Ground state at high density

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 (1945), Kirzhnits and Nepomnyashchii (1971), and Likos et al. (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 superposed on the sites of a close-packed lattice.

Note added

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Cited by in corpus (9)

• Existence of Ground States of Nonlocal-Interaction Energies
• Demixing cascades in cluster crystals
• A simplified approach to the repulsive Bose gas from low to high densities and its numerical accuracy
• Sequential Phase Transitions and Transient Structured Fluctuations in Two-Dimensional Systems with a High-Density Kagome Lattice Phase
• Optimal lattice configurations for interacting spatially extended particles
• Effect of periodic arrays of defects on lattice energy minimizers
• Classical Density Functional Theory: The Local Density Approximation
• The total momentum of quantum fluids
• Positive-density ground states of the Gross-Pitaevskii equation