相干态的非线性绝热定理
A Nonlinear Adiabatic Theorem for Coherent States
摘要：
本文研究了具有矩阵势的一维非线性薛定谔方程在半经典极限下波包的传播。对于初始相干态沿某一特征向量极化，我们证明了非线性演化保持模式的分离，在一个标度，使非线性效应是关键的（包络方程是非线性的）。证明依赖于光谱投影仪的作用，这是兼容的非线性处理的精细几何分析。我们还证明了这些绝热波包的非线性叠加原理。
英文摘要：
We consider the propagation of wave packets for a one-dimensional nonlinear Schrodinger equation with a matrix-valued potential, in the semi-classical limit. For an initial coherent state polarized along some eigenvector, we prove that the nonlinear evolution preserves the separation of modes, in a scaling such that nonlinear effects are critical (the envelope equation is nonlinear). The proof relies on a fine geometric analysis of the role of spectral projectors, which is compatible with the treatment of nonlinearities. We also prove a nonlinear superposition principle for these adiabatic wave packets.
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