Hostname: page-component-5c6d5d7d68-txr5j Total loading time: 0 Render date: 2024-08-16T09:47:11.419Z Has data issue: false hasContentIssue false
  • English
  • Français

Statistical Mechanics of Quantum Plasmas Path Integral Formalism

Published online by Cambridge University Press:  12 April 2016

A. Alastuey
A. Alastuey*
Affiliation:
Laboratoire de Physique. Ecole Normale Supérieure de Lyon, 69364 Lyon Cedex 07.France

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this review, we consider a quantum Coulomb fluid made of charged point particles (typically electrons and nuclei). We describe various formalisms which start from the first principles of statistical mechanics. These methods allow systematic calculations of the equilibrium quantities in some particular limits. The effective-potential method is evocated first, as well as its application to the derivation of low-density expansions. We also sketch the basic outlines of the standard many-body perturbation theory. This approach is well suited for calculating expansions at high density (for Fermions) or at high temperature. Eventually, we present the Feynman-Kac path integral representation which leads to the introduction of an auxiliary classical system made of extended objects, i.e., filaments (also called “polymers”). The familiar Abe-Meeron diagrammatic series are then generalized in the framework of this representation. The truncations of the corresponding virial-like expansions provide equations of state which are asymptotically exact in the low-density limit at fixed temperature. The usefulness of such equations for describing the inner regions of the sun is briefly illustrated.

Type
Reviews
Information
International Astronomical Union Colloquium , Volume 147: The Equation of State in Astrophysics , 1994 , pp. 43 - 77
Copyright
Copyright © Cambridge University Press 1994

References

Abe, R., Progr. Theor. Phys. 22, 213, (1959)CrossRefGoogle Scholar
Alastuey, A., Cornu, F. and Perez, A., to be published in Phys. Rev. E, (1994)Google Scholar
Alastuey, A. and Martin, Ph.A., Phys. Rev. A 40, 6485, (1989)Google Scholar
Alastuey, A. and Perez, A., Europhys. Lett. 20, 19, (1992)CrossRefGoogle Scholar
Bollé, D., Phys. Rev. A 36, 3259, (1987)CrossRefGoogle Scholar
Brydges, D. and Seiler, E., J. Stat. Phys. 42, 405, (1986)CrossRefGoogle Scholar
Chandler, D., “Studies in Statistical Mechanics”, edited by Montroll, E.W. and Lebowitz, J.L. (North Holland, Amsterdam, 1981)Google Scholar
Cohen, E.G.D. and Murphy, T.J., Phys. Fluids 12, 1404, (1969)Google Scholar
Cornu, F. and Martin, Ph.A., Phys. Rev. A 44, 4893, (1991)CrossRefGoogle Scholar
De Witt, H.E., J. Math. Phys. 3, 1216, (1962)CrossRefGoogle Scholar
De Witt, H.E., J. Math. Phys. 7, 616, (1966)Google Scholar
Dyson, F.J. and Lenard, A., J. Math. Phys. 8, 423, (1967)CrossRefGoogle Scholar
Ebeling, W., Ann. Phys. (Leipzig) 19, 104, (1967)Google Scholar
Fetter, A. and Walecka, J.D., “Quantum Theory of Many-Particle Systems” (McGraw-Hill, New York, 1971)Google Scholar
Feynman, R.P. and Hibbs, A.R., “Quantum Mechanics and Path Integrals” (McGraw-Hill, New York, 1965)Google Scholar
Gell-Mann, M. and Brueckner, K.A., Phys. Rev. 106, 364, (1957)CrossRefGoogle Scholar
Ginibre, J., “Statistical Mechanics and Quantum Field Theory “ (Les Houches Lectures, ed. by De Witt, C. and Stora, R. (Gordon and Breach, New York, 1971)Google Scholar
Jancovici, B., Physica 91 A, 152, (1978)CrossRefGoogle Scholar
Kraeft, W.D., Kremp, D., Ebeling, W. and Röpke, G., “Quantum Statistics of Charged Particle Systems” (Plenum Press, New York, 1986)Google Scholar
Lenard, A. and Dyson, F.J., J. Math. Phys. 9, 698, (1968)CrossRefGoogle Scholar
Lieb, E.H., Rev. Mod. Phys. 48, 553, (1976)Google Scholar
Lieb, E.H. and Lebowitz, J.L., Adv. Math. 9, 316, (1972)Google Scholar
Mayer, J.E., J. Chem. Phys. 18, 1426, (1950)Google Scholar
Meeron, E., J. Chem Phys. 28, 630, (1958)Google Scholar
Montroll, E.W. and Ward, J.C., Phys. Fluids 1, 55, (1958)Google Scholar
Morita, T., Prog. Theor. Phys. (Japan) 22, 757, (1959)Google Scholar
Pollock, E.L. and Hansen, J.P., Phys. Rev. A 8, 3110, (1973)Google Scholar
Rogers, F.J., Phys. Rev. A1O, 2441, (1974)Google Scholar
Salpeter, E.E., Ann. Phys.(New York) 5, 183, (1958)Google Scholar
Simon, B., “Functional Integration and Quantum Physics” (Academic, New York, 1979)Google Scholar