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

Abstract

The master equation of one-dimensional three-species reaction-diffusion processes is mapped onto an imaginary-time Schrödinger 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.

27 pages, plain Latex, 73 kB

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• Statistical mechanics of the coagulation-diffusion process with a stochastic reset
• Reaction-Diffusion Processes from Equivalent Integrable Quantum Chains
• EQUIVALENCES BETWEEN STOCHASTIC SYSTEMS
• A sufficient criterion for integrability of stochastic many-body dynamics and quantum spin chains
• Classical and Quantum sl(1|2) Superalgebras, Casimir Operators and Quantum Chain Hamiltonians
• Exact correlations in the one-dimensional coagulation-diffusion process by the empty-interval method
• The Irreducible String and an Infinity of Additional Constants of Motion in a Deposition-Evaporation Model on a Line
• Remarks on the multi-species exclusion process with reflective boundaries
• Cross-over between diffusion-limited and reaction-limited regimes in the coagulation-diffusion process