Abstract
The development of a systematic statistical theory for systems with Coulomb interactions is related to characteristic problems:
-
1.
Debye’s screening problem,
-
2.
Wigner’s problem of lattice formation,
-
3.
Herzfeld’s bound state problem.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Alastuey, A., and A. Perez. 1992. Virial Expansion of the Equation of State of a Quantum Plasma. Europhysics Letters 20: 19–24.
Alastuey, A., and A. Perez. 1996. Virial Expansions for Quantum Plasmas: Fermi-Bose Statistics. Physical Review E 53: 5714–5728.
Alastuey, A., V. Ballenegger, and W. Ebeling. 2015. Comment on ‘Direct Linear Term in the Equation of State of Plasmas’ by Kraeft et al. Physical Review E 92: 047101. (see also Kraeft et al. (2015b)).
Arkhipov, Yu.V., F.B. Baimbetov, and A.E. Davletov. 2000. Thermodynamics of Dense High-Temperature Plasmas: Semiclassical Approach. The European Physical Journal D 8: 299–304.
Arkhipov, Yu.V., F.B. Baimbetov, and A.E. Davletov. 2011. Self-Consistent Chemical Model of Partially Ionized Plasmas. Physical Review E 83: 016405.
Baimbetov, F.B., M.A. Bekenov, and T.S. Ramazanov. 1995. Effective Potential of a Semiclassical Hydrogen Plasma. Physics Letters A 197: 157–158.
Barker, A.A. 1968. Monte Carlo Study of a Hydrogenous Plasma Near the Ionization Temperature. Physical Review 171: 186–188.
Barker, A.A. 1969. Radial Distribution Functions for a Hydrogenous Plasma in Equilibrium. Physical Review 179: 129–134.
Beth, E., and G.E. Uhlenbeck. 1937. The Quantum Theory of the Non-ideal Gas. II. Behaviour at Low Temperatures. Physica 4: 915–924.
Bogolyubov, N.N. 1946. Kinetic Equations. Journal of Physics 10: 265–274.
Bogolyubov, N.N. 2005–2009. Collected Papers. Vols. 1–12. Moscow: Fizmatlit.
Brillouin, L. 1931a. Die Quantenstatistik und ihre Anwendung auf die Elektronentheorie der Metalle. Berlin: Springer.
Brillouin, L. 1931b. Les statistiques quantiques et leurs applications. Paris: Presses Universitaires de France - PUF.
Brown, L.S., and L.G. Yaffe. 2001. Effective Field Theory of Highly Ionized Plasmas. Physics Reports 340: 1–164.
Debye, P., and E. Hückel. 1923. Zur Theorie der Elektrolyte. I. Gefrierpunktserniedrigung und verwandte Erscheinungen. Physikalische Zeitschrift 24: 185–206.
Deutsch, C. 1977. Nodal Expansion in a Real Matter Plasma. Physics Letters A 60: 317–318.
DeWitt, H.E. 1962. Evaluation of the Quantum-Mechanical Ring Sum with Boltzmann Statistics. Journal of Mathematical Physics 3: 1216–1228.
DeWitt, H.E. 1976. Asymptotic Form of the Classical One-Component Plasma Fluid Equation of State. Physical Review A 14: 1290–1293.
DeWitt, H.E., M. Schlanges, A.Y. Sakakura, and W.D. Kraeft. 1995. Low Density Expansion of the Equation of State for a Quantum Electron Gas. Physics Letters A 197: 326–329.
Ebeling, W. 1967. Statistische Thermodynamik der Bindungszustände in Plasmen. Annalen der Physik (Berlin) 19: 104–112.
Ebeling, W. 1968a. Ableitung der freien Energie von Quantenplasmen kleiner Dichte aus den exakten Streuphasen. Annalen der Physik (Berlin) 477: 33–39.
Ebeling, W. 1968b. The Exact Free Energy of Low Density Quantum Plasmas. Physica 40: 290–292.
Ebeling, W. 1969. Zur Quantenstatistik der Bindungszustände in Plasmen. I Cluster- Entwicklungen. Annalen der Physik (Berlin) 22: 383–391.
