Recent measurements by Yorozu et al. (S. Yorozu, H. Fukuyama, and H. Ishimoto, Phys. Rev. B 48, 9660 (1993)) as well as by Simons and Mueller (R. Simons and R. M. Mueller, Czhechoslowak Journal of Physics Suppl. 46, 201 (1976)) have determined the effective mass of 3 He atoms in a 3 He-4 He-mixture with great accuracy. We here report theoretical calculations for the dependence of that effective mass on the 3 He concentration. Using correlated basis functions perturbation theory to infinite order to compute effective interactions in the appropriate channels, we obtain good agreement between theory and experiment.

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We study the effective mass and the Landé factor for the three-dimensional as well as the two-dimensional degenerate electron gas. The influences of specific approximations to the self-energy and the vertex, equivalently formulated in terms of static and local effective interactions, are examined, with the aim of developing a legitimate and straightforward description of realistic low-dimensional semiconductor structures. The results obtained are tested against reference data from the literature. We further apply the formalism to a Si-SiO2 metal oxide-semiconductor (MOS) structure and compare the predictions with experiment.

Ground-state properties of two-dimensional 3He- 4He mixtures are studied at zero temperature. A general argument based on the long-ranged attraction of the phonon exchange is given for the existence of 3He dimers in low-concentration mixtures with 4He. The binding energy of dimers ranges from milli- to microkelvins with increasing 4He density. By comparing the 3He impurity chemical potential in 4He with the one in pure 3He we conclude that at finite pressures 3He dimers form a mixture with 4He with a maximum solubility of approximately 3%.

We calculate the phase diagram of 3 He-4 He mixtures in two dimensions as a function of density and 3 He concentration. A number of features distinguish this system significantly from its three-dimensional counterpart. Specifically, we find that the 3 He phase consists, at low 3 He concentrations and positive pressures, of loosely bound dimers. The dimerized liquid phase separates at a 3 He concentration of 2-3 % because the chemical potential of the 3 He component in the mixture exceeds the chemical potential in the pure phase. Atomic 3 He-4 He mixtures can be found only in a metastable state in a concentration regime above 3%, where the mixture is stable against infinitesimal concentration fluctuations. The softening of concentration-fluctuation modes with decreasing 3 He concentration is accompanied by a divergence of the 3 He hydrodynamic effective mass, and the magnetic susceptibility vanishes. We verify, wherever possible, that our results are consistent with simulation data and exact estimates.