Time discretization of the spin Calogero-Moser model and the semi-discrete matrix KP hierarchy

TL;DR

This paper introduces a discrete-time version of the spin Calogero-Moser system, linking it to the dynamics of poles in rational solutions of the matrix KP hierarchy with discrete time, derived via an auxiliary linear problem.

Contribution

It develops a novel discrete-time formulation of the spin Calogero-Moser system connected to the matrix KP hierarchy, expanding understanding of integrable systems in discrete settings.

Findings

Discrete time spin Calogero-Moser equations derived from pole dynamics.

Connection established between discrete matrix KP hierarchy and spin Calogero-Moser system.

Method uses auxiliary linear problem for discrete flow.

Abstract

We introduce the discrete time version of the spin Calogero-Moser system. The equations of motion follow from the dynamics of poles of rational solutions to the matrix KP hierarchy with discrete time. The dynamics of poles is derived using the auxiliary linear problem for the discrete flow.