Quantum and semiclassical scattering dynamics

纳米技术的进步是进入电子、原子和分子的微观领域的一个窗口。 在这个层次上，动力学是量子力学的。 对于这样的系统，从精确量子动力学的计算中可以学到很多东西。 奇特的量子现象，在我们熟悉的经典世界中是无法比拟的，可以发挥核心作用--隧穿、非绝热跃迁和共振等现象。 通过一系列屏障的调谐引起传输共振-传输概率的峰值接近1。 由于在共振之间，传输概率非常小，这种现象可能是控制单个电子电流的量子开关的基础。然而，仔细观察传输电子会发现，它很有可能会粘在势垒上，需要很长时间才能传输。 这可能会限制设备在应用中的性能。 这个问题可以通过调整屏障来克服-有效地向阵列添加抗反射涂层-使得尖锐的传输谐振变形为呈现快速传输的平滑传输带。 反射共振也是可能的。 例如，它们产生于与传输方向以外的方向上的运动相关联的量子能级之间的避免交叉。 我们建议研究避免交叉阵列的修改，以混合尖锐的反射共振到平滑的反射带，用快速反射代替缓慢的反射。 除了精确的量子计算，将提供动力学的半经典处理。 这相当于将量子动力学描述为与穿过设备的特定路径相关的简单波的干涉-包括量子能级的反射和交换。 其他的研究解决了氟+甲烷化学激光反应中粒子数反转的时间发展，以及气相有机反应的意外速率。 如需详细信息，请参阅www.chemistry.mcmaster.ca/dumont/。

Advances in nanotechnology are a window into the microscopic realm of electrons, atoms and molecules.  The dynamics, at this level, is quantum mechanical.  There is much to be learned from the computation of exact quantum dynamics for such systems.  Exotic quantum phenomena, without parallel in the familiar classical world, can play a central role - phenomena such as tunneling, nonadiabatic transition and resonance.  Tunneling through an array of barriers gives rise to transmission resonances - peaks in transmission probability to near unity.  Since between resonances, transmission probability is very small, this phenomenon could be the basis for a quantum switch which controls the current of a single electron.  However, a closer look at the transmitting electron reveals that there is a significant chance of it sticking to the barriers, and taking a long time to transmit.  This could limit the performance of the device in an application.  The problem can be overcome by adjusting the barriers - effectively adding an anti-reflection coating to the array - such that the sharp transmission resonances morph into a smooth transmission band exhibiting rapid transmission.  Reflection resonances are also possible.  For example, they arise from avoided crossings between quantum levels associated with motion in directions other than the transmission direction.  We propose to investigate the modification of avoided-crossing arrays in order to blend sharp reflection resonances into smooth reflection bands, with slow reflection replaced by rapid reflection.  In addition to accurate quantum computations, a semiclassical treatment of the dynamics will be provided.  This amounts to a description of the quantum dynamics as the interference of simple waves associated with specific paths across the device - including reflections and interchange of quantum levels.  Other studies address the time development of population inversion in the fluorine + methane chemical laser reaction, and unexpected rates of gas phase organic reactions.  See www.chemistry.mcmaster.ca/dumont/ for more information.