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Foundations of Statistical Mechanics pp 161–196Cite as

External Fields

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Part of the book series: Fundamental Theories of Physics ((FTPH,volume 19))

Abstract

In this chapter we shall take the first step toward introducing interactions into the many body system. The study of particle-particle interactions will be deferred until the next chapter, while here we investigate some aspects of particle-field interactions. Essentially, the model is that of otherwise-free particles in the presence of external fields. Application of such fields often connotes a scenario in which the system is driven from equilibrium. This is certainly the case for time-dependent perturbing fields, but their study will not be taken up until Volume II. Here the system is presumed to remain in thermal equilibrium.

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References

  • Abramowitz, M., and I.A. Stegun (eds.): 1964, Handbook of Mathematical Functions, AMS 55,Natl. Bur. of Stds., Washington

    MATH  Google Scholar 

  • Baierlein, R.: 1971, Atoms and Information Theory, Freeman, San Francisco.

    Google Scholar 

  • Bardeen, J., L. Cooper, and J. Schrieffer: 1957, ‘Theory of Superconductivity’, Phys. Rev. 108, 1175.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Bjorken, J.D., and S.D. Drell: 1964, Relativistic Quantum Mechanics, McGraw-Hill, New York.

    Google Scholar 

  • Bohr, N.:1911, ‘Studier over metallernes elektrontheori’, Ph.D thesis, Copenhagen (unpublished).

    Google Scholar 

  • Canuto, V., and H.Y. Chiu: 1972, ‘Intense Magnetic Fields in Astrophysics’, in H.Y. Chiu and A. Muriel (eds.),Stellar Evolution, M.I.T. Press, Cambridge, MA, Chap.21.

    Google Scholar 

  • Chudnovsky, E.M.: 1981, ‘Magnetic Susceptibility of Relativistic Fermi Gas’, J. Phys. A: Math. Gen. 14, 2091.

    Article  ADS  Google Scholar 

  • Darwin, C.G.: 1930, ‘The Diamagnetism of the Free Electron’, Proc. Camb. Phil. Soc. 27, 86.

    Article  ADS  Google Scholar 

  • de Haas, W. J., and P.M. van Alphen: 1930, ‘The Dependence of the Susceptibility of DiamagneticMetals on the Field’, Proc. Acad. Amsterdam 33, 680, 1106.

    Google Scholar 

  • de Haas, W.J., and P.M. van Alphen: 1932, ‘The Dependence of the Susceptibility of BismuthSingle Crystals upon the Field’, Proc. Acad. Amsterdam 35, 454.

    Google Scholar 

  • Delsante, A.E., and N.E. Frankel: 1979, ‘Relativistic Paramagnetism: Quantum Statistics’, Phys. Rev. D 20, 1795.

    Article  ADS  Google Scholar 

  • Erdélyi, A. (ed.): 1953, Higher Transcendental Functions, Vol.1, McGraw-Hill, New York, p.32.

    Google Scholar 

  • Erdélyi, A. (ed.): 1954, Table of Integral Transforms, Vol.1, McGraw-Hill, New York, p.312.

    Google Scholar 

  • Evans, R.: 1979, ‘The Nature of the Liquid-Vapour Interface and Other Topics in the StatisticalMechanics of Non-Uniform Classical Fluids’, Adv. Physics 28, 143.

    Article  ADS  Google Scholar 

  • Felderhof, B.U., and S.P. Raval: 1975, ‘Diamagnetism of a Confined Electron Gas’, Physica 82a, 151.

    MathSciNet  ADS  Google Scholar 

  • Fisher, M.E.: 1964, ‘The Free Energy of a Macroscopic System’, Arch. Rati. Mech. Anal. 17, 377.

    Google Scholar 

  • Frankel, N.E., G.I. Opat, and J.J. Spitzer: 1967, ‘Exact Statistical Mechanics of a RelativisticMagnetic Anomaly’, Phys. Letters 25A, 716.

    ADS  Google Scholar 

  • Friar, J.L., and S. Fallieros: 1981, ‘Diamagnetism, Gauge Transformations, and Sum Rules’, Am. J. Phys. 49, 847.

    Article  ADS  Google Scholar 

  • Goldstein, L.: 1941, ‘On Some Points of the Bose-Einstein Condensation’, J. Chem. Phys. 9, 273.

    Article  ADS  Google Scholar 

  • Grandy, W.T., Jr.: 1983, ‘Pauli Paramagnetism Revisited’, Rev. Bras. Fis. 13, 469.

