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The reaction A+B --> B is studied when the reactants diffuse in phase space,i.e. their dynamics is described by the Langevin equation. The steady-staterate constants are calculated for both the target (static A and mobile B's) andtrapping (mobile A and static B's) problems when the reaction is assumed tooccur at the first contact. For Brownian dynamics (i.e., ordinary diffusion),the rate constant for both problems is a monotonically decreasing function ofthe friction coefficient $\gamma$. For Langevin dynamics, however, we find thatthe steady-state rate constant exhibits a turnover behavior as a function of$\gamma$ for the trapping problem but not for the target problem. This turnoveris different from the familiar Kramers' turnover of the rate constant forescape from a deep potential well because the reaction considered here is anactivationless process.Comment: 29 pages including 7 figure

Irreversible bimolecular reactions of Langevin particles