M. D. Miller

A Green's function method for multiple-spectra fermion systems:3He surface states on4He films

A Greens function method for multiple-spectra fermion systems is applied to3He surface states on superfluid4He films to accommodate the multiple transverse3He states. A matrix form of the Dyson equation indexed by the transverse states is inverted to obtain the Greens function matrix in terms of the self energy matrix. Results are shown through the Hartree-Fock approximation.

Fermi-liquid theory for 3He-4He thin film mixtures: Magnetic equation of state

AbstractFermi-liquid theory is adapted to describe the effective interactions of 3He adsorbed to a thin superfluid 4He film in an external magnetic field. We treat the 3He as a two-dimensional Fermi-liquid with both direct interactions and indirect interactions mediated by the film excitations, the ripplons. The Landau f-functions are state and field dependent. In this manuscript, we report on a calculation of the 3He magnetization as a function of coverage. We show that the magnetization is given as an integral over the magnetic field strength with the integrand expressed in terms of the Landau interaction functions

Competing solutions of Landau’s kinetic equation for zero sound and first sound in thin arbitrarily polarized Fermi-liquid films

f_{k_f \uparrow ,k_f \uparrow } ;f_{k_f \uparrow ,k_f \downarrow } ;f_{k_f \downarrow ,k_f \downarrow }

Calculation of third-sound velocities for superfluid4He films with3He impurities

(for clarity, we have suppressed thetransverse state indices). A few concluding comments are made about the contributions to the Landau f-functions from the direct and from the surface mediated indirect interactions as compared with the bulk situation.

The Phase of Submonolayer 4He Films Near Monolayer Completion

Third sound speeds in3He-4He thin films are sensitive to the transverse single-particle state occupied by the3He. The third sound speed in the low coverage region with the3He occupying the transverse ground-state can be understood quantitatively. The onset of occupation of the first excited transverse state is signaled by a high coverage feature in the third sound speed. Three third sound models for the high coverage region, differing in their assumptions about the spatial distribution of the excited states, are introduced. Using the experimental third sound data, these models can also be used to infer the fractional population of the3He in the first excited state as a function of coverage. It is found that the third sound analyses each predict a larger fractional population in the first excited state at monolayer completion than a recent analysis of magnetization step data taken on the same system.

Transport in thin polarized Fermi-liquid films

We examine in detail the method introduced by Sanchez-Castro, Bedell, and Wiegers (SBW) to solve Landau?s linearized kinetic equation, and compare it with the well-known standard method introduced by Abrikosov and Khalatnikov (AK). The SBW approach, hardly known, differs from AK in the way that moments are taken with respect to the angular functions of the Fourier transformed kinetic equation. We compare the SBW and AK solutions for zero-sound and first-sound propagation speeds and attenuation both analytically in the zero and full polarization limits, and numerically at arbitrary polarization using Landau parameters appropriate for thin 3He films. We find that the lesser known method not only yields results in close agreement with the standard method, but in most cases does so with far less analytic and computational effort.

Zero sound and first sound in thin arbitrarily polarized Fermi-liquid films

A new approach to the calculation of correlation energies in the random phase approximation (RPA) is introduced. The method is applied to the system of adsorbed 3He in thin 4He superfluid films. The 3He component interacts by means of the exchange of virtual surface interactions (ripplons) in addition to the usual atom-atom interaction. We report on a calculation of the RPA contribution to the 3He ground-state energy of a previously introduced model for this effective interaction called the one-ripplon-exchange potential (OREP). VOREP is manifestly frequency dependent and complex. In this paper we study the differences in the RPA contribution to the ground-state energy between the fully complex and frequency dependent VOREP and VOREP in the real, static limit.

Fermi-liquid theory for thin arbitrarily polarized3He films

The velocities of third sound in superfluid4He films containing submonolayer densities of3He are calculated from the variation of film height with the concentration of3He. The present model assumes that the population of the first-excited, transverse, surface state of the3He impurities directly increases the height of the film because these atoms are preferentially found within the film rather than on the surface. The relative populations of the ground-state and the first excited-state are calculated from a many-body, mean-field theory which takes account of the first two transverse branches of the spectra of the states. Intermolecular and one-ripplon exchange interactions are included. Graphs of the variation of third-sound velocity with3He density are given.