Skip to main content

Quantum Statistics of Dilute Plasmas

  • Chapter
  • First Online:

Part of the book series: Lecture Notes in Physics ((LNP,volume 953))

Abstract

The development of a systematic statistical theory for systems with Coulomb interactions is related to characteristic problems:

  1. 1.

    Debye’s screening problem,

  2. 2.

    Wigner’s problem of lattice formation,

  3. 3.

    Herzfeld’s bound state problem.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  • Alastuey, A., and A. Perez. 1992. Virial Expansion of the Equation of State of a Quantum Plasma. Europhysics Letters 20: 19–24.

    Article  ADS  Google Scholar 

  • Alastuey, A., and A. Perez. 1996. Virial Expansions for Quantum Plasmas: Fermi-Bose Statistics. Physical Review E 53: 5714–5728.

    Article  ADS  Google Scholar 

  • 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)).

    Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Arkhipov, Yu.V., F.B. Baimbetov, and A.E. Davletov. 2011. Self-Consistent Chemical Model of Partially Ionized Plasmas. Physical Review E 83: 016405.

    Article  ADS  Google Scholar 

  • Baimbetov, F.B., M.A. Bekenov, and T.S. Ramazanov. 1995. Effective Potential of a Semiclassical Hydrogen Plasma. Physics Letters A 197: 157–158.

    Article  ADS  Google Scholar 

  • Barker, A.A. 1968. Monte Carlo Study of a Hydrogenous Plasma Near the Ionization Temperature. Physical Review 171: 186–188.

    Article  ADS  Google Scholar 

  • Barker, A.A. 1969. Radial Distribution Functions for a Hydrogenous Plasma in Equilibrium. Physical Review 179: 129–134.

    Article  ADS  Google Scholar 

  • Beth, E., and G.E. Uhlenbeck. 1937. The Quantum Theory of the Non-ideal Gas. II. Behaviour at Low Temperatures. Physica 4: 915–924.

    Article  ADS  MATH  Google Scholar 

  • Bogolyubov, N.N. 1946. Kinetic Equations. Journal of Physics 10: 265–274.

    MathSciNet  MATH  Google Scholar 

  • Bogolyubov, N.N. 2005–2009. Collected Papers. Vols. 1–12. Moscow: Fizmatlit.

    Google Scholar 

  • Brillouin, L. 1931a. Die Quantenstatistik und ihre Anwendung auf die Elektronentheorie der Metalle. Berlin: Springer.

    Book  MATH  Google Scholar 

  • Brillouin, L. 1931b. Les statistiques quantiques et leurs applications. Paris: Presses Universitaires de France - PUF.

    MATH  Google Scholar 

  • Brown, L.S., and L.G. Yaffe. 2001. Effective Field Theory of Highly Ionized Plasmas. Physics Reports 340: 1–164.

    Article  ADS  MATH  Google Scholar 

  • Debye, P., and E. Hückel. 1923. Zur Theorie der Elektrolyte. I. Gefrierpunktserniedrigung und verwandte Erscheinungen. Physikalische Zeitschrift 24: 185–206.

    MATH  Google Scholar 

  • Deutsch, C. 1977. Nodal Expansion in a Real Matter Plasma. Physics Letters A 60: 317–318.

    Article  ADS  Google Scholar 

  • DeWitt, H.E. 1962. Evaluation of the Quantum-Mechanical Ring Sum with Boltzmann Statistics. Journal of Mathematical Physics 3: 1216–1228.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • DeWitt, H.E. 1976. Asymptotic Form of the Classical One-Component Plasma Fluid Equation of State. Physical Review A 14: 1290–1293.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Ebeling, W. 1967. Statistische Thermodynamik der Bindungszustände in Plasmen. Annalen der Physik (Berlin) 19: 104–112.

    Article  ADS  Google Scholar 

  • Ebeling, W. 1968a. Ableitung der freien Energie von Quantenplasmen kleiner Dichte aus den exakten Streuphasen. Annalen der Physik (Berlin) 477: 33–39.

    Article  ADS  Google Scholar 

  • Ebeling, W. 1968b. The Exact Free Energy of Low Density Quantum Plasmas. Physica 40: 290–292.

    Article  ADS  MATH  Google Scholar 

  • Ebeling, W. 1969. Zur Quantenstatistik der Bindungszustände in Plasmen. I Cluster- Entwicklungen. Annalen der Physik (Berlin) 22: 383–391.

    Article  ADS  MATH  Google Scholar 

  • Ebeling, W. 1974. Statistical Derivation of the Mass Action Law or Interacting Gases and Plasmas. Physica 73: 573–584.

