On the integrability of a system describing the stationary solutions in Bose--Fermi mixtures

TL;DR

This paper investigates the integrability of a Hamiltonian system modeling stationary solutions in Bose-Fermi mixtures, establishing that integrability occurs only under separability conditions using differential Galois theory.

Contribution

The paper applies the Differential Galois approach and Ziglin-Morales-Ramis method to determine the conditions for integrability in a Bose-Fermi mixture model.

Findings

System is integrable only when separable.

Integrability is characterized using differential Galois theory.

Provides criteria for integrability in Bose-Fermi systems.

Abstract

We study the integrability of a Hamiltonian system describing the stationary solutions in Bose--Fermi mixtures in one dimensional optical lattices. We prove that the system is integrable only when it is separable. The proof is based on the Differential Galois approach and Ziglin-Morales-Ramis method.