Path Integral Monte Carlo Simulations of Helium: From Superfluid Droplets to Quantum Crystals
Draeger, Erik Walter
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https://hdl.handle.net/2142/31313
Description
Title
Path Integral Monte Carlo Simulations of Helium: From Superfluid Droplets to Quantum Crystals
Author(s)
Draeger, Erik Walter
Issue Date
2001
Doctoral Committee Chair(s)
Ceperley, David M.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Quantum Crystals
Monte Carlo Simulations
Helium 4
Solid Helium
Language
en
Abstract
Below Tλ = 2.17 K, bulk 4He is a superfluid and has a non-zero Bose-Einstein condensate
fraction. This work will focus primarily on how phenomena such as superfluidity,
Bose condensation and superfluid vortices are manifested in microscopic, inhomogeneous
helium systems. Path Integral Monte Carlo is a powerful method for calculating
the equilibrium properties of quantum systems at finite temperature. We have
achieved linear scaling of computer time with number of particles through the use of
neighbor lists, allowing us to simulate systems of several thousand atoms.
We have derived a local superfluid estimator and used it to examine the microscopic
superfluid response around a molecule rotating in a helium nanodroplet. We
found that the first solvation layer is well-described by a two dimensional superfluid,
with thermal excitations occuring at a lower temperature than in bulk helium. The
effective moment of inertia of a linear impurity in a helium droplet is calculated, and
compared with experimental scattering results. In addition, we calculated the vortex
formation energy for both pure droplets and droplets doped with linear impurities,
and found that the linear impurities had a negligible impact on the formation energy.
A possible spectroscopic signature of vortices in doped helium droplets was suggested.
After deriving a local estimator, we calculated the condensate fraction throughout
the free helium surface of a semi-infinite slab. These results, along with densitydensity
correlation functions, were used to characterize the surface excitations and
calculate the extent to which ripplons are present. In addition, the ripplon dispersion
relation was calculated using imaginary-time correlation functions, and found to be
lll
in good agreement with experimental results.
Finally, we have calculated the Dey be-Waller factor in solid helium for a range of
temperatures and densities, and compared the scaling behavior with the predictions
of harmonic theory. The first non-Gaussian contribution to the density distribution
was calculated.
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