arXiv subjects

Ivan Sechin

Publications and source records attributed to Ivan Sechin.

3 recordsLinked to original sources

arXiv2025

Low-dimensional tori in Calogero-Moser-Sutherland systems

The main result of this paper is an explicit description of the stratification of the phase space of Calogero--Moser--Sutherland (CMS) integrable systems corresponding to Lie groups $SU(n)$. The phase space decomposes into symplectic strata of dimensions $2s$, where $s = 0, 1, \ldots, n - 1$. On each stratum of the positive dimension, we construct natural action-angle coordinates and compute the symplectic form explicitly, showing that every stratum is symplectomorphic to $\mathbb{R}_{> 0}^s \times \mathbb{T}^s$. The zero-dimensional stratum corresponds to the equilibrium point of the multi-time CMS dynamics.

nlin.SI↗

arXiv2024

Quantum Integrable Systems on a Classical Integrable Background

In this paper, we develop the framework for quantum integrable systems on an integrable classical background. We call them hybrid quantum integrable systems (hybrid integrable systems), and we show that they occur naturally in the semiclassical limit of quantum integrable systems. We start with an outline of the concept of hybrid dynamical systems. Then we give several examples of hybrid integrable systems. The first series of examples is a class of hybrid integrable systems that appear in the semiclassical limit of quantum spin chains. Then we look at the semiclassical limit of the quantum spin Calogero--Moser system. The result is a hybrid integrable system driven by usual classical Calogero--Moser (CM) dynamics. This system at the fixed point of the multi-time classical dynamics CM system gives commuting spin Hamiltonians of Haldane--Shastry model.

math-ph↗

arXiv2024

Ruijsenaars duality for B, C, D Toda chains

We use the Hamiltonian reduction method to construct the Ruijsenaars dual systems to generalized Toda chains associated with the classical Lie algebras of types $B, C, D$. The dual systems turn out to be the $B, C$ and $D$ analogues of the rational Goldfish model, which is, as in the type $A$ case, the strong coupling limit of rational Ruijsenaars systems. We explain how both types of systems emerge in the reduction of the cotangent bundle of a Lie group and provide the formulae for dual Hamiltonians. We compute explicitly the higher Hamiltonians of Goldfish models using the Cauchy--Binet theorem.

math-ph↗