Chaos in the three-site Bose-Hubbard model: Classical versus quantum
Goran Nakerst, Masudul Haque
Abstract
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.
Topics & Concepts
Lyapunov exponentQuantum chaosIntegrable systemQuantumPhysicsChaoticEigenvalues and eigenvectorsClassical limitStatistical physicsQuantum mechanicsLimit (mathematics)Mathematical physicsQuantum dynamicsMathematicsMathematical analysisNonlinear systemComputer scienceArtificial intelligenceQuantum many-body systemsQuantum chaos and dynamical systemsCold Atom Physics and Bose-Einstein Condensates