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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Blochinzew, D.J. 1953. Quantenmechanik. Berlin: Deutscher Verlag der Wissenschaften.
Dirac, P.A.M. 1932. Principles of Quantum Mechanics. Oxford: Clarendon Press.
Dyson, F.J. 1967. Ground-State Energy of a Finite System of Charged Particles. Journal of Mathematical Physics 8: 1538–1545.
Dyson, F.J., and A. Lenard. 1967. Stability of Matter. I. Journal of Mathematical Physics 8: 423–434.
Dyson, F.J., and A. Lenard. 1968. Stability of Matter. II. Journal of Mathematical Physics 9: 698–711.
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.
Ebeling, W., and I. Sokolov. 2005. Statistical Thermodynamics and Stochastic Theory of Nonequilibrium Systems. Singapore: World Scientific.
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.
Einstein, A. 1924. Quantentheorie des Einatomigen Idealen Gases. Sitzungsber. Preuss. Akad. Wiss. Phys.-math. Kl. 22: 261–267.
Einstein, A. 1925a. Quantentheorie des Einatomigen Idealen Gases. Zweite Abhandlung. Sitzungsber. Preuss. Akad. Wiss. Phys.-math. Kl. 23: 3–14.
Einstein, A. 1925b. Zur Quantentheorie des Idealen Gases. Sitzungsber. Preuss. Akad. Wiss. Phys.-math. Kl. 23: 18–25.
Eyring, H., J. Walter, and G.E. Kimball. 1944. Quantum Chemistry. New York: J. Wiley & Sons.
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.
Fermi, E. 1966. Molecules, Crystals and Quantum Statistics. New York: Benjamin.
Fetter, A.I., and J.D. Walecka. 1971. Quantum Theory of Many Particle Systems. New York: Mc Graw Hill.
Feynman, R.P. 1972. Statistical Mechanics. Reading Mass: Benjamin.
Fick, E. 1981. Einführung in die Grundlagen der Quantentheorie. Leipzig: Akademischer Verlag.
Hänggi, P., S. Hilbert, and J. Dunkel. 2016. Meaning of Temperature in Different Thermostatistical Ensembles. Philosophical Transactions. Royal Society of London A 374: 2064.
Hilbert, S., P. Hänggi, and J. Dunkel. 2014. Thermodynamic Laws in Isolated Systems. Physical Review E 90: 062116.
Kadanoff, L.P., and G. Baym. 1962. Quantum Statistical Mechanics. New York: Benjamin.
Klimontovich, Yu. L. 1982. Statistical Physics. Moscow: Nauka (in Russian).
Klimontovich, Yu. L. 1986. Statistical Physics. New York: Harwood.
Kraeft, W.D., D. Kremp, W. Ebeling, and G. Röpke. 1986. Quantum Statistics of Charged Particle Systems. Berlin: Akademie-Verlag.
Kremp, D., M. Schlanges, and W.D. Kraeft. 2005. Quantum Statistics of Nonideal Plasmas. Berlin: Springer.
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.
Landau, L.D., and E.M. Lifshitz. 1976. Statistical Physics (part I). Moscow: Nauka.
Landau, L.D., and E.M. Lifshitz. 1990. Statistical Physics. New York: Pergamon.
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.
Lifshitz, E.M., and L.P. Pitaevskii. 1981. Physical Kinetics. Vol. 10, Course of Theoretical Physics S. New York: Pergamon.
Machlup, S., and L. Onsager. 1953. Fluctuations and Irreversible Processes. Physics Review 91: 1512–1515.
Martin, P.C., and J. Schwinger. 1959. Theory of Many-Particle Systems I. Physics Review 115: 1342–1373.
Mishin, Y. 2015. Thermodynamic Theory of Equilibrium Fluctuations. Annals of Physics 363: 48–97.
Onsager, L. 1931a. Reciprocal Relations in Irreversible Processes. I. Physics Review 37: 405–426.
Onsager, L. 1931b. Reciprocal Relations in Irreversible Processes. II. Physics Review 38: 2265–2279.
Reichl, L.E. 1980. A Modern Course in Statistical Physics. Austin: University of Texas Press.
Slater, J.C. 1939. Introduction to Chemical Physics. New York, London: Mc Graw Hill.
Stratonovich, R.L. 1984. Nonlinear Nonequlibrium Thermodynamics. Berlin: Springer.
Taylor, G.I. 1922. Diffusion by Continuous Movements. Proceedings of the London Mathematical Society Series 2 20: 196–212.
ter Haar, D. 1995. Elements of Statistical Mechanics. Oxford: Butterworth-Heinemann.
Thirring, W.E. 1980. Lehrbuch der Mathematischen Physik. Vol. 3, Quantenmechanik von Atomen und Molekülen, Quantenmechanik großer Systeme. Berlin: Springer.
Thomas L.H. 1927. The Calculation of Atomic Fields. Mathematical Proceedings of the Cambridge Philosophical Society 23: 542–548.
Toda, M., R. Kubo, and N. Saito. 1983. Statistical Physics. Vols. I and II. Berlin: Springer.
Tolman, R. 1938. The Principles of Statistical Physics. Oxford: Oxford University Press.
von Neumann, J. 1932. Mathematische Grundlagen der Quantenmechanik. Berlin: Springer.
Zubarev, D.N., V. Morozov, and G. Röpke, eds. 1996. Statistical Mechanics of Nonequilibrium Processes. Vol. 1, Basic Concepts, Kinetic Theory. Weinheim: Wiley-VCH.
Zubarev, D.N., V. Morozov, and G. Röpke, eds. 1997. Statistical Mechanics of Nonequilibrium Processes. Vol. 2, Relaxation and Hydrodynamic Processes. Weinheim: Wiley-VCH.
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). Elements of Quantum Statistical Theory. In: Lectures on Quantum Statistics. Lecture Notes in Physics, vol 953. Springer, Cham. https://doi.org/10.1007/978-3-030-05734-3_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-05734-3_2
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)