Graduate Seminar: Indicating local structure in many-body systems

Supervisors: Prof. G. Hibbard, Prof. F. Parsch

ABSTRACT: A longstanding hypothesis is that local dynamics in many-body systems can be explained by local structure—that is, the relationship between a particle and its neighbourhood. Yet, despite the vast array of physical systems that take the form of many interacting particles, the general problem of indicating local particle structure lacks a satisfactory solution. The challenge in creating a general indicator of local structure is three-part: establishing (1) a robust means of demarcating particle neighbourhoods, (2) a suitable mathematical representation of particle neighbourhoods, and (3) a universal means of distinguishing between their geometries. Existing indicators work around these challenges by demanding prior knowledge on the particular form of structure that a given class of systems is inclined to exhibit. But the ad hoc nature of such approaches makes it impossible to compare systems from different classes. In this seminar, we discuss a mathematical (i.e. nonphysical) approach to this problem. Our approach is in principle able to perform local-structural indication in any lattice-like system of particles. We present numerical results from crystalline, quasicrystalline, and glassy settings.