Erratum: Diffusion-limited reaction for the one-dimensional trap system [Phys. Rev. E67, 056123 (2003)]

Phase transition in the bounded one-dimensional multitrap system

“…The corresponding initial and boundary balue problem associated with the one-dimensional bounded imperfect N trap system is [8,9,10] The third equation is the boundary value condition which introduces the velocity V that results from the field. The parameter k denotes the degree of imperfection of the traps (in [8] it is termed the trapping rate) so that in the limit k → ∞ the trap becomes ideal in which case any particle that approaches it is absorbed.…”

“…The set (3) is the imperfect trap problem which includes the external field and its initial condition contains only the first term of the corresponding condition of the general set (2). The solution of (2) may be written as in [9,10] (see Eq (4) there),…”

“…The ideal trap problem of (4) is the same as that discussed in [9,10] so, following the discussion there, we write for ρ 2 (x,x m , t)…”

“…We use in this section the N (2X2) transfer matrices method for V = 0 and write the general matrix equation [9,10] …”

“…The N T 's in Eq (8) are all two-dimensional transfer matrices that differ from each other by the value of x only [9]. Thus, a representative one which relates the two faces of the same trap that are located, for example, at x = x 1 and x = x 2 , where x 2 > x 1 , may be written as [9,10] T…”