Mukherjee, RickMirasola, Anthony E.Hollingsworth, JacobWhite, Ian G.Hazzard, Kaden R.A.2018-08-172018-08-172018Mukherjee, Rick, Mirasola, Anthony E., Hollingsworth, Jacob, et al.. "Geometric representation of spin correlations and applications to ultracold systems." <i>Physical Review A,</i> 97, no. 4 (2018) American Physical Society: https://doi.org/10.1103/PhysRevA.97.043606.https://hdl.handle.net/1911/102462We provide a one-to-one map between the spin correlations and certain three-dimensional shapes, analogous to the map between single spins and Bloch vectors, and demonstrate its utility. Much as one can reason geometrically about dynamics using a Bloch vector—e.g., a magnetic field causes it to precess and dissipation causes it to shrink—one can reason similarly about the shapes we use to visualize correlations. This visualization demonstrates its usefulness by unveiling the hidden structure in the correlations. For example, seemingly complex correlation dynamics can be described as simple motions of the shapes. We demonstrate the simplicity of the dynamics, which is obscured in conventional analyses, by analyzing several physical systems of relevance to cold atoms.engArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.Journal articlePhysRevA.97.043606https://doi.org/10.1103/PhysRevA.97.043606