arXiv subjects

S. Sergeev

Publications and source records attributed to S. Sergeev.

22 records · Page 2Linked to original sources

arXiv2001

Relativistic Toda chain at root of unity II. Modified Q-operator

Matrix elements of quantum intertwiner as well as the modified Q-operator for the quantum relativistic Toda chain at root of unity are constructed explicitly. Modified Q-operators make isospectrality transformations of quantum transfer matrices so that the classical counterparts of Q-operators correspond to the Baecklund isospectrality transformations of the classical transfer matrices. Separated vectors for the Functional Bethe Ansatz are constructed with the help of modified Q-operators.

nlin.SI↗

arXiv2001

Relativistic Toda chain at root of unity

We declare briefly several interesting features of the quantum relativistic Toda chain at N-th root of unity. We consider the finite dimensional representation of the Weyl algebra. The origin of the features mentioned is that we consider simultaneously the quantum finite dimensional part and the classical dynamics of N-th powers of Weyl's elements. As the main result, using the technique of Q-operators, we establish a correspondence between the separation of variables in the quantum model and the Baecklund transformations of its classical counterpart.

nlin.SI↗

arXiv2000

Relativistic Toda chain

Investigated is the relativistic periodic Toda chain, to each site of which the ultra-local Weyl algebra is associated. Weyl's $q$ we are considering here is restricted to be inside the unit circle. Quantum Lax operators of the model are intertwined by six vertex $R$-matrix. Both independent Baxter's $Q$-operators are constructed explicitly as seria over local Weyl generators. The operator-valued wronskian of $Q$-s is also calculated.

nlin.SI↗

arXiv1999

Solitons in a 3d integrable model

Equations of motion for a classical 3d discrete model, whose auxialiary system is a linear system, are investigated. The Lagrangian form of the equations of motion is derived. The Lagrangian variables are a triplet of "tau functions". The equations of motion for the Triplet of Tau functions are Three Trilinear equations. Simple solitons for the trilinear equations are given. Both the dispersion relation and the phase shift reflect the triplet structure of equations.

solv-int↗