Universal fragmentation in annihilation reactions with constrained kinetics
Abstract: In reaction-diffusion models of annihilation reactions in low dimensions, single-particle dynamics provides a bottleneck for reactions, leading to an anomalously slow approach to the empty state. Here, we construct a reaction model with a reciprocal bottleneck on particle dynamics where single-particle motion conserves the center of mass. We show that such a constrained reaction-diffusion dynamics does not approach an empty state but freezes at late times in a state with fragmented particle clusters, and that the late-time dynamics and asymptotic density are universal. Our setup thus constitutes a minimal model for the fragmentation of a one-dimensional lattice into independent particle clusters, and we provide exact results for the final density in the large-reaction rate limit. We suggest that the universal reaction dynamics could be observable in experiments with cold atoms or in the Auger recombination of exciton gases.
- N. G. van Kampen, Stochastic Processes in Physics and Chemistry (Third Edition), North-Holland Personal Library (Elsevier, Amsterdam, 2007).
- V. Volpert and S. Petrovskii, Physics of Life Reviews 6, 267 (2009).
- P. Meakin, Annual Review of Physical Chemistry 39, 237 (1988).
- F. Sciortino and P. Tartaglia, Advances in Physics 54, 471 (2005).
- P. G. de Gennes, The Journal of Chemical Physics 76, 3322 (1982).
- D. Toussaint and F. Wilczek, J. Chem. Phys. 78, 2642 (1983).
- F. Family and J. G. Amar, Journal of Statistical Physics 65, 1235 (1991).
- J. Cardy, Renormalisation group approach to reaction-diffusion problems (1996), arXiv:cond-mat/9607163 .
- L. Chen and M. W. Deem, Phys. Rev. E 65, 011109 (2001).
- S. Yuste and K. Lindenberg, Chemical Physics 284, 169 (2002).
- I. M. Sokolov, M. G. W. Schmidt, and F. Sagués, Phys. Rev. E 73, 031102 (2006).
- J. H. Han, E. Lake, and S. Ro, Phys. Rev. Lett. 132, 137102 (2024).
- V. Khemani, M. Hermele, and R. Nandkishore, Physical Review B 101, 174204 (2020).
- A. Morningstar, V. Khemani, and D. A. Huse, Phys. Rev. B 101, 214205 (2020).
- D. T. Gillespie, Annu. Rev. Phys. Chem. 58, 35 (2007).
- S.-C. Park, Phys. Rev. E 72, 036111 (2005).
- A. Weddig Karlsson, “Simulating nondiffusive dynamics in reaction-diffusion systems”, Master’s thesis, Chalmers University of Technology (2023).
- OEIS Foundation Inc., Entry A000029 in The On-Line Encyclopedia of Integer Sequences (2024), published electronically at http://oeis.org.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.
