Toric Networks, Geometric R-Matrices and Generalized Discrete Toda Lattices

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• 作者：Rei Inoue ; Thomas Lam ; Pavlo Pylyavskyy
• 刊名：Communications in Mathematical Physics
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：347
• 期：3
• 页码：799-855
• 全文大小：1,468 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Quantum Physics
  Quantum Computing, Information and Physics
  Complexity
  Statistical Physics
  Relativity and Cosmology
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0916
• 卷排序：347

文摘

We use the combinatorics of toric networks and the double affine geometric R-matrix to define a three-parameter family of generalizations of the discrete Toda lattice. We construct the integrals of motion and a spectral map for this system. The family of commuting time evolutions arising from the action of the R-matrix is explicitly linearized on the Jacobian of the spectral curve. The solution to the initial value problem is constructed using Riemann theta functions.