Chaos in the three-site Bose-Hubbard model: Classical versus quantum

We consider a quantum many-body system-the Bose-Hubbard system on three sites-which has a classical limit, and which is neither strongly chaotic nor integrable but rather shows a mixture of the two types of behavior. We compare quantum measures of chaos (eigenvalue statistics and eigenvector structure) in the quantum system, with classical measures of chaos (Lyapunov exponents) in the corresponding classical system. As a function of energy and interaction strength, we demonstrate a strong overall correspondence between the two cases. In contrast to both strongly chaotic and integrable systems, the largest Lyapunov exponent is shown to be a multivalued function of energy.

Automated summary

We investigate the relationship between chaos in a Bose-Hubbard system and its classical limit. By comparing quantum measures of chaos with classical measures, we find a strong correspondence between the two cases in terms of energy and interaction strength. Unlike strongly chaotic and integrable systems, the largest Lyapunov exponent is shown to be a multivalued function of energy.