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Ground state configurations of systems of interacting particles in one dimension under the potential $\phi(x)=\left(1+x^4\right)^{-1}$
We build on a 1985 paper by Nijboer and Ruijgrok, and prove results about ground state configurations under the potential $\phi(x)=\left(1+x^4\right)^{-1}$ at high densities (mean number of particles per unit volume) in one dimension. In particular, we show that for densities $\rho=\frac{n}{\sqrt{2}}$ with $n \in \mathbb{N}$, the configuration that places …