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Adiabatic Theory of Nonlinear Evolution of Quantum States

Jie Liu·Biao Wu·Qian Niu
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Abstract

We present a general theory for adiabatic evolution of quantum states as governed by the nonlinear Schrodinger equation, and provide examples of applications with a nonlinear tunneling model for Bose-Einstein condensates. Our theory not only spells out conditions for adiabatic evolution of eigenstates, but also characterizes the motion of non-eigenstates which cannot be obtained from the former in the absence of the superposition principle. We find that in the adiabatic evolution of non-eigenstates, the Aharonov-Anandan phases play the role of classical canonical actions.

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Jie Liu, Biao Wu, Qian Niu. 2002-08-02. Adiabatic Theory of Nonlinear Evolution of Quantum States. https://doi.org/10.1103/physrevlett.90.170404

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