Mikhail Vasilev (University of Glasgow) – Integrability of the Deformed Toda Systems

In 2020 M. Mucciconi and L. Petrov introduced a long-range deformation of the quantum
open non-relativistic Toda system.

We prove the integrability of the deformed Toda system by constructing a 2 × 2 Lax
operator, which produces the commutative family of differential operators containing the
Hamiltonian of the deformed Toda system. Moreover, we show that the same integrable
deformation exists on both classical and quantum levels and can be applied to both nonrelativistic and relativistic Toda systems.

For the open non-relativistic deformed Toda systems we also present an n × n Lax matrix
and prove that it produces the same family of Hamiltonians.