Bose-Hubbard dimers, Viviani's windows and pendulum dynamics

Abstract

The two-mode Bose-Hubbard model in the mean-field approximation is revisited emphasizing a geometric interpretation where the system orbits appear as intersection curves of a (Bloch) sphere and a cylinder oriented parallel to the mode axis, which provide a generalization of Viviani's curve studied already in 1692. In addition, the dynamics is shown to agree with the simple mathematical pendulum. The areas enclosed by the generalised Viviani curves, the action integrals, which can be used to semiclassically quantize the N-particle eigenstates, are evaluated. Furthermore the significance of the original Viviani curve for the quantum system is demonstrated.

18 pages, 9 figures

References in corpus (8)

• Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
• Quantum Classical Correspondence for a non-Hermitian Bose-Hubbard Dimer
• Beyond mean-field dynamics of small Bose-Hubbard systems based on the number-conserving phase space approach
• Exact number conserving phase-space dynamics of the M-site Bose-Hubbard model
• Semiclassical quantization of an N-particle Bose-Hubbard model
• The two-site Bose--Hubbard model
• Analytical results for Josephson dynamics of ultracold Bosons
• Global Phase Space of Coherence and Entanglement in a double-well BEC

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• Ray and caustic structure of Ince-Gauss beams
• Probabilistic Hysteresis in an Isolated Quantum System: The Microscopic Onset of Irreversibility from a Quantum Perspective
• Mapping repulsive to attractive interaction in driven-dissipative quantum systems
• Classical-quantum correspondence in bosonic two-mode conversion systems: polynomial algebras and Kummer shapes
• $N$-coherence vs. $t$-coherence: An alternative route to the Gross-Pitaevskii equation
• The Dynamics of the Hubbard Model through Stochastic Calculus and Girsanov Transformation