Two-species reaction-diffusion system with equal diffusion constants: Anomalous density decay at large times
Year: 2000
Type: article
Abstract: We study a two-species reaction-diffusion model where $A+\stackrel{\ensuremath{\rightarrow}}{A}\mathrm{\ensuremath{\emptyset}},A+\stackrel{\ensuremath{\rightarrow}}{B}\mathrm{\ensuremath{\emptyset}},$ and $B+\stackrel{\ensuremath{\rightarrow}}{B}\mathrm{\ensuremath{\emptyset}},$ with annihilation rates ${\ensuremath{\lambda}}_{0},$ ${\ensuremath{\delta}}_{0}>{\ensuremath{\lambda}}_{0},$ and ${\ensuremath{\lambda}}_{0},$ respectively. The initial particle configuration is taken to be randomly mixed with mean densities ${n}_{A}(0)>{n}_{B}(0),$ and with the two species A and B diffusing with the same diffusion constant. A field-theoretic renormalization group analysis suggests that, contrary to expectation, the large-time density of the minority species decays at the same rate as the majority when $d<~2.$ Monte Carlo data support the field theory prediction in $d=1,$ while in $d=2$ the logarithmically slow convergence to the large-time asymptotics makes a numerical test difficult.
Authors: Zoran Konkoli, Henrik Johannesson
Institution: Chalmers University of Technology
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1999100290