Quantum theory and applications

量子力学基本上支配着微观尺度及以下的所有现象。我打算研究量子力学及其更复杂的相关量子场论中的几个问题。包括四个独立的项目：1.小量子系统的退相干。所谓的第二次量子革命正在快速展开，催生了量子通信、计算和密码学等前景看好的技术。所有这些量子技术都依赖于小系统(特别是纠缠)的量子特性，这些系统由于系统与其环境之间的相互作用而变得脆弱，从而导致退相干，这是一种衡量“量子”退化的指标。在一个项目中，我们正在研究一个可能具有“边缘态”的系统上的量子比特的退相干，这是非常有理论意义的。我们发现量子比特的退相干很大程度上依赖于边缘态的存在，因此通过测量退相干速率可以推断边缘态的存在或不存在。在第二个项目中，我们正在研究略大于一个量子比特的状态(三态系统等)中的消相干，以确定将系统与其延长相干性的环境联系起来的方法。2.轻子数破坏过程和CP破坏。我们正在(从理论的角度)研究可能发生在大型加速器上的过程，例如大型强子对撞机，它结合了两个有趣但非常罕见的性质：轻子数破坏和CP破坏。(事实上，第一个问题从未被观察到，但在一些有希望的粒子物理模型中理论上是可能的。)3.磁场存在下软组织中的粒子轨迹模拟。癌症治疗中使用的主要技术之一是放射治疗，即用电子等带电粒子轰击癌症组织。为了在破坏癌组织的同时最大限度地减少对健康组织的损害，确定剂量沉积是很重要的。完善的算法可以准确地确定带电粒子在软组织中的路径和能量沉积。一种新的成像放射治疗技术涉及到磁共振成像。这项技术中使用的磁场会影响粒子轨迹，而当前的算法并不准确；我们正在开发考虑磁场的新算法，目标是在没有磁场的情况下获得与标准算法相当的精度。4.引力、量子力学和纠缠。将量子力学和引力结合起来是理论物理的主要挑战之一。我们正在研究一个更为温和的问题：由具有量子叠加和纠缠等量子属性的系统产生的(经典)引力场，如上所述。

Quantum mechanics governs essentially all phenomena at microscopic scales and below. I intend to examine several problems in quantum mechanics and its more sophisticated relative, quantum field theory. Four independent projects are included: 1. Decoherence of small quantum systems. The so-called second quantum revolution is unfolding at a rapid pace, giving rise to promising technologies such as quantum communication, computing and cryptology. All of these quantum technologies rely on quantum properties of small systems (entanglement in particular) which are fragile due to interactions between the system and its environment, causing decoherence, a measure of the degradation of ``quantumness". In one project, we are studying decoherence of a qubit attached to a system which might have ``edge states", which are of great theoretical interest. We find that the decoherence of the qubit depends dramatically on the presence of an edge state, so by measuring the decoherence rate one can infer the presence or absence of an edge state. In a second project, we are studying decoherence in states slightly bigger than a qubit (three-state systems, etc), to determine ways to connect the system to its environment which prolong coherence. 2. Lepton number violating processes and CP violation. We are studying (from a theoretical point of view) processes which could take place at large accelerators such as the Large Hadron Collider which combine two interesting yet very rare properties: lepton number violation and CP violation. (Indeed, the first has never been observed, but it is theoretically possible in some promising particle physics models.) 3. Particle trajectory simulation in soft tissue in the presence of magnetic fields. One of the main techniques used in cancer treatment is radiotherapy, bombardment of cancerous tissue with charged particles such as electrons. In order to destroy cancerous tissue while minimizing damage to healthy tissue, it is important to determine dose deposition. Well-developed algorithms permit accurate determination of the path and energy deposition of charged particles in soft tissue. A new technique of imaging radiotherapy involves magnetic resonance imaging. The magnetic fields used in this technique affect particle trajectories and current algorithms are not accurate; we are developing new algorithms that take into account magnetic fields, the goal being to attain accuracies comparable to standard algorithms in the absence of magnetic fields. 4. Gravitation, quantum mechanics and entanglement. Combining quantum mechanics and gravitation is one of the major challenges of theoretical physics. We are studying a much more modest problem: the (classical) gravitational field created by systems which have quantum properties such as quantum superposition and entanglement, which was mentioned above.