Chaotic delocalization of two interacting particles in the classical Harper model

Abstract

Abstract. We study the problem of two interacting particles in the classical Harper model in the regime when one-particle motion is absolutely bounded inside one cell of periodic potential. The interaction between particles breaks integrability of classical motion leading to emergence of Hamiltonian dynamical chaos. At moderate interactions and certain energies above the mobility edge this chaos leads to a chaotic propulsion of two particles with their diffusive spreading over the whole space both in one and two dimensions. At the same time the distance between particles remains bounded by one or two periodic cells demonstrating appearance of new composite quasi-particles called chaons. The effect of chaotic delocalization of chaons is shown to be rather general being present for Coulomb and short range interactions. It is argued that such delocalized chaons can be observed in experiments with cold atoms and ions in optical lattices.

Quantum chaos driven by long-range waveguide-mediated interactions

“…This is strongly reminiscent of an exactly solvable (integrable) one-dimensional model of two bosons in a box, that demonstrates fermionization in the limit of strong repulsion [25][26][27]. The integrability can be broken when the interaction becomes nonlocal [28], or there is an external potential [29], or if the bosons acquire different masses [30], which can be mapped to an irrational-angle billiard [31]. Since considered polaritons are locally interacting equivalent bosons and there is no external potential the integrability should persist at the first glance.…”

Quantum Chaos Driven by Long-Range Waveguide-Mediated Interactions

“…This is strongly reminiscent of an exactly solvable (integrable) one-dimensional model of two bosons in a box that demonstrates fermionization in the limit of strong repulsion [29][30][31]. The integrability can be broken when the interaction becomes nonlocal [32] or there is an external potential [33] or if the bosons acquire different masses [34], which can be mapped to an irrational-angle billiard [35]. Since the considered polaritons are locally interacting equivalent bosons and there is no external potential, the integrability should persist at the first glance.…”