快速振荡的无散射非厄米特势和Kapitza稳定化的缺失
Rapidly-oscillating scatteringless non-Hermitian potentials and the absence of Kapitza stabilization
摘要：
在一般的非相对论性量子力学框架下，由于动力学（Kapitza）稳定化现象，处于快速振荡且时间平均为零的束缚势中的量子粒子会被散射甚至俘获.对于光波的散射和捕获也会发生类似的现象。这样一个显著的结果源于这样一个事实，即即使粒子不能跟随电势的快速外部振荡，这些振荡仍然能够通过有效的（尽管很小）非零电势贡献来影响平均动力学。本文在薛定谔方程的非厄米延拓的框架下，考虑了具有振荡交流振幅$f(t)$的束缚势对物质或经典波的散射和动力学稳定问题，并预言，对于一类具有单边傅立叶谱的虚振幅调制$f(t)$，振荡势被有效地抵消，也就是说，它对粒子动力学没有任何影响，与厄米特情况相反
英文摘要：
In the framework of the ordinary non-relativistic quantum mechanics, it is known that a quantum particle in a rapidly-oscillating bound potential with vanishing time average can be scattered off or even trapped owing to the phenomenon of dynamical (Kapitza) stabilization. A similar phenomenon occurs for scattering and trapping of optical waves. Such a remarkable result stems from the fact that, even though the particle is not able to follow the rapid external oscillations of the potential, these are still able to affect the average dynamics by means of an effective -albeit small- nonvanishing potential contribution. Here we consider the scattering and dynamical stabilization problem for matter or classical waves by a bound potential with oscillating ac amplitude $f(t)$ in the framework of a non-Hermitian extension of the Schrödinger equation, and predict that for a wide class of imaginary amplitude modulations $f(t)$ possessing a one-sided Fourier spectrum the oscillating potential is effectively canceled, i.e. it does not have any effect to the particle dynamics, contrary to what happens in the Hermitian case
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