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We study diffusion-limited coalescence, A+A<-->A$, in one dimension, andderive an exact solution for the steady state in the presence of a trap.Without the trap, the system arrives at an equilibrium state which satisfiesdetailed balance, and can therefore be analyzed by classical equilibriummethods. The trap introduces an irreversible element, and the stationary stateis no longer an equilibrium state. The exact solution is compared to that of areaction-diffusion equation --- the habitual approximation method of choice.The exact solution allows us to determine the rate coefficients in thereaction-diffusion equation, without appealing to renormalization grouptechniques.Comment: 4 pages, typset with RevTe

physical review. e, statistical physics, plasmas, fluids, and related interdisciplinary topics

Diffusion-limited coalescence,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:mi>A</mml:mi><mml:mo>⇌</mml:mo><mml:mi>A</mml:mi><mml:mo>,</mml:mo></mml:math>with a trap

Diffusion-limited coalescence,A+A⇌A,with a trap