Exactly solvable irreversible processes on Bethe lattices

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Evans, James
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We consider the kinetics of processes where the sites of a Bethe lattice are filled irreversibly and, in general, cooperatively by monomers, dimers, or polyatomics. For nearest neighbor and sometimes more general cooperative effects (including random filling as a special case), we show that the infinite hierarchy of rate equations for probabilities of empty subconfigurations can be exacty truncated and solved using a shielding property of empty sites. We indicate, in certain cases, a connection between these Bethe lattice solutions and certain approximate truncation solutions for corresponding processes on ‘‘physical’’ 2‐D and 3‐D lattices with the same coordination number.


This article is published as Evans, J. W. "Exactly solvable irreversible processes on Bethe lattices." Journal of mathematical physics 25, no. 8 (1984): 2527-2532, doi:10.1063/1.526436. Posted with permission.

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Sun Jan 01 00:00:00 UTC 1984