Models for stopping of projectiles in quantum one-dimensional systems

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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.