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中的几个问题，以及它更为复杂的相关理论——量子场论。包括四个独立项目：小量子系统的退相干。所谓的第二次量子革命正在迅速展开，催生了量子通信、计算和密码学等有前途的技术。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，由于系统与其环境之间的相互作用，这些小系统是脆弱的，会导致退相干，这是“量子化”退化的一种度量。在一个项目中，我们正在研究一个量子比特与一个可能具有“边缘状态”的系统的退相干，这是一个非常有理论意义的问题。我们发现量子比特的退相干很大程度上取决于边缘状态的存在，因此通过测量退相干率可以推断边缘状态的存在或不存在。在第二个项目中，我们正在研究稍微大于量子位的状态（三态系统等）的退相干，以确定将系统与其环境连接起来的方法，从而延长相干性。2. 轻子数违反过程和CP违反。我们正在（从理论角度）研究可能发生在大型加速器（如大型强子对撞机）上的过程，这些过程结合了两个有趣但非常罕见的性质：轻子数违反和CP违反。（事实上，第一种现象从未被观测到，但在一些有前景的粒子物理模型中，理论上是可能的。）3. 磁场作用下软组织粒子轨迹模拟。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组织。为了在破坏癌变组织的同时尽量减少对健康组织的损害，确定剂量沉积是很重要的。完善的算法允许精确的路径和能量沉积的带电粒子在软组织的测定。磁共振成像是一种新的成像放射治疗技术。该技术中使用的磁场影响粒子轨迹，目前的算法不准确；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。将量子力学与万有引力相结合是理论物理学的主要挑战之一。我们正在研究一个更温和的问题：（经典的）引力场是由具有量子特性的系统产生的，比如上面提到的量子叠加和纠缠。

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.