Abstract
Energy level splitting from the unitary limit of contact interactions to the near unitary limit for a few identical atoms in an effectively one-dimensional well can be understood as an example of symmetry breaking. At the unitary limit in addition to particle permutation symmetry there is a larger symmetry corresponding to exchanging the N! possible orderings of N particles. In the near unitary limit, this larger symmetry is broken, and different shapes of traps break the symmetry to different degrees. This brief note exploits these symmetries to present a useful, geometric analogy with graph theory and build an algebraic framework for calculating energy splitting in the near unitary limit.
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This article belongs to the Topical Collection “The 23rd European Conference on Few-Body Problems in Physics”.
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Harshman, N.L. Identical Wells, Symmetry Breaking, and the Near-Unitary Limit. Few-Body Syst 58, 41 (2017). https://doi.org/10.1007/s00601-017-1214-5
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DOI: https://doi.org/10.1007/s00601-017-1214-5