Integrable Lattice Systems and Markov Processes

2002/10/17 by Sergio Albeverio, Shao-Ming Fei
Physics and Astronomy · #quant-ph

paper · pdf

published as Int. J. Theor. Phys., Group Theory and Nonlinear Optics 9(2002)39-68 · 30 pages, Latex

arxiv created 2002/10/17 · arxiv updated 2009/12/01

Abstract

Lattice systems with certain Lie algebraic or quantum Lie algebraic symmetries are constructed. These symmetric models give rise to series of integrable systems. As examples the A_n-symmetric chain models and the SU(2)-invariant ladder models are investigated. It is shown that corresponding to these A_n-symmetric chain models and SU(2)-invariant ladder models there are exactly solvable stationary discrete-time (resp. continuous-time) Markov chains with transition matrices (resp. intensity matrices) having spectra which coincide with the ones of the corresponding integrable models.

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