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Integrable models and stochastic processes

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Abstract

A general way for constructing square lattice systems with certain Lie algebraic or quantum Lie algebraic symmetries is presented. These models give rise to series of integrable (stochastic) systems. As examples theAn-symmetric chain models and theSU(2)-invariant ladder models are investigated.

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References

  1. V.E. Korepin, N.M. Bogoliubov and A.G. Izergin:Quantum Inverse Scattering Method and Correlation Functions, Cambridge University Press, 1993.

  2. L.D. Faddeev and L.A. Takhtadzhyan: Russ. Math. Surv.34 11 (1979).

    MathSciNet  Google Scholar 

  3. J.W. Evans: Rev. Mod. Phys.65 (1993) 1281.

    Article  ADS  Google Scholar 

  4. F.C. Alcaraz, M. Droz, M. Henkel and V. Rittenberg: Ann. Phys.230 (1994) 250.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. F.C. Alcaraz and V. Rittenberg: Phys. Lett. B314 (1993) 377.

    Article  ADS  Google Scholar 

  6. M. Henkel and H. Hinrichsen: J. Phys. A34 (2001) 1561.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  7. I. Peschel, V. Rittenberg, and U. Schultze: Nucl. Phys. B430 (1995) 633.

    Article  ADS  MathSciNet  Google Scholar 

  8. H. Simon: J. Phys. A28 (1995) 6585.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  9. M. Henkel, E Orlandini, and G.M. Schütz: J. Phys. A28 (1995) 6335.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  10. G.M. Schütz: J. Stat. Phys. A28 (1995) 243.

    Article  Google Scholar 

  11. S. Albeverio and S.-M. Fei: Rev. Math. Phys.10 (1998) 723.

    Article  MATH  MathSciNet  Google Scholar 

  12. S. Albeverio, S.-M. Fei, and Y.P. Wang: EuroPhys. Lett.47 (1999) 364.

    Article  ADS  Google Scholar 

  13. V. Chari and A. Pressley:A Guide to Quantum Groups, Cambridge University Press, 1994. Z.Q. Ma:Yang-Baxter Equation and Quantum Enveloping Algebras, World Scientific, 1993. S. Majid:Foundations of Quantum Group Theory, Cambridge University Press, 1995. K. Schmüdgen:Quantum Groups and Their Representations, Springer, 1997.

  14. D.L. Isaacson and R.W. Madsen:Markov Chains, Theory and Applications, Wiley Series in Probability and Mathematical Statistics, 1976. K.L. Chung:Markov Chains with Stationary Transition Probabilities, Springer, Berlin, 1967. S. Ross:Introduction to Probability Models, Academic Press, New York, 1972. M. Iosifescu:Finite Markov Processes and Applications, J. Wiley, Chichester, 1980.

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SFB 256; BiBoS; CERFIM(Locarno); Acc. Arch.; USI(Mendriso)

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Albeverio, S., Fei, SM. Integrable models and stochastic processes. Czech J Phys 51, 1241–1246 (2001). https://doi.org/10.1023/A:1013314430278

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  • DOI: https://doi.org/10.1023/A:1013314430278

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