The physics that result in the decoupling of a molecule from a bosonic solvent at 0 K are studied. Fixed-node diffusion Monte Carlo (FNDMC) coupled with a Genetic Algorithm is used to perform simulations of the bosonic droplets doped with various molecules. The efficacy and accuracy of this approach is tested on a strongly coupled 2-dimensional quartic oscillator with excellent results. This algorithm is then applied to 4He-CO and 4He-HCN clusters respectively in an effort to determine the factors that result in the onset of microscopic superfluidity. The decoupling of the doped molecule from the bosonic solvent is found to be, primarily, a result of the combined effect of the repulsive interaction between the helium atoms and bose symmetry. The effects of rotor size versus molecular anisotropy in a NH3 molecule seeded into a 4He droplet is studied as well. Simulations are done using the accurate rotational constants (B0=9.945 cm-1, C0=6.229 cm-1) and using "fudged" versions of the rotational constants (Bfudged=0.9945 cm-1, Cfudged=0.6229 cm-1) for the |0011〉state. The simulations done with the fudged rotational constants experience a slightly smaller reduction than those done using the accurate rotational constants. This is attributed to the importance of molecular anisotropy versus the size of larger rotational constants in molecules whose rotational constants fall in an intermediate regime.
The physics that result in the decoupling of a molecule from a bosonic solvent at 0 K are studied. Fixed-node diffusion Monte Carlo (FNDMC) coupled with a Genetic Algorithm is used to perform simulations of the bosonic droplets doped with various molecules. The efficacy and accuracy of this approach is tested on a strongly coupled 2-dimensional quartic oscillator with excellent results. This algorithm is then applied to 4He-CO and 4He-HCN clusters respectively in an effort to determine the factors that result in the onset of microscopic superfluidity. The decoupling of the doped molecule from the bosonic solvent is found to be, primarily, a result of the combined effect of the repulsive interaction between the helium atoms and bose symmetry. The effects of rotor size versus molecular anisotropy in a NH3 molecule seeded into a 4He droplet is studied as well. Simulations are done using the accurate rotational constants (B0=9.945 cm-1, C0=6.229 cm-1) and using "fudged" versions of the rotational constants (Bfudged=0.9945 cm-1, Cfudged=0.6229 cm-1) for the |0011〉state. The simulations done with the fudged rotational constants experience a slightly smaller reduction than those done using the accurate rotational constants. This is attributed to the importance of molecular anisotropy versus the size of larger rotational constants in molecules whose rotational constants fall in an intermediate regime.
The effective moment of inertia of a CO impurity molecule in 4HeN and p-(H2)N solvent clusters initially increases with N but then commences a nonclassical decrease at N=4 (4He) or N=6 (p-H2). This suggests molecule-solvent decoupling and a transition to microscopic superfluidity. However, the quantum decoupling mechanism has not been elucidated. To understand the decoupling mechanism, a one-dimensional model is introduced in which the 4He atoms are confined to a ring. This model captures the physics and shows that decoupling happens primarily because of bosonic solvent-solvent repulsion. Quantum Monte Carlo and basis set calculations suggest that the system can be modeled as a stirred Tonks-Girardeau gas. This allows the N-particle time-dependent Schrödinger equation to be solved directly. Computations of the integrated particle current reveal a threshold for stirring and current generation, indicative of superfluidity.
The first minimum appearing in molecular rotational constants as a function of helium droplet size has been previously associated with the onset of superfluidity in these finite systems. We investigate this relationship by bosonic density functional theory calculations of classical molecular rotors (OCS, N2O, CO, and HCN) interacting with the surrounding helium. The calculated rotational constants are in fair agreement with the existing experimental data, demonstrating the applicability of the theoretical model. Inspection of the spatial evolution of the global phase and density shows the increase in the rotational constant after the first minimum correlates with continuous coverage of the molecule by helium and the appearance of angular phase coherence rather than completion of the first solvent shell. We assign the observed phenomenon to quantum phase transition between a localized state and one-dimensional superfluid, which represents the onset of rotational superfluidity in small helium droplets.
In this paper, quantum fluctuations of a carbonyl sulfide molecule in helium-4 clusters are studied as a function of cluster size N in a small-to-large size regime (2<or=N<or=64). The molecular rotation of the dopant shows nonmonotonic size dependence in the range of 10<or=N<or=20, reflecting the density distribution of the helium atoms around the molecule. The size dependence on the rotational constant shows a plateau for N>or=20, which is larger than the experimental nanodroplet value. Superfluid response of the doped cluster is found to show remarkable anisotropy especially for N<or=20. The superfluid fraction regarding the axis perpendicular to the molecular axis shows a steep increase at N=10, giving the significant enhancement of the rotational fluctuation of the molecule. On the other hand, the superfluid fraction regarding the axis parallel to the molecular axis reaches 0.9 at N=5, arising from the bosonic exchange cycles of the helium atoms around the molecular axis. The anisotropy in the superfluid response is found to be the direct consequence of the configurations of the bosonic exchange cycles.
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.
Small (4)He clusters doped with various molecules allow for the study of "quantum solvation" as a function of cluster size. A peculiarity of quantum solvation is that, as the number of (4)He atoms is increased from N = 1, the solvent appears to decouple from the molecule which, in turn, appears to undergo free rotation. This is generally taken to signify the onset of "microscopic superfluidity." Currently, little is known about the quantum mechanics of the decoupling mechanism, mainly because the system is a quantum (N + 1)-body problem in three dimensions which makes computations difficult. Here, a one-dimensional model is studied in which the (4)He atoms are confined to revolve on a ring and encircle a rotating CO molecule. The Lanczos algorithm is used to investigate the eigenvalue spectrum as the number of (4)He atoms is varied. Substantial solvent decoupling is observed for as few as N = 5 (4)He atoms. Examination of the Hamiltonian matrix, which has an almost block diagonal structure, reveals increasingly weak inter-block (solvent-molecule) coupling as the number of (4)He atoms is increased. In the absence of a dopant molecule the system is similar to a Lieb-Liniger (LL) gas and we find a relatively rapid transition to the LL limit as N is increased. In essence, the molecule initially-for very small N-provides a central, if relatively weak, attraction to organize the cluster; as more (4)He atoms are added, the repulsive interactions between the identical bosons start to dominate as the solvation ring (shell) becomes more crowded which causes the molecule to start to decouple. For low N, the molecule pins the atoms in place relative to itself; as N increases the atom-atom repulsion starts to dominate the Hamiltonian and the molecule decouples. We conclude that, while the notion of superfluidity is a useful and correct description of the decoupling process, a molecular viewpoint provides complementary insights into the quantum mechanism of the transition from a molecular cluster to a quantum solvated molecule.