Chaos in the three-site Bose-Hubbard model -- classical vs quantum

• URL: http://arxiv.org/abs/2203.09953v1
• Date: Fri, 18 Mar 2022 13:44:26 GMT
• Title: Chaos in the three-site Bose-Hubbard model -- classical vs quantum
• Authors: Goran Nakerst and Masudul Haque
• Abstract summary: We consider a quantum many-body system - the Bose-Hubbard system on three sites - which is neither strongly chaotic nor integrable. We compare quantum measures of chaos in the quantum system, with classical measures of chaos (Lyapunov exponents) in the corresponding classical system. In contrast to both strongly chaotic and integrable systems, the largest Lyapunov exponent is shown to be a multi-valued function of energy.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 multi-valued function of energy.

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