Journal of Statistical Physics

, Volume 78, Issue 5–6, pp 1429–1470 | Cite as

Finite-size scaling studies of one-dimensional reaction-diffusion systems. Part I. Analytical results

  • Klaus Krebs
  • Markus P. Pfannmüller
  • Birgit Wehefritz
  • Haye Hinrichsen


We consider two single-species reaction-diffusion models on one-dimensional lattices of lengthL: the coagulation-decoagulation model and the annihilation model. For the coagulation model the system of differential equations describing the time evolution of the empty interval probabilities is derived for periodic as well as for open boundary conditions. This system of differential equations grows quadratically withL in the latter case. The equations are solved analytically and exact expressions for the concentration are derived. We investigate the finite-size behavior of the concentration and calculate the corresponding scaling functions and the leading corrections for both types of boundary conditions. We show that the scaling functions are independent of the initial conditions but do depend on the boundary conditions. A similarity transformation between the two models is derived and used to connect the corresponding scaling functions.

Key Words

Reaction-diffusion systems finite-size scaling nonequilibrium statistical mechanics coagulation model annihilation model 


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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Klaus Krebs
    • 1
  • Markus P. Pfannmüller
    • 2
  • Birgit Wehefritz
    • 1
  • Haye Hinrichsen
    • 3
  1. 1.Physikalisches InstitutUniversität BonnBonnGermany
  2. 2.Institut für Theoretische PhysikUniversität HannoverHannoverGermany
  3. 3.Fachbereich PhysikFreie Universität BerlinBerlinGermany

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