Solvable reaction-diffusion processes without exclusion

Abstract

For reaction-diffusion processes without exclusion, in which the particles can exist in the same site of a one-dimensional lattice, we study all the integrable models which can be obtained by imposing a boundary condition on the master equation of the asymmetric diffusion process. The annihilation process is also added. The Bethe ansatz solution and the exact N-particle conditional probabilities are obtained.Comment: 13 pages, accepted for publication in Jour. Math. Phy

A class of solvable reaction–diffusion processes on a Cayley tree

“…The first one is the creation-reactions (1)-(3) of eq. (1), with master equation (6). The P l (m; t)s for two cases r 3 = r 2 + 2r 1 and r 3 = r 2 + 2r 1 have been considered in section 3, with the final exact results (13) and (22), respectively.…”

“…These boundary terms, which determine the probabilities at the boundary of the space of the parameters, are chosen such that the studying of the various reactions becomes possible via a simple master equation. The basic quantity in these models is the conditional probability P (α 1 , · · · , α N , x 1 , · · · , x N ; t|β 1 , · · · , β N , y 1 , · · · , y N ; 0), which is the probability of finding particles α 1 , · · · , α N at time t at sites x 1 , · · · , x N , respectively, if at t = 0 we have particles β 1 , · · · , β N at sites y 1 , · · · , y N , respectively [1][2][3][4][5][6].…”

“…which is the probability of finding particles α 1 , • • • , α N at time t at sites x 1 , • • • , x N , respectively, if at t = 0 we have particles β 1 , • • • , β N at sites y 1 , • • • , y N , respectively [1][2][3][4][5][6].…”