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Integrable Lattice Systems and Markov Processes

Sergio Albeverio·Shao-Ming Fei
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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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Sergio Albeverio, Shao-Ming Fei. 2002-10-17. Integrable Lattice Systems and Markov Processes. https://arxiv.org/abs/quant-ph/0210130

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