Asymptotic behavior of densities in diffusion-dominated annihilation reactions

Maury Bramson, Joel L. Lebowitz

Research output: Contribution to journalArticlepeer-review

82 Scopus citations


We obtain rigorous bounds on the long-time behavior of the densities A(t) and B(t) of species A and B, which diffuse and annihilate upon meeting, i.e., A+ Binert. For equal initial densities A(0)=B(0), the density goes to zero asymptotically as t-d4 for dimensions d4 and as t-1 for d4. When A(0)<B(0), A(t)exp(-1t), A(t)exp(-2tInt) for d=1,2, respectively,andA(t)exp(-dt) for d 3

Original languageEnglish (US)
Pages (from-to)2397-2400
Number of pages4
JournalPhysical review letters
Issue number21
StatePublished - 1988


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