Integrable Lattice Systems and Markov Processes

Details Integrable Lattice Systems and Markov Processes Integrable Lattice Systems and Markov Processes

2002-10-17

arxiv.org/abs/quant-ph/0210130v1

Int. J. Theor. Phys., Group Theory and Nonlinear Optics 9(2002)39-68

Physics

Quantum Physics

30 pages, Latex

Scientific paper

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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