相干态通过避免能级交叉的非线性传输
Nonlinear Propagation of Coherent States through Avoided Energy Level Crossing
摘要：
本文研究了具有立方非线性项的一维耦合薛定谔方程系统在半经典极限下波包的传播。耦合是由非线性和潜在的，其特征值提出了一个“避免交叉”：在一个给定的点，它们之间的差距减少的半经典参数变得更小。对于沿势的本征矢量极化的相干态数据，我们证明了当波函数传播通过避免的交叉点时，在首阶本征空间之间存在跃迁。我们分析的非线性效应，这是明显的远离交叉点，但看到，在一个小的时间间隔在这一点附近，非线性的作用是可以忽略不计的领导阶，和转移概率可以计算与线性朗道-齐纳公式。
英文摘要：
We study the propagation of wave packets for a one-dimensional system of two coupled Schrödinger equations with a cubic nonlinearity, in the semi-classical limit. Couplings are induced by the nonlinearity and by the potential, whose eigenvalues present an "avoided crossing": at one given point, the gap between them reduces as the semi-classical parameter becomes smaller. For data which are coherent states polarized along an eigenvector of the potential, we prove that when the wave function propagates through the avoided crossing point, there are transitions between the eigenspaces at leading order. We analyze the nonlinear effects, which are noticeable away from the crossing point, but see that in a small time interval around this point, the nonlinearity's role is negligible at leading order, and the transition probabilities can be computed with the linear Landau-Zener formula.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
