English

On spectral equations for an evolution operator of a $q$-oscillator lattice

Mathematical Physics 2026-01-01 v1 math.MP

Abstract

We propose a set of algebraic equations describing eigenvalues and eigenstates of a relativistic evolution operator for a two-dimensional qq-oscillator Kagom\'e lattice. Evolution operator is constructed with the help of qq-oscillator solution of the Tetrahedron Equation. We focus on the unitary regime of the evolution operator, so our results are related to 3d integrable systems of the quantum mechanics. Our conjecture is based on a two-dimensional lattice version of the coordinate Bethe-Ansatz.

Keywords

Cite

@article{arxiv.2512.24043,
  title  = {On spectral equations for an evolution operator of a $q$-oscillator lattice},
  author = {Sergey Sergeev},
  journal= {arXiv preprint arXiv:2512.24043},
  year   = {2026}
}