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Pavel Drozdov

Publications and source records attributed to Pavel Drozdov.

5 recordsLinked to original sources
arXiv2026

Superintegrability of discrete-time rational Ruijsenaars-Schneider model and deformed polynomial symmetry algebras

We explicitly construct the additional integrals of motion, ensuring maximal superintegrability of the discrete-time rational Ruijsenaars-Schneider model. Using them, we investigate the algebraic aspects of superintegrability in both continuous- and discrete-time settings. In particular, we determine the complete structures of the polynomial symmetry algebras associated with both the rational Ruijsenaars-Schneider model and its discretization. We demonstrate that discretization leads to a nontrivial deformation of the continuous symmetry algebra with respect to the discretization parameter, thereby extending recent analogous results from the rational Calogero-Moser system to its relativistic generalization.

nlin.SI↗
arXiv2026

Discrete-time maximally superintegrable systems and deformed symmetry algebras: the Calogero-Moser case

We determine the complete structure of the symmetry algebras associated with the N-body Calogero-Moser system and its maximally superintegrable discretization. We prove that the discretization naturally leads to a nontrivial deformation of the continuous symmetry algebra, with the discretization parameter playing the rôle of a deformation parameter. This phenomenon illustrates how discrete superintegrable systems can be viewed as natural sources of deformed polynomial algebraic structures. As a byproduct of these results, we also reveal a connection between the above-mentioned symmetry algebras and the Bell polynomials, as a consequence of the trace properties.

math-ph↗
arXiv2025

Explicit isomorphisms for the symmetry algebras of continuous and discrete isotropic oscillators

We present a detailed study of a parametric Lie algebra encompassing the symmetry algebras of various models, both continuous and discrete. This algebraic structure characterizes the isotropic oscillator (with positive, purely imaginary, and zero frequency) and one of its possible nonlinear deformations. We demonstrate a novel occurrence of this Lie algebra in the framework of maximally superintegrable discretizations of the isotropic harmonic oscillator. In particular, we also show that the continuous model and one of its discretizations admit a Nambu-Hamiltonian structure. Through an in-depth analysis of the properties characterizing the Lie algebra in the abstract setting, for different values of the parameter, we find explicit expressions of the Killing forms and construct explicit isomorphism maps to $\mathfrak{u}_N$, $\mathfrak{gl}_N(\mathbb{R})$, and a semidirect sum of $\mathfrak{so}_N(\mathbb{R})$ with $\mathbb{R}^{N(N+1)/2}$. Notably, due to the above isomorphisms, our formulas hold true for $\mathfrak{su}_N$ and $\mathfrak{sl}_N(\mathbb{R})$ and are valid for arbitrary $N$.

math-ph↗
arXiv2024

Discrete-time systems in quasi-standard form and the $\mathfrak{h}_6$ coalgebra symmetry

In this paper, we characterize all discrete-time systems in quasi-standard form admitting coalgebra symmetry with respect to the Lie--Poisson algebra $\mathfrak{h}_{6}$. The outcome of this study is a family of systems depending on an arbitrary function of three variables, playing the rôle of the potential. Moreover, using a direct search approach, we classify discrete-time systems from this family that admit an additional invariant at most quadratic in the physical variables. We discuss the integrability properties of the obtained cases, their relationship with known systems, and their continuum limits.

math-ph↗