Ebeling, W. 1974. Statistical Derivation of the Mass Action Law or Interacting Gases and Plasmas. Physica 73: 573–584.
Ebeling, W. 2016. The Work of Baimbetov on Nonideal Plasmas and Some Recent Developments. Contributions to Plasma Physics 56: 163–175.
Ebeling, W., and G.E. Norman. 2003. Coulombic Phase Transitions in Dense Plasmas. Journal of Statistical Physics 110: 861–877.
Ebeling, W., H.J. Hoffmann, and G. Kelbg. 1967. Quantenstatistik des Hochtemperatur-Plasmas im thermodynamischen Gleichgewicht. Contributions to Plasma Physics 7: 233–248.
Ebeling, W., G. Kelbg, and K. Rohde. 1968. Binäre SLATER-Summen und Verteilungsfunktionen für quantenstatistische Systeme mit COULOMBWechselwirkung. II. Annalen der Physik (Berlin) 476 (5–6): 235–243.
Ebeling, W., W.D. Kraeft, and D. Kremp. 1976. Theory of Bound States and Ionisation Equilibrium in Plasmas and Solids. Berlin: Akademie-Verlag.
Ebeling, W., V.E. Fortov, and V.S. Filinov. 2017. Quantum Statistics of Dense Gases and Nonideal Plasmas. Springer Series in Plasma Science and Technology. Cham: Springer.
Eggert, J. 1919. Über den Dissoziationzustand der Fixsterngase. Physikalische Zeitschrift 20: 570–574.
Falkenhagen, H. 1971. Theorie der Elektrolyte. Leipzig: Hirzel.
Falkenhagen, H., and W. Ebeling. 1971. Equilibrium Properties of Ionized Dilute Electrolytes. In Ionic Interactions, ed. S. Petrucci, vol. 1, 1–59. New York/London: Academic.
Filinov, V.S., M. Bonitz, W. Ebeling, and V.E. Fortov. 2001. Thermodynamics of Hot Dense H-Plasmas: Path Integral Monte Carlo Simulations and Analytical Approximations. Plasma Physics and Controlled Fusion 43 (6): 743–759.
Filinov, A.V., M. Bonitz, and W. Ebeling. 2003. Improved Kelbg Potential for Correlated Coulomb Systems. Journal of Physics A: Mathematical and General 36 (22): 5957–5962.
Filinov, V.S., M. Bonitz, P. Levashov, V.E. Fortov, W. Ebeling, M. Schlanges, and S.W. Koch. 2003. Plasma Phase Transition in Dense Hydrogen and Electron–Hole Plasmas. Journal of Physics A: Mathematical and General 36 (22): 6069–6076.
Filinov, A.V., V.O. Golubnychiy, M. Bonitz, W. Ebeling, and J.W. Dufty. 2004. Temperature-Dependent Quantum Pair Potentials and Their Application to Dense Partially Ionized Hydrogen Plasmas. Physical Review E 70: 046411.
Fortov, V.E. 2009. Extreme States of Matter (in Russian). Moskva: Fiz-MatGis.
Fortov, V.E. 2011. Extreme States of Matter: On Earth and in the Cosmos. Berlin: Springer.
Friedman, H.L. 1962. Ionic Solution Theory. New York: Interscience.
Gombás, P. 1965. Pseudopotentiale. Fortschritte der Physik 13: 137–156.
Hansen, J.P., and I.R. McDonald. 1981. Microscopic Simulation of a Strongly Coupled Hydrogen Plasma. Physical Review A 23: 2041–2059.
Hellmann, H. 1935. A New Approximation Method in the Problem of Many Electrons. The Journal of Chemical Physics 3: 61–61.
Hemmer, P.C., H. Helge, and S. Kjelstrup Ratkje, eds. 1996. The Collected Works of Lars Onsager. Singapore: World Scientific.
Hoffmann, H.J., and W. Ebeling. 1968a. On the Equation of State of Fully Ionized Quantum Plasmas. Physica 39: 593–598.
Hoffmann, H.J., and W. Ebeling. 1968b. Quantenstatistik des Hochtemperatur-Plasmas im thermodynamischen Gleichgewicht. II. Die freie Energie im Temperaturbereich 106 bis 108 oK. Contributions to Plasma Physics 8 (1): 43–56.
