On Quantum Integrable Systems

TL;DR

This paper explores the extension of classical nonlinear integrable systems to the quantum realm using the Ermakov transformation, bridging accelerator physics and quantum integrability.

Contribution

It introduces a method to transfer classical nonlinear integrable lattice results into nonrelativistic quantum systems using the Ermakov transformation.

Findings

Classical integrable systems successfully extended to quantum systems.

The Ermakov transformation effectively maps classical results to quantum cases.

Potential applications in quantum accelerator physics and plasma traps.

Abstract

Many quantum integrable systems are obtained using an accelerator physics technique known as Ermakov (or normalized variables) transformation. This technique was used to create classical nonlinear integrable lattices for accelerators and nonlinear integrable plasma traps. Now, all classical results are carried over to a nonrelativistic quantum case.