Geodesic
Permittivity and one-particle distribution functions in the thermodynamics of a Coulomb system
Teoretičeskaâ i matematičeskaâ fizika, Tome 179 (2014) no. 2, pp. 251-266 Cet article a éte moissonné depuis la source Math-Net.Ru

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Using the grand canonical distribution and the virial theorem, we show that the Gibbs thermodynamic potential of a nonrelativistic system of charged particles is uniquely determined by its permittivity and the distribution functions of electrons and nuclei without using perturbation theory. This means that consistent approximations for the permittivity and one-particle distribution functions of electrons and nuclei must be used to calculate thermodynamic functions of the Coulomb system. To construct such self-consistent approximations, we propose using a decoupling procedure based on separating the ‘`connected" and "regular" parts of the temperature Green’s functions in the equations of motion. We consider the self-consistent Hartree–Fock approximation corresponding to this procedure.
Mots-clés : Coulomb model of a substance
Keywords: permittivity, virial theorem, one-particle distribution function, temperature Green's function. 
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V. B. Bobrov. Permittivity and one-particle distribution functions in the thermodynamics of a Coulomb system. Teoretičeskaâ i matematičeskaâ fizika, Tome 179 (2014) no. 2, pp. 251-266. http://geodesic.mathdoc.fr/item/TMF_2014_179_2_a6/

[1] E. H. Lieb, R. Seiringer, The Stability of Matter in Quantum Mechanics, Cambridge Univ. Press, Cambridge, 2009 | MR | Zbl

[2] W.-D. Kraeft, D. Kremp, W. Ebeling, G. Ropke, Quantum Statistics of Charged Particle Systems, Plenum, New York, 1986

[3] L. P. Kadanoff, G. Baym, Quantum Statistical Mechanics. Green's Function Methods in Equilibrium and Nonequilibrium Problems, Benjamin, New York, 1962 | MR | Zbl

[4] A. A. Abrikosov, L. P. Gorkov, I. E. Dzyaloshinskii, Metody kvantovoi teorii polya v statisticheskoi fizike, Fizmatgiz, M., 1962 | MR | MR

[5] V. B. Bobrov, I. M. Sokolov, S. A. Trigger, Phys. Plasmas, 19:6 (2012), 062101, 8 pp. | DOI

[6] T. Matsubara, Progr. Theoret. Phys., 14:4 (1955), 351–378 | DOI | MR | Zbl

[7] A. A. Vedenov, A. I. Larkin, ZhETF, 36:4 (1959), 1133–1142 | MR | Zbl

[8] A. N. Starostin, V. K. Rerikh, ZhETF, 127:1 (2005), 186–219 | DOI

[9] D. Kremp, M. Schlanges, W.-D. Kraeft, Quantum Statistics of Nonideal Plasmas, Atomic, Optical, and Plasma Physics, 25, Springer, Berlin, 2005 | MR

[10] D. Pines, P. Nozières, The Theory of Quantum Liquids, Benjamin, New York, 1966

[11] R. Redmer, G. Röpke, Contr. Plasma Phys., 50:10 (2010), 970–985 | DOI

[12] E. Montroll, J. Ward, Phys. Fluids, 1 (1958), 55–72 | DOI | MR | Zbl

[13] Yu. G. Krasnikov, ZhETF, 53:6 (1967), 2223–2232

[14] F. J. Rogers, H. E. DeWitt, Phys. Rev. A, 8:2 (1973), 1061–1076 | DOI

[15] A. Alastuey, V. Ballenegger, F. Cornu, Ph. A. Martin, J. Stat. Phys., 130:6 (2008), 1119–1176 | DOI | MR | Zbl

[16] A. Alastuey, V. Ballenegger, Phys. Rev. E, 86:6 (2012), 066402, 20 pp. | DOI

[17] E. W. Brown, B. K. Clark, J. L. DuBois, D. M. Ceperley, Phys. Rev. Lett., 110:14 (2013), 146405, 5 | DOI

[18] Y. A. Omarbakiyeva, C. Fortmann, T. S. Ramazanov, G. Röpke, Phys. Rev. E, 82:2 (2010), 026407, 14 pp., arXiv: 1003.4459 | DOI

[19] W. Ebeling, W. D. Kraeft, G. Röpke, Contr. Plasma Phys., 52:1 (2012), 7–16 | DOI

[20] W. Ebeling, W. D. Kraeft, G. Röpke, Ann. Phys. (Berlin), 524:6007 (2012), 311–326 | DOI | Zbl

[21] V. B. Bobrov, N. I. Klyuchnikov, S. A. Triger, TMF, 89:2 (1991), 263–277 | DOI

[22] V. B. Bobrov, N. I. Klyuchnikov, S. A. Trigger, Physica A, 181:1–2 (1992), 150–172 | DOI | MR

[23] D. N. Zubarev, Neravnovesnaya statisticheskaya termodinamika, Nauka, M., 1971

[24] V. B. Bobrov, S. A. Trigger, G. J. F. van Heijst, P. P. J. M. Schram, Phys. Rev. E, 82:1 (2010), 010102(R), 3 pp. | DOI

[25] V. B. Bobrov, S. A. Trigger, A. Zagorodny, Phys. Rev. A, 82:4 (2010), 044105, 4 pp. | DOI

[26] V. B. Bobrov, J. Phys.: Cond. Matt., 2:13 (1990), 3115–3118 | DOI

[27] V. B. Bobrov, S. A. Trigger, Virial theorem and Gibbs thermodynamic potential for Coulomb systems, arXiv: 1310.7703

[28] J. M. Luttinger, J. C. Ward, Phys. Rev., 118:5 (1960), 1417–1427 | DOI | MR | Zbl

[29] M. Potthoff, M. Aichhorn, C. Dahnken, Phys. Rev. Lett., 91:20 (2003), 206402, 4 pp. | DOI

[30] M. Potthoff, M. Balzer, Phys. Rev. B, 75:12 (2007), 125112, 22 pp., arXiv: cond-mat/0610217 | DOI

[31] H. Suhl, N. Werthamer, Phys. Rev., 122:2 (1960), 359–366 | DOI | MR

[32] E. R. Caianiello (ed.), Lectures on the Many-Body Problem, v. 2, Academic Press, New York, 1964 | MR | Zbl

[33] D. N. Zubarev, UFN, 71:5 (1960), 71–116 | DOI | MR

[34] V. D. Ozrin, TMF, 4:1 (1970), 66–75 | DOI

[35] V. B. Bobrov, Teplofizika vysokikh temperatur, 32:4 (1994), 497–502

[36] V. B. Bobrov, Teplofizika vysokikh temperatur, 33:6 (1995), 867–573 | MR

[37] V. B. Bobrov, R. Redmer, G. Repke, S. A. Triger, TMF, 86:2 (1991), 300–311 | DOI

[38] V. B. Bobrov, R. Redmer, G. Repke, S. A. Triger, TMF, 86:3 (1991), 425–437 | DOI

[39] V. D. Gorobchenko, E. G. Maksimov, UFN, 130:1 (1980), 65–111 | DOI

[40] V. B. Bobrov, ZhETF, 102:6 (1992), 1808–1815