Tunnelling of molecules and quantum decay

在我们的日常经验中，被困在能量威尔斯阱中的粒子只有在能量大于能垒时才能逃脱;被困在碗中的弹珠除非有足够的能量升到碗的顶部并出去，否则它会一直呆在里面。对于微观粒子，即使其能量小于势垒，粒子也有可能逃逸。这种现象被称为“隧道效应”。“隧道效应几乎只针对单个粒子进行了研究。对分子隧道效应的研究是最近才开始的。最简单的分子有两个原子，因此具有拉长的结构。分子隧穿的研究是有趣和具有挑战性的，因为为了逃离能量势垒内的限制，两个原子都需要隧穿出去。 在拟议的研究中，我们将研究如何将分子捕获在阱内，并将其从阱中隧穿出来的可能性降到最低。我们将包括分子保持在束缚态或分裂成两个原子的情况。我们的结果将与实验研究进行比较。我们将考虑分子作直线运动或作三维运动的情况。在后者中，我们将扩展我们的工作，包括隧道和反射的分子与许多未结合的状态，也就是说，在许多方面，我们有两个相互作用的原子，这是不是在一个绑定的分子状态。它将是感兴趣的，以确定的方式，其中未结合状态的影响概率的隧道和反射在三维空间。我们的研究还将包括让一个分子入射到一个随时间变化的势垒上，这使我们的工作更接近真实的系统。此外，我们将研究具有许多束缚态的分子，这也更现实。我们的最终目标是产生一个理论的图片，是补充真实的实验系统。我们还将研究一个圆柱体在重力井中的寿命;我们将计算这样一个圆柱体在倾斜和福尔斯之前保持直立的时间，这是微观圆柱体的量子力学特征。我们的工作对重要的技术进步有意义，如“量子极限静电计”和“量子逻辑门”。"

In our everyday experience, particles trapped inside energy wells can escape only if they have more energy than the energy barrier; a marble trapped in a bowl stays inside unless it has enough energy to rise to the top of the bowl and get out. For microscopic particles it is possible for the particle to escape even if its energy is less than the barrier. This phenomenon is called "tunnelling." Tunnelling has been investigated almost solely for single particles. Investigation into the tunnelling of molecules began relatively recently. The simplest molecule has two atoms and thus has an elongated structure. The study of tunnelling of molecules is interesting and challenging because, in order to escape confinement inside an energy barrier, both atoms need to tunnel out. In the proposed research we will investigate ways to trap a molecule inside a well and to minimize the probability that it can tunnel out of the trap. We will include cases where the molecule remains in a bound state or breaks up into two atoms. Our results will be compared to experimental studies. We will consider cases where the molecule moves in a straight line or the motion is in three dimensions. In the latter, we will extend our work to include tunnelling and reflection of a molecule with many unbound states; that is, many ways in which we have two interacting atoms which are not in a bound molecular state. It will be of interest to determine the manner in which the unbound states affect the probabilities of tunnelling and of reflection in three dimensions. Our study will also include having a molecule incident upon a potential barrier that changes with time, which brings our work even closer to real systems. Further, we will look into molecules having many bound states, which is also more realistic. Our ultimate goal is to generate a theoretical picture that is complementary to real experimental systems. There will also be an investigation into the lifetime of a cylinder standing in a gravity well; we will calculate the time that such a cylinder can remain upright before it tips and falls, a quantum mechanical feature of microscopic cylinders. Our work has implications for important technological advances, such as the "quantum limited electrometer" and "quantum logic gates."