Journal of Statistical Physics

, Volume 86, Issue 5–6, pp 1203–1235 | Cite as

Universality properties of the stationary states in the one-dimensional coagulation-diffusion model with external particle input

  • Haye Hinrichsen
  • Vladimir Rittenberg
  • Horatin Simon


We investigate with the help of analytical and numerical methods the reactionA+A→A on a one-dimensional lattice opened at one end and with an input of particles at the other end. We show that if the diffusion rates to the left and to the right are equal, for largex, the particle concentrationc(x) behaves likeA s x−1 (x measures the distance to the input end). If the diffusion rate in the direction pointing away from the source is larger than the one corresponding to the opposite direction, the particle concentration behaves likeA a x−1/2. The constantsA s andA a are independent of the input and the two coagulation rates. The universality ofA a comes as a surprise, since in the asymmetric case the system has a massive spectrum.

Key Words

Nonequilibrium statistical mechanics reaction-diffusion systems coagulation model universality 


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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Haye Hinrichsen
    • 1
  • Vladimir Rittenberg
    • 2
  • Horatin Simon
    • 2
  1. 1.Department of Physics of Complex SystemsWeizmann Institute of ScienceRehovotIsrael
  2. 2.Physikalisches InstitutUniversität BonnBonnGermany

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