Models for stopping of projectiles in quantum one-dimensional systems

了解物质中的辐射损伤（从材料到活组织）对于解决社会中的不同问题非常重要，包括核废料的安全储存（我们已经拥有的问题），核聚变装置新材料的设计，提高航空航天工业材料对宇宙射线的弹性，以及改进放射治疗。关于高速弹丸穿越物质的物理过程，特别是对物质中电子的影响的研究历史悠久，直到最近从第一性原理在真实材料中模拟了这些过程。然而，对于中等速度离子（约为光速的百分之一）来说，理解这些过程的最有力的范例要么局限于线性响应理论，要么局限于以均质电子液体为目标。在这个项目中，我们提出利用问题中存在的时空平移对称性，开发和探索新的周期固体（金属或绝缘体）中等速弹丸的简单模型。我们将从一维目标系统开始，它表现出一种特殊的反应，因此对今天的基本模型特别具有挑战性。

The understanding of radiation damage in matter (from materials to living tissue) is important for addressing different problems in society, including the safe storage of nuclear waste (the one we already have), the design of new materials for nuclear fusion installations, improving the resilience to cosmic rays of materials for the aerospace industry, and the improvement of radiotherapy.There is a long history of research in the physics of processes related to high-velocity projectiles traversing matter, in particular the effect on the electrons in matter, up to the recent simulation of such processes in real materials from first principles. The most powerful paradigms for understanding these processes for ions of intermediate velocities (around one hundredth of the speed of light) are however limited either to linear-response theory or to the homogeneous electron liquid as target. In this project we propose the development and exploration of new simple models for a constant-velocity projectile in a periodic solid (metal or insulator) making use of the translational symmetry in space-time present in the problem. We will start with one dimensional target systems, that display a peculiar response and therefore especially challenging to today's basic models.