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Open Quantum Systems Decoherence Quantum Simulation Entanglement Theory Quantum Correlations

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

arXiv
Authors: Eva-Maria Graefe, Hans Jürgen Korsch, Martin P. Strzys

Year

2013

Paper ID

33192

Status

Preprint

Abstract Read

~2 min

Abstract Words

95

Citations

N/A

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.

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  • 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...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1308.3569 [2] arXiv https://arxiv.org/abs/1308.3569 [3] Publisher https://arxiv.org/abs/1308.3569

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