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arXiv · 1701.00949

Identical Wells, Symmetry Breaking, and the Near-Unitary Limit

N. L. Harshman
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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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N. L. Harshman. 2017-01-04. Identical Wells, Symmetry Breaking, and the Near-Unitary Limit. https://doi.org/10.1007/s00601-017-1214-5

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