Portal de Periódicos da CAPES

Discrete to continuous-time crossover due to anisotropy in diffusion-limited two-particle annihilation reactions

1993; Springer Science+Business Media; Volume: 72; Issue: 3-4 Linguagem: Inglês

10.1007/bf01048035

1572-9613

Vladimir Privman,

Stochastic processes and statistical mechanics

The diffusion-limited reaction A + A → inert with anisotropic hopping on thed=1 lattice is solved exactly for a simultaneous updating, discrete time-step dynamics. Diffusion-dominated processes slow down as the anisotropy increases. For large times or large anisotropy, one can invoke the appropriate continuum limits. In these limits the effects of the anisotropy on the variation of particle density can be absorbed in time rescaling. However, in other regimes, when the discreteness of the time steps is nonnegligible, the anisotropy effects are nontrivial, although they are always quite small numerically.