Restricted Thermalization for Two Interacting Atoms in a Multimode Harmonic Waveguide

In this article, we study the thermalizability of a system consisting of two atoms in a circular, transversely harmonic waveguide in the multimode regime. While showing some signatures of the quantum-chaotic behavior, the system fails to reach a thermal equilibrium in a relaxation from an initial state, even when the interaction between the atoms is infinitely strong. We relate this phenomenon to the previously addressed unattainability of a complete quantum chaos in the Seba billiard [P. Seba, Phys. Rev. Lett., 64, 1855 (1990)], and we conjecture the absence of a complete thermalization to be a generic property of integrable quantum systems perturbed by a non-integrable but well localized perturbation.