Adiabatic Theory of Nonlinear Evolution of Quantum States
arXiv:quant-ph/0205152 · doi:10.1103/PhysRevLett.90.170404
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.
substantial revision, 5 pages and 3 figures
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