Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2003-07-09
J. Stat. Mech. (2005) P04003
Physics
Condensed Matter
Statistical Mechanics
20 pages, 1 figure, 1 table, IOP format. Two appendices added. Published in Journal of Statistical Mechanics: Theory and Exper
Scientific paper
10.1088/1742-5468/2005/04/P04003
We consider a stochastic many-body system where a source refills uniformly the empty sites of a hypercubic lattice, on which each particle is allowed to jump (symmetrically) onto neighboring vacant sites. In addition, there is a local {\it trap}, in competition with the injection reaction, which perturbs the dynamics by removing particles from the system. In dimensions $d=1, 2$ and 3, for an ``imperfect'' and a ``perfect'' trap, the spatiotemporal effect of the local perturbation of the dynamics is investigated by computing the exact concentration of particles in the system and it is shown that the density profile exhibits a depletion (in one and two dimensions) which properties depend on the space dimension. The exact reactive (fluctuating) steady state and the long-time behavior of the concentration of particles are explicitly computed.
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