Coincidence Structures and Hard-Core Few-Body Interactions
Abstract
The symmetry and topology of the coincidence structure, i.e. the locus of points in configuration space corresponding to particles in the same position, plays a critical role in extracting universal properties for few-body models with hard-core interactions. The coincidence structure is a scale-invariant union of manifolds possessing rich symmetry. When there are zero-range hard-core two-body interactions, the coincidence structure forms a nodal surface for finite-energy wave functions in configuration space. More generally, it acts like a defect that changes the topology of configuration space in a way that depends on the dimension of the underlying space, the total number of particles, and the number of particles in the hard-core interaction. We show that for the specific case of three-body hard-core interactions in one-dimension, the configuration space is no longer simply-connected, providing a topological explanation for several models that exhibit anyonic behavior.
Keywords
Cite
@article{arxiv.1801.08753,
title = {Coincidence Structures and Hard-Core Few-Body Interactions},
author = {N. L. Harshman and Adam Knapp},
journal= {arXiv preprint arXiv:1801.08753},
year = {2018}
}
Comments
9 pages, 2 figures, 26 refs; submitted to Few-Body Systems as part of Workshop on Critical Stability of Quantum Few-Body Systems, Dresden 2017