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

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.

arXiv comment6 pages, 1 figure, accepted in Few-Body Systems

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Cited by in corpus (5)

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• Infinite Barriers and Symmetries for a Few Trapped Particles in One Dimension
• The Goldilocks model of separable, zero-range, few-body interactions in one-dimensional harmonic traps
• Coincidence Structures and Hard-Core Few-Body Interactions
• Impact of dark states on the stationary properties of quantum particles with off-centered interactions in one dimension