We study the long-time behavior of the Schrödinger flow in a heterogeneous potential \(\lambda V\) with small intensity \(0<\lambda \ll 1\) (or alternatively at high frequencies). The main new ingredient, which we introduce in the general setting of a stationary ergodic potential, is an approximate stationary Floquet–Bloch theory that is used to put the perturbed Schrödinger operator into approximate normal form. We apply this approach to quasiperiodic potentials and establish a Nehorošev-type stability result. In particular, this ensures asymptotic ballistic transport up to a stretched exponential timescale \(\exp (\lambda ^{-\frac{1}{s}})\) for some \(s>0\). More precisely, the approximate normal form leads to an accurate long-time description of the Schrödinger flow as an effective unitary correction of the free flow. The approach is robust and generically applies to linear waves. For classical waves, for instance, this allows to extend diffractive geometric optics to quasiperiodically perturbed media.

我们研究了小强度\（0 <\ lambda \ ll 1 \）（或在高频下）的非均质势\（\ lambda V \）中Schrödinger流的长期行为。我们在稳态遍历电势的一般设置中引入的主要新成分是近似稳态Floquet-Bloch理论，该理论用于将受扰动的Schrödinger算子转化为近似正规形式。我们将这种方法应用于准电位，并建立了Nehorošev型稳定性结果。特别是，对于某些\（s> 0 \），这可确保直至拉伸的指数时标\（\ exp（\ lambda ^ {-\ frac {1} {s}}）\）的渐近弹道传输。。更准确地说，近似法线形式可以对Schrödinger流量进行长时间的准确描述，作为对自由流的有效统一校正。该方法是鲁棒的，并且通常适用于线性波。例如，对于经典波，这允许将衍射几何光学扩展到准周期性扰动的介质。