Sr. Dahmen, REACTION-DIFFUSION PROCESSES DESCRIBED BY 3-STATE QUANTUM CHAINS AND INTEGRABILITY, Journal of physics. A, mathematical and general, 28(4), 1995, pp. 905-922
The master equation of one-dimensional three-species reaction-diffusio
n processes is mapped onto an imaginary-time Schrodinger equation. In
many cases the Hamiltonian obtained is that of an integrable quantum c
hain with known properties. Within this approach we search for three-s
tate integrable quantum chains with known spectra and which are relate
d to diffusive-reactive systems. Two integrable models are found to ap
pear naturally in this context: the U-q ($$$) over cap SU(2)-invariant
model with external fields and the three-state UqSU(P/M)-invariant Pe
rk-Schultz models with external fields. A non-local similarity transfo
rmation which brings the Hamiltonian governing the chemical processes
to the known standard forms is described, leading in the case of perio
dic boundary conditions to a generalization of the Dzialoshinsky-Moriy
a interaction for N-state Hamiltonians (N > 2).