Guardiola, R., & Navarro, J. (2011). On the Lindemann Criterion for Quantum Clusters at Very Low Temperature. J. Phys. Chem. A, 115(25), 6843–6850.
Abstract: The Lindemann criterion to discern the solid-like or liquid-like nature of a quantum cluster at T = 0 is discussed. A critical analysis of current Lindemann parameters is presented and a new parameter is proposed that is appropriate to study quantum clusters made of identical particles. A simple model wave function is introduced to fix the range of variation of these parameters. The model presents two extreme limits that correspond to either a liquid-like or a solid-like system; besides, it fulfills the Bose symmetry and also permits evaluations without symmetrization. Variational and diffusion Monte Carlo calculations are also performed for clusters of spinless bosons interacting through Lennard-Jones potentials. It is shown that the liquid-like or solid-like character of quantum clusters at zero temperature cannot be simply established in terms of a single parameter.
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Navarro, J., & Guardiola, R. (2011). Thermal Effects on Small Para-Hydrogen Clusters. Int. J. Quantum Chem., 111(2), 463–471.
Abstract: A brief review of different quantum Monte Carlo simulations of small (p-H-2)(N) clusters is presented. The clusters are viewed as a set of N structureless p-H-2 molecules, interacting via an isotropic pairwise potential. Properties as superfluidity, magic numbers, radial structure, excitation spectra, and abundance production of (p-H-2)(N) clusters are discussed and, whenever possible, a comparison with He-4(N) droplets is presented. All together, the simulations indicate that temperature has a paradoxical effect of the properties of (p-H-2)(N) clusters, as they are solid-like at high T and liquid-like at low T, due to quantum delocalization at the lowest temperature.
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Warnecke, S., Sevryuk, M. B., Ceperley, D. M., Toennies, J. P., Guardiola, R., & Navarro, J. (2010). The structure of para-hydrogen clusters. Eur. Phys. J. D, 56(3), 353–358.
Abstract: The path integral Monte Carlo calculated radial distributions of para-hydrogen clusters (p-H-2) N consisting of N = 4-40 molecules interacting via a Lennard-Jones potential at T = 1.5 K show evidence for additional peaks compared to radial distributions calculated by diffusion Monte Carlo (T = 0 K) and path integral Monte Carlo at T <= 0.5 K. The difference in structures is attributed to quantum delocalization at the lowest temperature. The new structures at finite temperatures appear to be consistent with classical structures calculated for an effective Morse potential, which in order to account for the large zero point energy, is substantially softer than the Lennard-Jones potential.
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