Green's functions methods for justifying quasi-particle models
Craig, Richard Anderson
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https://hdl.handle.net/2142/23992
Description
Title
Green's functions methods for justifying quasi-particle models
Author(s)
Craig, Richard Anderson
Issue Date
1966
Doctoral Committee Chair(s)
Kadanoff, L.P.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Green's Function Method
quasi-particle modles
many body systems
Language
en
Abstract
The individual particle theory of many body systems was studied
starting from a microscopic point of view. A technique which is equivalent
to a generalized thermodynamics was used to show that, under the appropriate
conditions of temperature and external field, the quasi-particle approach is
correct for three very dissimilar systemsi the normal degenerate Fermi system,
the metallic electron-phonon system, and the polaron. The fact that an
approach like this works for such dissimilar systems emphasizes the underlying
unity of the quasi-particle models.
The concept that the real t~me non-equilibrium self-energy and
the incoherent part of the density-density correlation function may be
generated as functional derivatives of a generalized thermodynamic potential
(~), together with local translational and rotational invariance and
Galilean relativity, leads to a transformation from the microscopic particle
density variables g«p,m,R,T) to those of the quasi-particle theory n (R,T).
~ - p-
It was shown that, for zero temperature, such a ~ derivability is
exact; at low temperature and for slowly varying fields, this ~ derivability
is approximately true. This was shown by a procedure which is eqUivalent
to an expansion in terms of the real scattering probability for quasiparticles.
At low temperature and for slowly varying fields, such real
scattering is very improbable and the expansion parameter is small.
Perturbation theory was used only to determine the actual size of terms
which, on physical grounds are necessarily small. As such, this approach
is non-perturbative, depending only on properties of the exact selfenergies
and correlation functions.
In addition to demonstrating that the quasi-particle models
are correct, information on the regions of validity for ~hese models is
obtained. .As by-products of these derivations, microscopic expressions for
the parameters of the quasi-particle theory and simple microscopic expressions
for the currents in degenerate Fermi systems and the electron-phonon system
are obtained.
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