Ichimaru, S. 1992. Statistical Plasma Physics. Redwood: Addison-Wesley.
Kalman, G.J., J.M. Rommel, and K. Blagoev, eds. 1998. Strongly Coupled Coulomb Systems. New York: Springer.
Kelbg, G. 1963a. Quantenstatistik der Gase mit Coulomb-Wechselwirkung. Annalen der Physik 467: 354–360.
Kelbg, G. 1963b. Theorie des Quanten-Plasmas. Annalen der Physik 467: 219–224.
Kelbg, G. 1964. Klassische statistische Mechanik der Teilchen-Mischungen mit sortenabhängigen weitreichenden zwischenmolekularenWechselwirkungen. Annalen der Physik (Leipzig) 14: 394–403.
Kelbg, G. 1972. Einige Methoden der statistischen Thermodynamik hochionisierter Plasmen, Ergebnisse der Plasmaphysik und Gaselektronik. Vol. Bd. III. Berlin: Akademie-Verlag.
Kelbg, G., and H.J. Hoffmann. 1964. Quantenstatistik realer Gase und Plasmen. Annalen der Physik 469: 310–318.
Kleinert, H. 1995. Path Integrals in Quantum Mechanics, Statistics and Polymer Physics. Berlin: Springer.
Klimontovich, Yu.L. 1982. Statistical Physics (in Russian) Moscow: Nauka.
Klimontovich, Yu.L., and W. Ebeling. 1972. Quantum Kinetic Equations for a Nonideal Gas and a Nonideal Plasma. Journal of Experimental and Theoretical Physics 36: 476–481.
Kraeft, W.D., and D. Kremp. 1968. Quantum-Statistical Mechanics of a System of Charged Particles at High Temperatures. Zeitschrift für Physik 208 (5): 475–485.
Kraeft, W.D., D. Kremp, W. Ebeling, and G. Röpke. 1986. Quantum Statistics of Charged Particle Systems. Berlin: Akademie-Verlag.
Kraeft, W.D., D. Kremp, and G. Röpke. 2015a. Direct Linear Term in the Equation of State of Plasmas. Physical Review E 91: 013108.
Kraeft, W.D., D. Kremp, and G. Röpke. 2015b. Reply to Alastuey, Ballenegger, and Ebeling 2015. Physical Review E 92: 047102.
Kremp, D., and W.D. Kraeft. 1972. Analyticity of the Second Virial Coefficient as a Function of the Interaction Parameter and Compensation Between Bound and Scattering States. Physical Review A 38: 167–168.
Kremp, D., M. Schlanges, and W.D. Kraeft. 2005. Quantum Statistics of Nonideal Plasmas. Berlin: Springer.
Landau, L.D., and E.M. Lifshitz. 1980. Statistical Physics. Oxford: Butterworth-Heinemann.
Larkin, A.I. 1960. Thermodynamic Functions of a Low-Temperature Plasma. Journal of Experimental and Theoretical Physics 11: 1363–1364.
Macke, W. 1950. Über dieWechselwirkungen im Fermi-Gas. Zeitschrift für Naturforschung A 5a: 192–208.
Mayer, J.E. 1950. The Theory of Ionic Solutions. The Journal of Chemical Physics 18: 1426–1436.
Milner, S.R. 1912. The Virial of a Mixture of Ions. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 23: 551–578.
Montroll, E., and J. Ward. 1958. Quantum Statistics of Interacting Particles. The Physics of Fluids 1: 55–72.
Morita, T. 1959. Equation of State of High Temperature Plasma. Progress of Theoretical Physics (Kyoto) 22: 757–774.
Ortner, J. 1999. Equation of States for Classical Coulomb Systems: Use of the Hubbard-Schofield Approach. Physical Review E 59: 6312–6327.
Ortner, J., I. Valuev, and W. Ebeling. 1999. Semiclassical Dynamics and Time Correlations in Two-component Plasmas. Contributions to Plasma Physics 39 (4): 311–321.
Ortner, J., I. Valuev, and W. Ebeling. 2000. Electric Microfield Distribution in Two-Component Plasmas. Theory and Simulations. Contributions to Plasma Physics 40: 555–568.
