Coincidence Structures and Hard-Core Few-Body Interactions
arXiv:1801.08753 · doi:10.1007/s00601-018-1400-0
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.
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
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