Title: | Finite temperature contributions to the thermodynamic properties of a normal fermi liquid |
Author(s): | Carneiro, Gilson Matheus |
Director of Research: | Pethick, C.J. |
Doctoral Committee Chair(s): | Pethick, C.J. |
Doctoral Committee Member(s): | Klein, Miles V.; Ginsberg, Donald M.; Ravenhall, David G. |
Department / Program: | Physics |
Discipline: | Physics |
Degree Granting Institution: | University of Illinois at Urbana-Champaign |
Degree: | Ph.D. (doctoral) |
Genre: | Dissertation |
Subject(s): | Fermi liquids |
Abstract: | Landau Fermi liquid theory and microscopic theory are used to investigate finite-temperature contributions to the thermodynamic properties of a normal Fermi liquid . The contribution from long wavelength spin and density fluctuations to the total energy is expressed in terms of the energy of interaction of a quasiparticle and a quasihole with small total momentum. The interaction energy is related to the scattering amplitude , which is known in terms of Landau parameters . By functional differentiation of the expression for the total energy the quasiparticle energy and the Landau quasiparticle interaction are calculated . It is shown that for small q the spin-symmetric quasiparticle interaction fs p, p+q has a term varying as (p x q)^2 which gives rise to a T^3ln(T) term in the specific heat. The coefficient of this T^3lnT term is then evaluated in terms of Landau parameters . We also calculate the spin-antisymmetric quasiparticle interaction f^a p, p+q and show that, for the case when Fo^s and Fo^a are the only nonzero Landau paremeters, there are no T^2ln(T) terms in the magnetic susceptibility.
Starting from the expression for the thermodynamic potential as a functional of the renormalized single particle propagator we derive microscopic expressions for the thermodynamic functions. From this we obtain the entropy as the sum of a "dynamical quasi particle contribution", plus a correction term. When the width of the single particle states can be neglected the dynamical quasiparticle contribution to the entropy is identical to the entropy of a system of independent quasiparticles whose energies are given by the poles of the single particle propagator. We discuss the correction term, which comes from terms in perturbation theory having vanishing energy denominators, and develop methods for evaluating the leading contributions to it at low temperatures. We show that the microscopic calculations give results identical to the Landau theory calculations, and also discuss the difference between the statistical quasiparticle energy, defined as a functional derivative, and the dynamical quasiparticle energy, given by the pole of the single-particle propagator. |
Issue Date: | 1973 |
Publisher: | Department of Physics. College of Engineering. Graduate College. University of Illinois at Urbana-Champaign. |
Genre: | Dissertation / Thesis |
Type: | Text |
Language: | English |
URI: | http://hdl.handle.net/2142/55618 |
Rights Information: | Copyright 1973 Gilson Matheus Carneiro |
Date Available in IDEALS: | 2014-10-30 |