    Article  ADS  Google Scholar 

  • Ebeling, W. 2016. The Work of Baimbetov on Nonideal Plasmas and Some Recent Developments. Contributions to Plasma Physics 56: 163–175.

    Article  ADS  Google Scholar 

  • Ebeling, W., and G.E. Norman. 2003. Coulombic Phase Transitions in Dense Plasmas. Journal of Statistical Physics 110: 861–877.

    Article  MATH  Google Scholar 

  • Ebeling, W., H.J. Hoffmann, and G. Kelbg. 1967. Quantenstatistik des Hochtemperatur-Plasmas im thermodynamischen Gleichgewicht. Contributions to Plasma Physics 7: 233–248.

    Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Ebeling, W., W.D. Kraeft, and D. Kremp. 1976. Theory of Bound States and Ionisation Equilibrium in Plasmas and Solids. Berlin: Akademie-Verlag.

    Google Scholar 

  • 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.

    MATH  Google Scholar 

  • Eggert, J. 1919. Über den Dissoziationzustand der Fixsterngase. Physikalische Zeitschrift 20: 570–574.

    Google Scholar 

  • Falkenhagen, H. 1971. Theorie der Elektrolyte. Leipzig: Hirzel.

    MATH  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  MATH  Google Scholar 

  • 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.

    Article  ADS  MATH  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Fortov, V.E. 2009. Extreme States of Matter (in Russian). Moskva: Fiz-MatGis.

    Google Scholar 

  • Fortov, V.E. 2011. Extreme States of Matter: On Earth and in the Cosmos. Berlin: Springer.

    Book  MATH  Google Scholar 

  • Friedman, H.L. 1962. Ionic Solution Theory. New York: Interscience.

    Google Scholar 

  • Gombás, P. 1965. Pseudopotentiale. Fortschritte der Physik 13: 137–156.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Hansen, J.P., and I.R. McDonald. 1981. Microscopic Simulation of a Strongly Coupled Hydrogen Plasma. Physical Review A 23: 2041–2059.

    Article  ADS  Google Scholar 

  • Hellmann, H. 1935. A New Approximation Method in the Problem of Many Electrons. The Journal of Chemical Physics 3: 61–61.

    Article  ADS  Google Scholar 

  • Hemmer, P.C., H. Helge, and S. Kjelstrup Ratkje, eds. 1996. The Collected Works of Lars Onsager. Singapore: World Scientific.

    Google Scholar 

  • Hoffmann, H.J., and W. Ebeling. 1968a. On the Equation of State of Fully Ionized Quantum Plasmas. Physica 39: 593–598.

    Article  ADS  Google Scholar 

  • 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.

    Google Scholar 

  • Ichimaru, S. 1992. Statistical Plasma Physics. Redwood: Addison-Wesley.

    MATH  Google Scholar 

  • Kalman, G.J., J.M. Rommel, and K. Blagoev, eds. 1998. Strongly Coupled Coulomb Systems. New York: Springer.

    Google Scholar 

  • Kelbg, G. 1963a. Quantenstatistik der Gase mit Coulomb-Wechselwirkung. Annalen der Physik 467: 354–360.

    Article  ADS  MathSciNet  Google Scholar 

  • Kelbg, G. 1963b. Theorie des Quanten-Plasmas. Annalen der Physik 467: 219–224.

    Article  ADS  MathSciNet  Google Scholar 

  • Kelbg, G. 1964. Klassische statistische Mechanik der Teilchen-Mischungen mit sortenabhängigen weitreichenden zwischenmolekularenWechselwirkungen. Annalen der Physik (Leipzig) 14: 394–403.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Kelbg, G. 1972. Einige Methoden der statistischen Thermodynamik hochionisierter Plasmen, Ergebnisse der Plasmaphysik und Gaselektronik. Vol. Bd. III. Berlin: Akademie-Verlag.

    Google Scholar 

  • Kelbg, G., and H.J. Hoffmann. 1964. Quantenstatistik realer Gase und Plasmen. Annalen der Physik 469: 310–318.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Kleinert, H. 1995. Path Integrals in Quantum Mechanics, Statistics and Polymer Physics. Berlin: Springer.

    Book  MATH  Google Scholar 

  • Klimontovich, Yu.L. 1982. Statistical Physics (in Russian) Moscow: Nauka.

    Google Scholar 

  • 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.

    ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Kraeft, W.D., D. Kremp, W. Ebeling, and G. Röpke. 1986. Quantum Statistics of Charged Particle Systems. Berlin: Akademie-Verlag.

    Book  Google Scholar 

  • Kraeft, W.D., D. Kremp, and G. Röpke. 2015a. Direct Linear Term in the Equation of State of Plasmas. Physical Review E 91: 013108.

