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Elements of Quantum Statistical Theory

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

Abstract

Quantum statistics is a many body theory describing macroscopic matter. Let us first summarize concepts of classical many body theory and subsequently concepts of many body quantum theory, just what we need in the following. After this we will proceed to the simplest quantum statistical ensembles.

References

  1. Blochinzew, D.J. 1953. Quantenmechanik. Berlin: Deutscher Verlag der Wissenschaften.Google Scholar
  2. Dirac, P.A.M. 1932. Principles of Quantum Mechanics. Oxford: Clarendon Press.Google Scholar
  3. Dyson, F.J. 1967. Ground-State Energy of a Finite System of Charged Particles. Journal of Mathematical Physics 8: 1538–1545.ADSMathSciNetCrossRefGoogle Scholar
  4. Dyson, F.J., and A. Lenard. 1967. Stability of Matter. I. Journal of Mathematical Physics 8: 423–434.ADSMathSciNetCrossRefGoogle Scholar
  5. Dyson, F.J., and A. Lenard. 1968. Stability of Matter. II. Journal of Mathematical Physics 9: 698–711.ADSMathSciNetCrossRefGoogle Scholar
  6. Ebeling, W., and D. Hoffmann. 2014. Eine Vorlage Einsteins in der Preußischen Akademie der Wissenschaften. Leibniz Online. http://www.leibnizsozietaet.de/wp-content/uploads/2014/12/EbelingHoffmann.pdf.
  7. Ebeling, W., and I. Sokolov. 2005. Statistical Thermodynamics and Stochastic Theory of Nonequilibrium Systems. Singapore: World Scientific.CrossRefGoogle Scholar
  8. Einstein, A. 1905. Über die von der Molekularkinetischen Theorie der Wärme Geforderte Bewegung von in Ruhenden Flüssigkeiten Suspendierten Teilchen. Annales de Physique 17: 549–560.CrossRefGoogle Scholar
  9. Einstein, A. 1924. Quantentheorie des Einatomigen Idealen Gases. Sitzungsber. Preuss. Akad. Wiss. Phys.-math. Kl. 22: 261–267.Google Scholar
  10. Einstein, A. 1925a. Quantentheorie des Einatomigen Idealen Gases. Zweite Abhandlung. Sitzungsber. Preuss. Akad. Wiss. Phys.-math. Kl. 23: 3–14.zbMATHGoogle Scholar
  11. Einstein, A. 1925b. Zur Quantentheorie des Idealen Gases. Sitzungsber. Preuss. Akad. Wiss. Phys.-math. Kl. 23: 18–25.zbMATHGoogle Scholar
  12. Eyring, H., J. Walter, and G.E. Kimball. 1944. Quantum Chemistry. New York: J. Wiley & Sons.Google Scholar
  13. Fermi, E. 1928. Eine Statistische Methode zur Bestimmung Einiger Eigenschaften des Atoms und ihre Anwendung auf die Theorie des Periodischen Systems der Elemente. Zeitschrift für Physik 48 (1): 73–79.ADSCrossRefGoogle Scholar
  14. Fermi, E. 1966. Molecules, Crystals and Quantum Statistics. New York: Benjamin.Google Scholar
  15. Fetter, A.I., and J.D. Walecka. 1971. Quantum Theory of Many Particle Systems. New York: Mc Graw Hill.Google Scholar
  16. Feynman, R.P. 1972. Statistical Mechanics. Reading Mass: Benjamin.Google Scholar
  17. Fick, E. 1981. Einführung in die Grundlagen der Quantentheorie. Leipzig: Akademischer Verlag.zbMATHGoogle Scholar
  18. Hänggi, P., S. Hilbert, and J. Dunkel. 2016. Meaning of Temperature in Different Thermostatistical Ensembles. Philosophical Transactions. Royal Society of London A 374: 2064.CrossRefGoogle Scholar
  19. Hilbert, S., P. Hänggi, and J. Dunkel. 2014. Thermodynamic Laws in Isolated Systems. Physical Review E 90: 062116.ADSCrossRefGoogle Scholar
  20. Kadanoff, L.P., and G. Baym. 1962. Quantum Statistical Mechanics. New York: Benjamin.zbMATHGoogle Scholar
  21. Klimontovich, Yu. L. 1982. Statistical Physics. Moscow: Nauka (in Russian).Google Scholar
