Hybrid integrable systems
Organizers
Speaker
Time
Friday, November 7, 2025 1:00 PM - 2:30 PM
Venue
A3-4-301
Online
Zoom 242 742 6089
(BIMSA)
Abstract
In this talk, I will discuss an attempt to define quantum integrable systems on classical integrable backgrounds, which we call hybrid integrable systems. I will show how such systems naturally appear in the semiclassical limit of quantum integrable models and how they can be constructed geometrically using a flat connection on a bundle of algebras over a symplectic manifold.
My main example will come from the semiclassical limit of the quantum spin Calogero–Moser model. In this case, we obtain a hybrid system governed by the usual classical Calogero–Moser dynamics (without spin). At the fixed points of the multi-time Calogero–Moser flow, this construction provides commuting Hamiltonians corresponding to a long-range spin chain of the Haldane–Shastry type.
Based on arXiv:2405.17865 (with A. Liashyk and N. Reshetikhin).
My main example will come from the semiclassical limit of the quantum spin Calogero–Moser model. In this case, we obtain a hybrid system governed by the usual classical Calogero–Moser dynamics (without spin). At the fixed points of the multi-time Calogero–Moser flow, this construction provides commuting Hamiltonians corresponding to a long-range spin chain of the Haldane–Shastry type.
Based on arXiv:2405.17865 (with A. Liashyk and N. Reshetikhin).
Speaker Intro
Ivan Sechin has defended a PhD thesis on Mathematical Physics at Skoltech in 2022 and joined BIMSA in 2022. His research interests are mainly devoted to classical and quantum integrable systems.