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text Kadanoff, L.P. Craig, Richard Anderson 2011-05-20T18:02:20Z 2011-05-20T18:02:20Z 10000-01-01 1966 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. Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-05-20T18:02:20Z No. of bitstreams: 1 1966_craig.pdf: 4945317 bytes, checksum: 8caf84970cd209f85197aa3e34ea5b77 (MD5) Made available in DSpace on 2011-05-20T18:02:20Z (GMT). No. of bitstreams: 1 1966_craig.pdf: 4945317 bytes, checksum: 8caf84970cd209f85197aa3e34ea5b77 (MD5) Previous issue date: 1966 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-05-20T18:02:20Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:15:16-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis Thesis U of I Only 6170221 http://hdl.handle.net/2142/23992 en 1966 Richard Anderson Craig Green's Function Method quasi-particle modles many body systems Green's functions methods for justifying quasi-particle models Dissertation / Thesis Physics Physics University of Illinois at Urbana-Champaign Dissertation Ph.D.