Reaction-Diffusion Processes Described by Three-State Quantum Chains and Integrability

Details Reaction-Diffusion Processes Described by Three-State Quantum Chains and Integrability Reaction-Diffusion Processes Described by Three-State Quantum Chains and Integrability

1994-05-11

arxiv.org/abs/cond-mat/9405031v1

Physics

Condensed Matter

27 pages, plain Latex, 73 kB

Scientific paper

10.1088/0305-4470/28/4/016

The master equation of one-dimensional three-species reaction-diffusion processes is mapped onto an imaginary-time Schr\"odinger equation. In many cases the Hamiltonian obtained is that of an integrable quantum chain. Within this approach we search for all $3$-state integrable quantum chains whose spectra are known and which are related to diffusive-reactive systems.Two integrable models are found to appear naturally in this context: the $U_{q}\widehat{SU(2)}$-invariant model with external fields and the $3$-state $U_q Su(P/M)$-invariant Perk-Schultz models with external fields. A nonlocal similarity transformation which brings the Hamiltonian governing the chemical processes to the known standard forms is described, leading in the case of periodic boundary conditions to a generalization of the Dzialoshinsky-Moriya interaction.

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