Quantum discrete Dubrovin equations

DOI10.1088/0305-4470/37/33/007zbMATH Open1061.81079arXivnlin/0406040OpenAlexW3100432870MaRDI QIDQ4654592

Publication date: 8 March 2005

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Abstract: The discrete equations of motion for the quantum mappings of KdV type are given in terms of the Sklyanin variables (which are also known as quantum separated variables). Both temporal (discrete-time) evolutions and spatial (along the lattice at a constant time-level) evolutions are considered. In the classical limit, the temporal equations reduce to the (classical) discrete Dubrovin equations as given in a previous publication. The reconstruction of the original dynamical variables in terms of the Sklyanin variables is also achieved.

Full work available at URL: https://arxiv.org/abs/nlin/0406040

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Many-body theory; quantum Hall effect (81V70) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Groups and algebras in quantum theory and relations with integrable systems (81R12) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Operator algebra methods applied to problems in quantum theory (81R15)