论文标题
高场极限中翻译不变的磁schrödinger方程的有效动力学
Effective Dynamics of Translationally Invariant Magnetic Schrödinger Equations in the High Field Limit
论文作者
论文摘要
我们研究了Schrödinger方程中具有磁性矢量电势的较大磁场限制，这些电位描述了相对于$ z $轴的翻译不变的$ b $ fields。在第一步中，使用常规的扰动理论，我们得出了解决方案的近似描述，前提是在\ \ Mathbb r $中的傅立叶变量双重二元对$ z \ to $ z \中的初始数据得到紧凑。因此，可以看到有效的动力学可产生高频振荡和较大的磁性漂移。在第二步中，我们通过使用几乎不变子空间的理论表明，这种渐近描述是在多个以上的扰动下稳定的，这些扰动消失了，这些扰动消失了。
We study the large field limit in Schrödinger equations with magnetic vector potentials describing translationally invariant $B$-fields with respect to the $z$-axis. In a first step, using regular perturbation theory, we derive an approximate description of the solution, provided the initial data is compactly supported in the Fourier-variable dual to $z\in \mathbb R$. The effective dynamics is thereby seen to produce high-frequency oscillations and large magnetic drifts. In a second step we show, by using the theory of almost invariant subspaces, that this asymptotic description is stable under polynomially bounded perturbations that vanish in the vicinity of the origin.
