Identical Wells, Symmetry Breaking, and the Near-Unitary Limit
arXiv:1701.00949 · doi:10.1007/s00601-017-1214-5
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 possible orderings of 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.
6 pages, 1 figure, accepted in Few-Body Systems
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