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The grand partition function Z ({alpha},{beta}) of a quantum system is studied, using diagrammatic representations of the perturbation expansion; La grande fonction de partition Z ({alpha},{beta}) d'un systeme quantique est etudies en utilisant des representations diagrammatiques du developpement en serie des perturbations

Abstract

The grand partition function Z ({alpha},{beta}) of a quantum system is studied, using diagrammatic representations of the perturbation expansion. For a fermions system, it is possible to show, by proper resummation, without approximations but under some 'regularity hypothesis', that Log Z ({alpha},{beta}) takes a form where, besides trivial dependences, {alpha} and {beta} only appear through a statistical factor F{sub k}{sup -} = [1 + e{sup -{alpha}}{sup +{beta}}{sup {epsilon}{sub k}{sup 0}}{sup -{beta}}{sup W{sub k}}]{sup -1}. W{sub k} is a (real) self-consistent potential, generalized to all orders and can be defined by a stationary condition on Log Z ({alpha},{beta}) under variations of F{sub k}{sup -}. The thermodynamical quantities take a form analogous to the expressions Landau introduced for the Fermi liquids. The zero temperature limit (for isotropic systems) gives back Goldstone expressions for the ground state of a system. (author) [French] La grande fonction de partition Z ({alpha},{beta}) d'un systeme quantique est etudiee en utilisant des representations diagrammatiques du developpement en serie des perturbations. Pour un systeme de fermions on peut, par des resommations adequates, sans approximations mais sous reserve d'une 'hypothese de regularite', mettre Log Z ({alpha},{beta}) sous une forme ou, en dehors de dependances triviales, {alpha} et {beta} n'interviennent que  More>>
Authors:
Dominicis, C de [1] 
  1. Commissariat a l'Energie Atomique, Saclay (France).Centre d'Etudes Nucleaires
Publication Date:
Jul 01, 1961
Product Type:
Technical Report
Report Number:
CEA-R-1873
Resource Relation:
Other Information: 54 refs
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANNIHILATION OPERATORS; BLOCH THEORY; CREATION OPERATORS; DELTA FUNCTION; FERMI GAS; FERMIONS; FREE ENTHALPY; GOLDSTONE DIAGRAMS; GROUND STATES; HAMILTONIAN FUNCTION; LANDAU QUASI PARTICLES; MANY-BODY PROBLEM; PARTICLE INTERACTIONS; PARTITION FUNCTIONS; PAULI PRINCIPLE; PERTURBATION THEORY; QUANTUM MECHANICS; SECOND QUANTIZATION; SLATER METHOD; STATISTICAL MECHANICS; TEMPERATURE ZERO K; THERMODYNAMICS; WAVE FUNCTIONS; WICK THEOREM
OSTI ID:
20972190
Research Organizations:
CEA Saclay, 91 - Gif-sur-Yvette (France)
Country of Origin:
France
Language:
French
Other Identifying Numbers:
TRN: FR07R1873001510
Availability:
Available from INIS in electronic form
Submitting Site:
FRN
Size:
282 pages
Announcement Date:
Jan 17, 2008

Citation Formats

Dominicis, C de. The grand partition function Z ({alpha},{beta}) of a quantum system is studied, using diagrammatic representations of the perturbation expansion; La grande fonction de partition Z ({alpha},{beta}) d'un systeme quantique est etudies en utilisant des representations diagrammatiques du developpement en serie des perturbations. France: N. p., 1961. Web.
Dominicis, C de. The grand partition function Z ({alpha},{beta}) of a quantum system is studied, using diagrammatic representations of the perturbation expansion; La grande fonction de partition Z ({alpha},{beta}) d'un systeme quantique est etudies en utilisant des representations diagrammatiques du developpement en serie des perturbations. France.
Dominicis, C de. 1961. "The grand partition function Z ({alpha},{beta}) of a quantum system is studied, using diagrammatic representations of the perturbation expansion; La grande fonction de partition Z ({alpha},{beta}) d'un systeme quantique est etudies en utilisant des representations diagrammatiques du developpement en serie des perturbations." France.
@misc{etde_20972190,
title = {The grand partition function Z ({alpha},{beta}) of a quantum system is studied, using diagrammatic representations of the perturbation expansion; La grande fonction de partition Z ({alpha},{beta}) d'un systeme quantique est etudies en utilisant des representations diagrammatiques du developpement en serie des perturbations}
author = {Dominicis, C de}
abstractNote = {The grand partition function Z ({alpha},{beta}) of a quantum system is studied, using diagrammatic representations of the perturbation expansion. For a fermions system, it is possible to show, by proper resummation, without approximations but under some 'regularity hypothesis', that Log Z ({alpha},{beta}) takes a form where, besides trivial dependences, {alpha} and {beta} only appear through a statistical factor F{sub k}{sup -} = [1 + e{sup -{alpha}}{sup +{beta}}{sup {epsilon}{sub k}{sup 0}}{sup -{beta}}{sup W{sub k}}]{sup -1}. W{sub k} is a (real) self-consistent potential, generalized to all orders and can be defined by a stationary condition on Log Z ({alpha},{beta}) under variations of F{sub k}{sup -}. The thermodynamical quantities take a form analogous to the expressions Landau introduced for the Fermi liquids. The zero temperature limit (for isotropic systems) gives back Goldstone expressions for the ground state of a system. (author) [French] La grande fonction de partition Z ({alpha},{beta}) d'un systeme quantique est etudiee en utilisant des representations diagrammatiques du developpement en serie des perturbations. Pour un systeme de fermions on peut, par des resommations adequates, sans approximations mais sous reserve d'une 'hypothese de regularite', mettre Log Z ({alpha},{beta}) sous une forme ou, en dehors de dependances triviales, {alpha} et {beta} n'interviennent que par l'intermediaire d'un facteur statistique F{sub k}{sup -} = [1 + e{sup -{alpha}}{sup +{beta}}{sup {epsilon}{sub k}{sup 0}}{sup -{beta}}{sup W{sub k}}]{sup -1}. W{sub k} est ici un potentiel self-consistant (reel) generalise a tous les ordres et peut etre defini par une condition de stationnarite de Log Z ({alpha},{beta}) pour des variations de F{sub k}{sup -}. Les grandeurs thermodynamiques prennent une forme analogue aux expressions que LANDAU a introduites pour les liquides de FERMI. A la limite de la temperature nulle (et pour un systeme isotrope) on retrouve terme a terme les expressions de GOLDSTONE relatives a l'etat fondamental d'un systeme. (auteur)}
place = {France}
year = {1961}
month = {Jul}
}