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

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posted on 2023-08-04, 06:06 authored by Nathan HarshmanNathan Harshman

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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ArXiv

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http://hdl.handle.net/1961/auislandora:69962

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