Nonlinear Double-well Schrödinger Equations in the Semiclassical Limit
Nonlinear Double-well Schrödinger Equations in the Semiclassical Limit
复制标题
半经典极限下的非线性双阱薛定谔方程
DOI：
10.1007/s10955-005-3766-x
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发表时间：
2005
影响因子：
1.6
通讯作者：
A. Sacchetti
中科院分区：
文献类型：
--
作者：
A. Sacchetti
我们考虑具有双势垒势和外部非线性局域和非局域扰动的含时薛定谔方程。在半经典极限下，与线性算子的最低本征值相关的有限维本征值空间在拍频周期的数量级内几乎不变，波函数的优势项由有限维动力系统的解给出。在局部非线性扰动的情况下，我们假设空间维度=1阶=2。
We consider time-dependent Schrödinger equations with a double well potential and an external nonlinear, both local and non-local, perturbation. In the semiclassical limit, the finite dimensional eigenspace associated to the lowest eigenvalues of the linear operator is almost invariant for times of the order of thebeating periodand the dominant term of the wavefunction is given by means of the solutions of a finite dimensional dynamical system. In the case of local nonlinear perturbation, we assume the spatial dimensiond=1 ord=2.