  22. Klimontovich, Yu. L. 1986. Statistical Physics. New York: Harwood.Google 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., M. Schlanges, and W.D. Kraeft. 2005. Quantum Statistics of Nonideal Plasmas. Berlin: Springer.zbMATHGoogle Scholar
  25. Kubo, R. 1957. Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems. Journal of the Physical Society of Japan 12: 570–586.ADSMathSciNetCrossRefGoogle Scholar
  26. Landau, L.D., and E.M. Lifshitz. 1976. Statistical Physics (part I). Moscow: Nauka.Google Scholar
  27. Landau, L.D., and E.M. Lifshitz. 1990. Statistical Physics. New York: Pergamon.zbMATHGoogle Scholar
  28. Lieb, E.H., and W.E. Thirring. 1975. Bound for the Kinetic Energy of Fermions which proves the Stability of Matter. Physical Review Letters 35: 687–689.ADSCrossRefGoogle Scholar
  29. Lifshitz, E.M., and L.P. Pitaevskii. 1981. Physical Kinetics. Vol. 10, Course of Theoretical Physics S. New York: Pergamon.Google Scholar
  30. Machlup, S., and L. Onsager. 1953. Fluctuations and Irreversible Processes. Physics Review 91: 1512–1515.ADSMathSciNetCrossRefGoogle Scholar
  31. Martin, P.C., and J. Schwinger. 1959. Theory of Many-Particle Systems I. Physics Review 115: 1342–1373.ADSMathSciNetCrossRefGoogle Scholar
  32. Mishin, Y. 2015. Thermodynamic Theory of Equilibrium Fluctuations. Annals of Physics 363: 48–97.ADSMathSciNetCrossRefGoogle Scholar
  33. Onsager, L. 1931a. Reciprocal Relations in Irreversible Processes. I. Physics Review 37: 405–426.ADSCrossRefGoogle Scholar
  34. Onsager, L. 1931b. Reciprocal Relations in Irreversible Processes. II. Physics Review 38: 2265–2279.ADSCrossRefGoogle Scholar
  35. Reichl, L.E. 1980. A Modern Course in Statistical Physics. Austin: University of Texas Press.zbMATHGoogle Scholar
  36. Slater, J.C. 1939. Introduction to Chemical Physics. New York, London: Mc Graw Hill.Google Scholar
  37. Stratonovich, R.L. 1984. Nonlinear Nonequlibrium Thermodynamics. Berlin: Springer.Google Scholar
  38. Taylor, G.I. 1922. Diffusion by Continuous Movements. Proceedings of the London Mathematical Society Series 2 20: 196–212.CrossRefGoogle Scholar
  39. ter Haar, D. 1995. Elements of Statistical Mechanics. Oxford: Butterworth-Heinemann.zbMATHGoogle Scholar
  40. Thirring, W.E. 1980. Lehrbuch der Mathematischen Physik. Vol. 3, Quantenmechanik von Atomen und Molekülen, Quantenmechanik großer Systeme. Berlin: Springer.CrossRefGoogle Scholar
  41. Thomas L.H. 1927. The Calculation of Atomic Fields. Mathematical Proceedings of the Cambridge Philosophical Society 23: 542–548.CrossRefGoogle Scholar
  42. Toda, M., R. Kubo, and N. Saito. 1983. Statistical Physics. Vols. I and II. Berlin: Springer.zbMATHGoogle Scholar
  43. Tolman, R. 1938. The Principles of Statistical Physics. Oxford: Oxford University Press.zbMATHGoogle Scholar
  44. von Neumann, J. 1932. Mathematische Grundlagen der Quantenmechanik. Berlin: Springer.zbMATHGoogle Scholar
  45. Zubarev, D.N., V. Morozov, and G. Röpke, eds. 1996. Statistical Mechanics of Nonequilibrium Processes. Vol. 1, Basic Concepts, Kinetic Theory. Weinheim: Wiley-VCH.zbMATHGoogle Scholar
  46. Zubarev, D.N., V. Morozov, and G. Röpke, eds. 1997. Statistical Mechanics of Nonequilibrium Processes. Vol. 2, Relaxation and Hydrodynamic Processes. Weinheim: Wiley-VCH.zbMATHGoogle Scholar

Copyright information

© 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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