MANY-BODY EFFECTS IN THE TRAPPING PROBLEM WITH A FIELD

We study how an external bias field influences the Brownian particle s urvival in a medium with traps. The emphasis is on the many-body aspec t of the problem. A general path integral approach is used to present the particle survival probability P(t) in the form providing a uniform description of the process over the whole range of time and for any v alue of the field strength. It is shown that at low fields the many-bo dy effects determine the long-time behavior of P(t). At high fields, t hey manifest themselves only as a small correction to the rate constan t predicted by the single-body theory. Particular attention is given t o the one-dimensional case where an exact solution can be obtained. A major observation is that the difference between the exact and the mea n-field expressions for P(t) (considered as a measure of the magnitude of the many-body effects) behaves nonmonotonically with the field. Th is suggests that an optimal choice of the field may facilitate an expe rimental observation of the many-body effects in the trapping kinetics . (C) 1998 American Institute of Physics. [S0021-9606(98)52015-6].