    Article  ADS  Google Scholar 

  • Kraeft, W.D., D. Kremp, and G. Röpke. 2015b. Reply to Alastuey, Ballenegger, and Ebeling 2015. Physical Review E 92: 047102.

    Article  ADS  Google Scholar 

  • 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.

    Google Scholar 

  • Kremp, D., M. Schlanges, and W.D. Kraeft. 2005. Quantum Statistics of Nonideal Plasmas. Berlin: Springer.

    MATH  Google Scholar 

  • Landau, L.D., and E.M. Lifshitz. 1980. Statistical Physics. Oxford: Butterworth-Heinemann.

    MATH  Google Scholar 

  • Larkin, A.I. 1960. Thermodynamic Functions of a Low-Temperature Plasma. Journal of Experimental and Theoretical Physics 11: 1363–1364.

    Google Scholar 

  • Macke, W. 1950. Über dieWechselwirkungen im Fermi-Gas. Zeitschrift für Naturforschung A 5a: 192–208.

    Google Scholar 

  • Mayer, J.E. 1950. The Theory of Ionic Solutions. The Journal of Chemical Physics 18: 1426–1436.

    Article  ADS  Google Scholar 

  • 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.

    Article  MATH  Google Scholar 

  • Montroll, E., and J. Ward. 1958. Quantum Statistics of Interacting Particles. The Physics of Fluids 1: 55–72.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Morita, T. 1959. Equation of State of High Temperature Plasma. Progress of Theoretical Physics (Kyoto) 22: 757–774.

    Article  ADS  MATH  Google Scholar 

  • Ortner, J. 1999. Equation of States for Classical Coulomb Systems: Use of the Hubbard-Schofield Approach. Physical Review E 59: 6312–6327.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Pines, D., and P. Nozieres. 1966. The Theory of Quantum Liquids. New York: Benjamin.

    MATH  Google Scholar 

  • Planck, M. 1924. Zur Quantenstatistik des Bohrschen Atommodells. Annalen der Physik 75: 673–684.

    Article  ADS  Google Scholar 

  • Riewe, K., and R. Rompe. 1938. Über die Besetzungszahlen der Elektronenterme in einem teilweise ionisierten Gas. Zeitschrift für Physik 111: 79–94.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Sadykova, S., and W. Ebeling. 2007. Electric Microfield Distributions in Dense One- and Two-component Plasmas. Contributions to Plasma Physics 47: 659–669.

    Article  ADS  Google Scholar 

  • Saha, M.N. 1920. Ionization in the Solar Chromosphere. Philosophical Magazine Series VI 40: 472–478.

    Article  Google Scholar 

  • Schmitz, G., and D. Kremp. 1967. Quantenmechanische Verteilungsfunktion für ein Elektronengas. Zeitschrift für Naturforschung A 23: 1392–1395.

    ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Storer, R.G. 1968a. Path-Integral Calculation of the Quantum-Statistical Density Matrix for Attractive Coulomb Forces. Journal of Mathematical Physics 9: 964–970.

    Article  ADS  Google Scholar 

  • Storer, R.G. 1968b. Radial Distribution Function for a Quantum Plasma. Physical Review 176: 326–331.

    Article  ADS  Google Scholar 

  • 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.

    Google Scholar 

  • Trubnikov, B.A., and V.F. Elesin. 1965. Quantum Correlation Functions in a Maxwellian Plasma. Journal of Experimental and Theoretical Physics 20: 866–872.

    MathSciNet  MATH  Google Scholar 

  • 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.

    Article  ADS  MATH  Google Scholar 

  • Vedenov, A.A., and A.I. Larkin. 1959. Equation of State of Plasmas (in Russian) Zhurnal Ehksperimental’noj i Teoreticheskoj Fiziki 36: 1133.

    Google Scholar 

  • von Neumann, J. 1932. Mathematische Grundlagen der Quantenmechanik. Berlin: Springer.

    MATH  Google Scholar 

  • Wigner, E. 1934. On the Interaction of Electrons in Metals. Physical Review 46: 1002–1011.

    Article  ADS  MATH  Google Scholar 

  • Wigner, E. 1938. The Transition State Method. Transactions of the Faraday Society 34: 29–41.

    Article  Google Scholar 

  • Zamalin, V.M., G.E. Norman, and V.S. Filinov. 1977. The Monte Carlo Method in Statistical Thermodynamics (in Russian). Moscow: Nauka.

    Google Scholar 

  • Zelener, B.V., G.E. Norman, and V.S. Filinov. 1981. Perturbation Theory and Pseudopotential in Statistical Thermodynamics (in Russian). Moscow: Nauka.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

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

Publish with us

Policies and ethics