Wave-functions of small quantum clusters

Marius Lewerenz

We report accurate ground state energies and structural properties for small clusters of 4He computed with the diffusion quantum Monte Carlo (DMC) method combined with high quality trial wave functions and using the recent analytical pair potential of Tang, Toennies, and Yiu [Phys. Rev. Lett. 74, 1546 (1995)]. Calculations based on the older HFD-B(He) potential are reported for comparison. The clusters are found to be extremely floppy and to be characterized by very diffuse wave functions. The DMC results for 4He2 and 4He3 are in excellent agreement with other calculations using conventional methods. 4He3 is found to have a noticeable contribution from nearly linear geometries. The internal structure of the clusters is described by a three particle correlation function which reveals a significantly non-spherical internal cluster structure. The energies for all cluster sizes are found to be slightly higher than those obtained with the HFD-B(He) pair potential. Exploratory calculations on the helium trimer indicate that the effects of three body interactions do not exceed the uncertainty margin provided by different state of the art pair potentials.

Thomas Maier, Orlando González, Mark Jarrell +1 more

E. Cheng, Michele A. McMahon, K. Birgitta Whaley

Recent quantum Monte Carlo calculations of small quantum clusters have shown that it is feasible to study their rotationally excited states directly. [M. A. McMahon, R. N. Barnett, and K. B. Whaley, J. Chem. Phys. 99, 8816 (1993).] We extend this work by sampling, from optimized variational wave functions, the current and Bose condensate distributions in (4He)7, (H2)7, and (4He)40 clusters. We demonstrate that these distributions are useful tools in identifying the location and nature of rotational excitations. With different constructions of rotational wave functions, the excitations can be either localized (as surface modes), or delocalized throughout the cluster analogous to the bulk superfluid vortex states. Condensate depletions in the excited states are observed, except for the delocalized excitation, where we find a higher condensate fraction than in the ground state.

Gayanath Fernando, James H. Davenport, ARMEN N. KOCHARIAN

Fung-kiu Chow

Igor Romanovsky, Constantine Yannouleas, Uzi Landman

The properties of a special class of correlated many-body wave functions, named rotating vortex clusters (RVCs), that preserve the total angular momentum of a small cloud of trapped rotating bosons are investigated. They have lower energy and provide a superior description for the formation of vortices compared to the mean-field Gross-Pitaevskii (GP) states that break the rotational symmetry. The GP vortex states are shown to be wave packets composed of such RVC states. Our results suggest that, for a small number of bosons, the physics is different from that of ideal Bose-Einstein condensates which characterize larger assemblies.