Microscopic Approaches to Quantum Liquids in Confined Geometries

The following sections are included:

• Contents

• Preface

The following sections are included:

• Introduction

• General Observations on Confined and Inhomogeneous Liquid Helium

• Droplets

• Films

• Other Systems of Recent Interest

• Theories

• Conclusions

• References

Quantum Monte Carlo methods which work at zero temperature are reviewed and discussed. These methods are nowadays standard tools in condensed matter physics, a field where they have proven their reliability and accuracy. The present review is mainly concerned with recent results obtained by using quantum Monte Carlo for studying the energetics and structural properties of homogeneous liquid helium in different geometries.

We review the use of the path integral Monte Carlo (PIMC) methodology to the study of finite-size quantum clusters, with particular emphasis on recent applications to pure and impurity-doped ⁴He clusters. We describe the principles of PIMC, the use of the multilevel Metropolis method for sampling particle permutations, and the methods used to accurately incorporate anisotropic moleculehelium interactions into the path integral scheme. Applications to spectroscopic studies of embedded atoms and molecules are summarized, with discussion of the new concepts of local and nanoscale superfluidity that have been generated by recent PIMC studies of the impurity-doped ⁴He clusters.

The following sections are included:

• Introduction

• Variational theory of quantum fluid mixtures
  • Exact Euler equation for the pair–distribution function
    • Fermi–hypernetted–chain equations
    • Single–loop approximation
    • Euler equations in the single–loop approximation
  • Variational energy in the HNC approximation
  • Collective excitations and stability

• Correlated basis functions

• Results for dilute ³He-⁴He mixtures in 2D and 3D
  • Pure liquid ⁴He: a performance test
  • Single–impurity limit
  • Two–impurity limit
    • Bound states in two–dimensional mixtures
  • Finite–concentration mixtures in 2D

• Dynamic structure of quantum fluids
  • Equations-of-motion method
    • Least-action principle
  • Continuity equations
  • Feynman approximation
  • CBF approximation
    • Convolution approximation
    • Approximating the two-body continuity equation
    • Solving the one–body equation: dynamic response
  • Beyond the CBF approximation (“full optimization”)
    • Continuity equations revisited
    • Solving the continuity equations in momentum space
  • Results: dynamic structure and related applications
    • Phonon-roton spectrum in liquid ⁴He
    • Dynamic structure function
    • Transition currents
    • Liquid-solid phase transition

• Summary

• Acknowledgments

• References

We describe a quantitative microscopic theory of non-uniform quantum liquids to explore the structure and the dynamics of inhomogeneous quantum Uquids. Such systems are manifested, most prominently, in thin films of ⁴He adsorbed to a substrate or in helium clusters; most recent developments also look at quasi-onedimensional systems like nano-tubes, or quasi-two-dimensional systems between hectorite sheets.

The physical problem at hand is particularly well suited for highlighting the interconnections between decisive experiments and properly executed theory. We base our theoretical methods on the time-honored Jastrow-Feenberg variational theory, but we shall try to take, whenever appropriate, the “view from the top” and try to highlight the physical content behind the sometimes lengthy equations.

In this chapter we review the applications of density functional theory to configurations of ³He atoms in restricted geometries. The confinement may be imposed by an external field, like the adsorbing wells provided by planar substrates and porous environments, or can originate in the saturation properties of the many body system, as in the case of droplets containing a sufficiently large number of ³He particles. For these arrangements of fermions theoretical investigations of the ground state properties and excitations are inhibited by the restriction to a fully antisymmetric subspace of the many body Hilbert space. Density functional techniques become then advantageous instruments, which for several purposes may override the practical limitations of more fundamental methods of many-body theory. We discuss the density functional forms and parametrizations proposed by different authors, starting from the basic descriptions of the homogeneous liquids ⁴He, ³He and their mixture, and show their extensions to treat various cases of symmetry-breaking. We summarize the present experimental scenarios and density functional descriptions of helium atoms adsorbed on substrates of diverse geometries, emphasizing on the abilities of this approach to anticipate the excitation spectrum of these systems. We review the current developments concerning the energy systematics, the structural and the excitation properties of pure and doped ³He drops within density functional theory, including the case of mixed ³He-⁴He clusters with and without impurities.

The status of homogeneous cavitation in liquid helium is reviewed. Thermal and quantum regimes in pure and isotopic mixtures are described, and special attention is paid to experimental and theoretical findings together with questions that still remain open. The effect of vortices and electrons as seeds of heterogeneous nucleation is also discussed.

Neutron inelastic scattering studies of the elementary excitations in confined superfluid ⁴He are reviewed. Both recent work on helium in porous silica glass (aerogel, Vycor, etc.) and earlier work on helium films on graphite surfaces are discussed. The global picture emerging from these studies is that the three-dimensional excitations are essentially the same as in bulk helium. The characteristic feature of confined helium is the existence of additional layer modes that propagate in the first few liquid layers near the solid-liquid interface. The dispersion and gap energy of these layers modes depend on the substrate. The layer modes axe believed to be at the origin of the differences in macroscopic properties compared to bulk helium. Experiments suggest the existence of a localized condensate in Vycor.

The present review describes recent molecular beam experiments in which large ⁴He or ³He liquid droplets consisting typically of 10³ to 10⁴ atoms are produced and doped by pick-up of single atomic or molecular chromophores. The spectroscopy of these single particles has led to new detailed insight into the elementary microscopic interactions of the probe particles with their environment. In the visible the spectral features are unusually sharp with line widths comparable to those of the free molecules. The phonon wings of vibronic transitions give direct evidence that the droplets are supernuid. In the infra-red well defined rotational lines appear that indicate that the molecules rotate freely inside the Uquid. From the intensities of the sharp lines temperatures of 0.37 K and about 0.14 K are determined for ⁴He and ³He droplets, respectively. These experiments demonstrate that supernuid ⁴He droplets provide a new ultra cold uniquely gentle matrix for high resolution spectroscopy. At the same time the molecular spectra contribute new microscopic insight into the intriguing phenomenon of superfluidity. This last aspect will be emphasized in this review. Several reviews which emphasize more the new opportunities for high resolution spectroscopy, ^{1 – 4} an introductory overview ⁵ and a special issue of the Journal of Chemical Physics have recently been published. ^{6 – 8}

The following sections are included:

• Index