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Commutability between Semiclassical Limit and Adiabatic Limit

Biao Wu·Jie Liu
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Abstract

We study the semiclassical limit and the adiabatic limit with a second-quantized two-mode model, which describes a many-boson interacting system. When its mean-field interaction is small, these two limits are commutable. However, when the interaction is strong and over a critical value, the two limits become incommutable. This change of commutability is associated with a topological change in the structure of the energy bands. These results reveal that nonlinear mean-field theories, such as Gross-Pitaevskii equations for Bose-Einstein condensates, can be invalid in the adiabatic limit.

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Biao Wu, Jie Liu. 2005-07-30. Commutability between Semiclassical Limit and Adiabatic Limit. https://doi.org/10.1103/physrevlett.96.020405

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