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

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 نشر من قبل N. L. Harshman
 تاريخ النشر 2017
  مجال البحث فيزياء
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 تأليف N.L. Harshman




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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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