15 citations · 49 across the 11 of their papers we have counts for
11 papers
An application of the max-plus spectral theory to an ultradiscrete analogue of the Lax pair
Sergei Sergeev
We study the ultradiscrete analogue of Lax pair proposed by Willox et al. This "pair" is a max-plus linear system comprising four equations. Our starting point is to treat this sys…
Evolution operators for quantum chains
S. M. Sergeev
Discrete-time evolution operators in integrable quantum lattice models are sometimes more fundamental objects then Hamiltonians. In this paper we study an evolution operator for th…
Lattice system of interacting spins in the thermodynamical limit
S. Sergeev
In this paper we investigate some particular spin lattice (a higher dimensional generalization of a spin chain) related to Zamolodchikov model, in the limit when both sizes of the…
Spectral curves and parameterizations of a discrete integrable 3-dimensional model
S. Pakuliak, S. Sergeev
We consider a discrete classical integrable model on the 3-dimensional cubic lattice. The solutions of this model can be used to parameterize the Boltzmann weights of the different…
Quantum relativistic Toda chain at root of unity: isospectrality, modified Q-operator and functional Bethe ansatz
S. Pakuliak, S. Sergeev
We investigate an N-state spin model called quantum relativistic Toda chain and based on the unitary finite dimensional representations of the Weyl algebra with q being N-th primit…
Relativistic Toda chain at root of unity III. Relativistic Toda chain hierarchy
S. Pakuliak, S. Sergeev
The hierarchy of the classical nonlinear integrable equations associated with relativistic Toda chain model is considered. It is formulated for the N-th powers of the quantum opera…