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Ground State at High Density

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Abstract

Weak limits as the density tends to infinity of classical ground states of integrable pair potentials are shown to minimize the mean-field energy functional. By studying the latter we derive global properties of high-density ground state configurations in bounded domains and in infinite space. Our main result is a theorem stating that for interactions having a strictly positive Fourier transform the distribution of particles tends to be uniform as the density increases, while high-density ground states show some pattern if the Fourier transform is partially negative. The latter confirms the conclusion of earlier studies by Vlasov (in J. Phys. (USSR) IX:25–40, 1945), Kirzhnits and Nepomnyashchii (in Sov. Phys. JETP 32:1191–1197, 1971), and Likos et al. (in J. Chem. Phys. 126:224502, 2007). Other results include the proof that there is no Bravais lattice among high-density ground states of interactions whose Fourier transform has a negative part and the potential diverges or has a cusp at zero. We also show that in the ground state configurations of the penetrable sphere model particles are superimposed on the sites of a close-packed lattice.

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  1. Research Institute for Solid State Physics and Optics, Hungarian Academy of Sciences, P. O. B. 49, 1525, Budapest, Hungary

    András Sütő

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  1. András Sütő
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Correspondence to András Sütő.

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Communicated by H. Spohn

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Sütő, A. Ground State at High Density. Commun. Math. Phys. 305, 657–710 (2011). https://doi.org/10.1007/s00220-011-1276-z

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