Pines, D., and P. Nozieres. 1966. The Theory of Quantum Liquids. New York: Benjamin.
Planck, M. 1924. Zur Quantenstatistik des Bohrschen Atommodells. Annalen der Physik 75: 673–684.
Riewe, K., and R. Rompe. 1938. Über die Besetzungszahlen der Elektronenterme in einem teilweise ionisierten Gas. Zeitschrift für Physik 111: 79–94.
Rohde, K., G. Kelbg, and W. Ebeling. 1968. Binäre SLATER-Summen und Verteilungsfunktionen für quantenstatistische Systeme mit COULOMBWechselwirkung. I. Annalen der Physik (Berlin) 477: 1–14.
Sadykova, S., and W. Ebeling. 2007. Electric Microfield Distributions in Dense One- and Two-component Plasmas. Contributions to Plasma Physics 47: 659–669.
Saha, M.N. 1920. Ionization in the Solar Chromosphere. Philosophical Magazine Series VI 40: 472–478.
Schmitz, G., and D. Kremp. 1967. Quantenmechanische Verteilungsfunktion für ein Elektronengas. Zeitschrift für Naturforschung A 23: 1392–1395.
Starostin, A.N., and V.C. Roerich. 2006. Bound States in Nonideal Plasmas: Formulation of the Partition Function and Application to the Solar Interior. Plasma Sources Science and Technology 15: 410–415.
Starostin, A.N., V.C. Roerich, and R.M. More. 2003. How Correct is the EOS of Weakly Nonideal Hydrogen Plasmas? Contributions to Plasma Physics 43: 369–372.
Stolzmann, W., and W. Ebeling. 1998. New Padé Approximations for the Free Charges in Two-Component Strongly Coupled Plasmas Based on the Unsöld-Berlin-Montroll Asymptotics. Physics Letters A 248: 242–246.
Storer, R.G. 1968a. Path-Integral Calculation of the Quantum-Statistical Density Matrix for Attractive Coulomb Forces. Journal of Mathematical Physics 9: 964–970.
Storer, R.G. 1968b. Radial Distribution Function for a Quantum Plasma. Physical Review 176: 326–331.
Trigger, S.A., W. Ebeling, V.S. Filinov, V.E. Fortov, and M. Bonitz. 2003. Internal Energy of High Density Hydrogen: Analytic Approximations Compared with Path Integral Monte Carlo Calculations. Zhurnal Ehksperimental’noj i Teoreticheskoj Fiziki 123: 527–542.
Trubnikov, B.A., and V.F. Elesin. 1965. Quantum Correlation Functions in a Maxwellian Plasma. Journal of Experimental and Theoretical Physics 20: 866–872.
Uhlenbeck, G.E., and E. Beth. 1936. The Quantum Theory of the Non-ideal Gas I. Deviations from the Classical Theory. Physica 3: 729–745.
Vedenov, A.A., and A.I. Larkin. 1959. Equation of State of Plasmas (in Russian) Zhurnal Ehksperimental’noj i Teoreticheskoj Fiziki 36: 1133.
von Neumann, J. 1932. Mathematische Grundlagen der Quantenmechanik. Berlin: Springer.
Wigner, E. 1934. On the Interaction of Electrons in Metals. Physical Review 46: 1002–1011.
Wigner, E. 1938. The Transition State Method. Transactions of the Faraday Society 34: 29–41.
Zamalin, V.M., G.E. Norman, and V.S. Filinov. 1977. The Monte Carlo Method in Statistical Thermodynamics (in Russian). Moscow: Nauka.
Zelener, B.V., G.E. Norman, and V.S. Filinov. 1981. Perturbation Theory and Pseudopotential in Statistical Thermodynamics (in Russian). Moscow: Nauka.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Ebeling, W., Pöschel, T. (2019). Quantum Statistics of Dilute Plasmas. In: Lectures on Quantum Statistics. Lecture Notes in Physics, vol 953. Springer, Cham. https://doi.org/10.1007/978-3-030-05734-3_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-05734-3_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-05733-6
Online ISBN: 978-3-030-05734-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)