Separation of variables for the quantum relativistic Toda lattices

TL;DR

This paper introduces new $2\times 2$ $L$-operators for quantum relativistic Toda lattices, enabling the reduction of the spectral problem to one-dimensional separation equations, advancing the understanding of quantum integrable systems.

Contribution

It provides novel $L$-operators and applies variable separation to simplify the spectral problem of quantum relativistic Toda lattices.

Findings

New $2\times 2$ $L$-operators for quantum relativistic Toda lattices.

Reduction of spectral problem to one-dimensional separation equations.

Facilitates analysis of quantum integrals of motion.

Abstract

We consider quantum analogs of the relativistic Toda lattices and give new $2\times 2$ $L$-operators for these models. Making use of the variable separation the spectral problem for the quantum integrals of motion is reduced to solving one-dimensional separation equations.