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The understanding of the effect of the interactions between electrons on the metallic state which is based on the Landau's Fermi-liquid theory provides the basis for understanding metals in terms of weakly interacting quasi-particles. At zero temperature a Fermi liquid has a Fermi surface, similar to the non-interacting Fermions [1]. The low lying excitations of the Fermi liquid are called quasi-particles (or Landau quasi-particles). Landau quasi-particles consist of electrons, surrounded by a cloud of spin and charge polarization. They share the same quantum numbers as free electrons but their masses can be strongly renormalized by the back flow of the surrounding fluid [2]. When materials undergo Thermodynamical change, the energy received is in form of heat hence, its temperature rises and thereby changes in dimension [3]. Heat capacities, thermal expansion, thermal conductivities are few important properties often critical in the practical and engineering applications of solids. Nodar, and Levan, [4] generalized the Landau’s theory of Fermi liquids by incorporating the de Broglie waves diffraction. A newly derived kinetic equation of the Fermi particles is used to derive a general dispersion relation and the excitation of zero sound is studied. A new mode is found due to the quantum correction. It is shown that the zero sound can exist even in an ideal Fermi gas. They also disclose a new branch of frequency spectrum due to the weak interaction. Sykes and Brooker [5] derived exact expressions for the transport properties of a degenerate Fermi liquid. The coefficients of shear viscosity, thermal conductivity, diffusion and second viscosity were evaluated giving solution for shear viscosity, and diffusion that agree within 25% with those originally quoted. However, the thermal conductivity is reduced by a factor of about 2. The coefficient of second viscosity was shown to vary with temperature like T2. Gangadharaiah, et al. [6] consider a system of 2D fermions with a short-range interaction. A straight forward perturbation theory is shown to be ill defined even for an infinitesimally weak interaction, as the perturbative series for the self-energy diverges near the mass shell. They show that the divergences result from the interaction of fermions with the zero-sound collective mode. By re-summing the most divergent diagrams, they obtain a closed form of the self-energy near the mass shell. The spectral function exhibits a threshold feature at the onset of the emission of the zero-sound waves. They also show that the interaction ABSTRACT

Quasi-particle Contribution in Thermal Expansion and Thermal Conductivity in Metals