Several topics in quantum liquids are discussed including the elementary excitation spectrum of 3 He under pressure, spin polarized 3 He, and an early attempt to formulate a Fermi liquid theory to describe the low temperature thermodynamic and transport properties of the heavy electron system UPt3. The elementary excitation spectrum of ordinary liquid 3 He is calculated at several pressures using the polarization potential theory of Aldrich and Pines together with a simple model to describe the effect of multipair excitations. The calculated elementary excitation spectra, with no adjustable parameters, agree well with the recent experiment of Scherm et al. The effective interactions between quasi particles in fully spin polarized 3 He are obtained from physical arguments and sum rules. The interactions between two down spin impurities and that between an up and down spin are also deduced. The volume occupied by a down spin impurity is found to be 17% to 7% less than that occupied by an up· spin. Nonlocal scalar pseudopotentials of the Aldrich-Pines form are developed along with two extreme models for the momentum dependent backflow potential. The transport properties are calculated and found to be two to three orders of magnitude larger than those of the unpolarized liquid at the same density. The elementary excitation spectrum is found to be quite sensitive to the momentum dependence of the backflow potential. The regime of small polarization is considered next. Using the phenomenological model of Bedell and Sanchez-Castro together with an ansatz form for the spin flip interaction, a large increase in the singlet scattering rate as a function of polarization is obtained. The transport properties are calculated as a function of polarization and the viscosity obtained is found to be in good agreement with the recent experiment of P. Kopietz et al. Finally, an early attempt at describing the low temperature thermodynamic and transport properties of the heavy electron system UPt3 by an extension of Landau Fermi liquid theory is described. Although the Fermi surface geometry is treated naively, the transport calculations underscore the importance of electron-electron scattering in these systems.
Derivation of a reduced effective model allows for a unified treatment and discussion of the ${J}_{1}\text{\ensuremath{-}}{J}_{2}\phantom{\rule{4pt}{0ex}}S=1/2$ Heisenberg model on triangular and kagome lattices. Calculating thermodynamic quantities, i.e., the entropy
s(T) and uniform susceptibility ${\ensuremath{\chi}}_{0}(T)$, numerically on systems up to effectively
N=42 sites, we show by comparing to full-model results that low-
T properties are qualitatively well represented within the effective model. Moreover, we find in the spin-liquid regime similar variation of
s(T) and ${\ensuremath{\chi}}_{0}(T)$ in both models down to $T\ensuremath{\ll}{J}_{1}$. In particular, studied spin liquids appear to be characterized by the Wilson ratio vanishing at low
T, indicating that the low-lying singlets are dominating over the triplet excitations.