilate (W+W\ensuremath{\rightarrow}0) with the respective probabilities ${\mathit{p}}_{\mathit{c}}$=(q-2)/(q-1) and ${\mathit{p}}_{\mathit{a}}$=1/(q-1); a B particle and a W particle annihilate (W+B\ensuremath{\rightarrow}0) with probability 1. The exponent \ensuremath{\theta}(q,\ensuremath{\lambda}=${\mathit{D}}_{\mathit{B}}$/${\mathit{D}}_{\mathit{W}}$) describing the asymptotic time decay of the minority B species concentration can be viewed as a generalization of the exponent of persistent spins in the zero-temperature Glauber dynamics of the 1D q-state Potts model starting from a random initial condition: the W particles represent domain walls, and the exponent \ensuremath{\theta}(q,\ensuremath{\lambda}) characterizes the time decay of the probability that a diffusive ``spectator'' does not meet a domain wall up to time t. We extend the methods introduced by Derrida, Hakim, and Pasquier [Phys. Rev. Lett. 75, 751 (1995); J. Stat. Phys. (to be published)] for the problem of persistent spins, to compute the exponent \ensuremath{\theta}(q,\ensuremath{\lambda}) in perturbation at first order in (q-1) for arbitrary \ensuremath{\lambda} and at first order in \ensuremath{\lambda} for arbitrary q. \textcopyright{} 1996 The American Physical Society.
Author: Cécile Monthus
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2068554309