1999/07/02 by A. Rebei, Rebei, A., W. N. G. Hitchon +1
Mathematics · Physics and Astronomy · #Action (physics) #Advanced Chemical Physics Studies #Anomaly (physics) #Applied mathematics #Cold Atom Physics and Bose-Einstein Condensates #Condensed Matter (cond-mat) #Electron #Energy (signal processing) #FOS: Physical sciences #Fermi gas #First order #Ground state #Mathematics #Phase (matter) #Phase diagram #Physics #Quantum mechanics #Quantum, superfluid, helium dynamics #Random phase approximation #Statistical physics #Zero (linguistics) #Zero order #Zero temperature #Zero-point energy #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/9907025
61 pages, 20 figures
arxiv created 1999/07/02 · openalex publication_date 1999/07/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Correlated systems at both zero and nonzero temperature are treated here from a novel angle using a functional method. This functional method is an extension of the usual effective potential method. Here, however the effective action is made to depend explicitly on the correlation effects that are inherent in the physics involved. This will enable us to obtain new expressions for the free energy, the specific heat and the ground state energy. The new expansion is shown to give the expected results for the homogeneous case at zero temperature. However at non-zero temperature we are able to get new sets of diagrams that have a vanishing effect at zero temperature. To lowest order these diagrams if summed properly will solve a ln T anomaly in the specific heat of an electron gas at low temperature. We are also able to show that this method provides a very clear way to extend the RPA approximation. We calculate the effect of exchange on the ring diagrams at zero temperature and show how to include some of the ladder digrams. Our results agree well with known numerical calculations. We conclude by showing that this method is in fact a variant of the time dependent density functional method and can in principle be applied to study the effects of correlation in the nonhomogeneous case.