Real Gas Quantum Statistics

  • Werner Ebeling
  • Thorsten Pöschel
Part of the Lecture Notes in Physics book series (LNP, volume 953)


From the classical kinetic theory of gases we know the equation of state of the ideal gas, βp = n (see Chap.  1). For real gases, the interaction forces between the molecules lead to corrections to the ideal gas equation of state. We mention the classical theory by van der Waals and the systematic expansions with respect to density, called virial expansions.


  1. Beth, E., and G.E. Uhlenbeck. 1937. The Quantum Theory of the Non-Ideal Gas. II. Behaviour at Low Temperatures. Physica 4: 915–924.ADSCrossRefGoogle Scholar
  2. Blochinzew, D.J. 1953. Quantenmechanik. Berlin: Deutscher Verlag der Wissenschaften.Google Scholar
  3. Bobrov, V.B., and S. Trigger. 2018. Bose–Einstein Condensate and Singularities of the Frequency Dispersion of the Permittivity in a Disordered Coulomb System. Theoretical and Mathematical Physics 194: 404–414.MathSciNetCrossRefGoogle Scholar
  4. Chetverikov, A.P., W. Ebeling, and M.G. Velarde. 2009. Local Electron Distributions and Diffusion in Anharmonic Lattices Mediated by Thermally Excited Solitons. European Physical Journal B 70: 217–227.ADSCrossRefGoogle Scholar
  5. Costa, É., N.H.T. Lemes, M.O. Alves, R.C.O. Sebastião, and J.P. Braga. 2013. Quantum Second Virial Coefficient Calculation for the 4He Dimer on a Recent Potential. Journal of the Brazilian Chemical Society 24: 363–368.CrossRefGoogle Scholar
  6. Ebeling, W. 1974. Statistical Derivation of the Mass Action Law or Interacting Gases and Plasmas. Physica 73: 573–584.ADSCrossRefGoogle Scholar
  7. 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
  8. 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
  9. Ebeling, W., W.D. Kraeft, and G. Röpke. 2012. On the Quantum Statistics of Bound States within the Rutherford Model of Matter. Annals of Physics 524: 311–326.CrossRefGoogle Scholar
  10. Feynman, R.P. 1972. Statistical Mechanics. Reading: Benjamin.Google Scholar
  11. Friedman, H.L. 1962. Ionic Solution Theory. New York: Interscience.Google Scholar
  12. Friedman, H.L., and W. Ebeling. 1979. Theory of Interacting and Reacting Particles. Rostocker Physikalische Manuskripte 4: 330–348.Google Scholar
  13. Hill, T.L. 1956. Statistical Mechanics. New York: McGraw Hill.zbMATHGoogle Scholar
  14. Hirschfelder, J.O., C.F. Curtis, and R.B. Bird. 1954. Molecular Theory of Gases and Liquids. New York. Wiley.zbMATHGoogle Scholar
  15. Hoffmann, H.J., and W. Ebeling. 1968a. On the Equation of State of Fully Ionized Quantum Plasmas. Physica 39: 593–598.ADSCrossRefGoogle Scholar
  16. Hoffmann, H.J., and W. Ebeling. 1968b. Quantenstatistik des Hochtemperatur-Plasmas im Thermodynamischen Gleichgewicht. II. Die Freie Energie im Temperaturbereich 106 bis 108 K. Contributions to Plasma Physics 8 (1): 43–56.Google Scholar
  17. Huang, K. 1963. Statistical Mechanics. New York: Wiley.Google Scholar
  18. Huang, K. 2001. Introduction to Statistical Physics. London: Taylor & Francis.zbMATHGoogle Scholar
  19. Kelbg, G., and H.J. Hoffmann. 1964. Quantenstatistik Realer Gase und Plasmen. Annalen der Physik 469: 310–318.ADSMathSciNetCrossRefGoogle Scholar
  20. Kilimann, K., and W. Ebeling. 1990. Energy Gap and Line Shifts for H-Like Ions in Dense Plasmas. Zeitschrift fr Naturforschung 45a: 613–617.Google Scholar
  21. Kilpatrick, J.E., W.E. Keller, E.F. Hammel, and N. Metropolis. 1954. Second Virial Coefficients of He3 and He4. Physical Review 94: 1103–1110.ADSCrossRefGoogle Scholar
  22. Kraeft, W.D., W. Ebeling, D. Kremp. 1969. Complex Representation of the Quantumstatistical Second Virial Coefficient. Physics Letters A 29: 466–467.ADSCrossRefGoogle Scholar
  23. Kraeft, W.D., D. Kremp, W. Ebeling, and G. Röpke. 1986. Quantum Statistics of Charged Particle Systems. Berlin: Akademie-Verlag.CrossRefGoogle Scholar
  24. 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. Physics Letters A 38: 167–168.ADSCrossRefGoogle Scholar
  25. Kremp, D., W.D. Kraeft, and W. Ebeling. 1971. Quantum-Statistical Second Virial Coefficient and Scattering Theory. Physica 51: 146–164.ADSMathSciNetCrossRefGoogle Scholar
  26. Kremp, D., M. Schlanges, and W.D. Kraeft. 2005. Quantum Statistics of Nonideal Plasmas. Berlin: Springer.zbMATHGoogle Scholar
  27. Landau, L.D., and E.M. Lifshitz. 1976. Statistical Physics (Part I). Moscow: Nauka.Google Scholar
  28. Landau, L.D., and E.M. Lifshitz. 1980. Statistical Physics. Oxford: Butterworth-Heinemann.zbMATHGoogle Scholar
  29. Langin, T.K., T. Strickler, N. Maksimovic, P. McQuillen, T. Pohl, D. Vrinceanu, et al. 2016. Demonstrating Universal Scaling for Dynamics of Yukawa One-Component Plasmas After an Interaction Quench. Physical Review E 93: 023201.ADSCrossRefGoogle Scholar
  30. Morita, T. 1959. Equation of State of High Temperature Plasma. Progress in Theoretical Physics 22: 757–774.ADSCrossRefGoogle Scholar
  31. Ott, T., M. Bonitz, L.G. Stanton, and M.S. Murillo. 2014. Coupling Strength in Coulomb and Yukawa One-Component Plasmas. Physics of Plasmas 21: 113704.CrossRefGoogle Scholar
  32. Pines, D., and P. Nozieres. 1966. The Theory of Quantum Liquids. New York: Benjamin.zbMATHGoogle Scholar
  33. Rogers, F.J., H.C. Graboske, and D.J. Harwood. 1970. Bound Eigenstates of the Static Screened Coulomb Potential. Physical Review A 1: 1577–1586.ADSCrossRefGoogle Scholar
  34. Slater, J.C. 1939. Introduction to Chemical Physics. New York: Mc Graw Hill.Google Scholar
  35. 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.ADSCrossRefGoogle Scholar
  36. Yukawa, H. 1935. On the Interaction of Elementary Particles. I. Proceedings of the Physico-Mathematical Society of Japan 17: 48–57.zbMATHGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Werner Ebeling
    • 1
  • Thorsten Pöschel
    • 2
  1. 1.FB PhysikHumboldt Universität zu BerlinBerlinGermany
  2. 2.Friedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany

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