1994/05/11 by Silvio R. Dahmen, S R Dahmen · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #Quantum many-body systems #cond-mat
paper · pdf · doi:10.1088/0305-4470/28/4/016
27 pages, plain Latex, 73 kB
arxiv created 1994/05/11 · openalex publication_date 1995/02/21 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
The master equation of one-dimensional three-species reaction-diffusion processes is mapped onto an imaginary-time Schrodinger equation. In many cases the Hamiltonian obtained is that of an integrable quantum chain with known properties. Within this approach we search for three-state integrable quantum chains with known spectra and which are related to diffusive-reactive systems. Two integrable models are found to appear naturally in this context: the U q SU(2)-invariant model with external fields and the three-state U q SU(P/M)-invariant Perk-Schultz models with external fields. A non-local 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 for N-state Hamiltonians (N>2).