    Google Scholar 

  • Herring, C.: 1966, ‘Exchange Interactions among Itinerant Electrons’, in G.T. Rado and H. Suhl(eds.), Magnetism, Vol.4, Academic Press, New York, Chap.5.

    Google Scholar 

  • Jancovici, B.: 1969, ‘Radiative Correction to the Ground-State Energy of an Electron in an IntenseMagnetic Field’, Phys. Rev. 187, 2275.

    Article  ADS  Google Scholar 

  • Lamb, W.E., Jr., and A. Nordsieck: 1941, ‘On the Einstein Condensation Phenomenon’, Phys. Rev. 59, 677.

    Article  ADS  Google Scholar 

  • Landau, L.: 1930, ‘Diamagnetismus der Metalle’, Z. Phys. 64, 629.

    Article  ADS  Google Scholar 

  • Lebowitz, J.L., and J.K. Percus: 1963, ‘Statistical Thermodynamics of Nonuniform Fluids’, J. Math. Phys. 4, 116.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Lee, H. J., V. Canuto, H.Y. Chiu, and C. Chiuderi: 1969, ‘New State of Ferromagnetism in Degenerate Electron Gas and Magnetic Fields in Collapsed Bodies’, Phys. Rev. Letters 23, 390.

    Article  ADS  Google Scholar 

  • Lifshitz, I.M. and A.M. Kosevich: 1954, ‘K teorii effekta de Haasa-van Afena dlya chastits sproizvoluym zakonom dispersii’, Doklady Akad. Nauk. (U.S.S.R.) 96, 963.

    Google Scholar 

  • May, R.M.: 1965, ‘Magnetic Properties of Charged Ideal Quantum Gases in n Dimensions’, J. Math. Phys. 6, 1462.

    Article  ADS  Google Scholar 

  • Mermin, N.D.: 1965, thermal Properties of the Inhomogeneous Electron Gas’, Phys. Rev. 137, A1441.

    Article  MathSciNet  ADS  Google Scholar 

  • Newton, R.G.: 1971, ‘Atoms in Superstrong Magnetic Fields’, Phys. Rev. D 3, 626.

    Article  ADS  Google Scholar 

  • Onsager, L.: 1952, ‘Interpretation of the de Haas-van Alphen Effect’, Phil. Mag. 43, 1006.

    Google Scholar 

  • Pauli, W.: 1927, ‘Uber Geisentartung und Paramagnetisms’, Z. Phys. 41, 81.

    Article  ADS  Google Scholar 

  • Peierls, R.: 1933, ‘Zur Theorie der Diamagnetismus von Leitungselektronen.II. Starke Magnetfelder’, Z. Phys. 81, 186.

    Article  ADS  MATH  Google Scholar 

  • Rainville, E.D.: 1945, ‘The Contiguous Function Relations for p F q with Applications to Bateman’s J%’ v and Rice’s H(ζ,р,v)’, Bull. Am. Math. Soc. 51, 714.

    Article  MathSciNet  MATH  Google Scholar 

  • Rainville, E.D.: 1960, Special Functions, Macmillan, New York, Chap.5.

    MATH  Google Scholar 

  • Rehr, J.J., and N.D. Mermin: 1970, ‘Condensation of the Rotating Two-Dimensional Ideal Bose Gas’, Phys. Rev. B 1, 3160.

    Article  ADS  Google Scholar 

  • Robinson, J.E.: 1951, ‘Note on the Bose-Einstein Integral Functions’, Phys. Rev. 83, 678.

    Article  ADS  MATH  Google Scholar 

  • Rosa, S.G., and W.T. Grandy, Jr.: 1973, ‘The Magnetic Properties of Ideal Quantum Gases’, Rev. Bras. Fis. 3, 537.

    Google Scholar 

  • Scalapino, D.J.: 1961, ‘Irreversible Statistical Mechanics’, Ph.D thesis, Stanford Univ. (unpublished).

    Google Scholar 

  • Sondheimer, E.H., and A.H. Wilson: 1951, ‘The Diamagnetism of Free Electrons’, Proc. Roy. Soc. (London) A210, 173.

    ADS  Google Scholar 

  • Stillinger, F.H., Jr., and F.P. Buff: 1962, ‘Equilibrium Statistical Mechanics of Inhomogeneous Fluids’, J. Chem Phys., 37. 1.

    Article  ADS  Google Scholar 

  • Stoner, E.C.: 1935, ‘The Temperature Dependence of Free Electron Susceptibility’, Proc. Roy. Soc. (London) A152, 672.

    ADS  Google Scholar 

  • Taylor, J.R.: 1972, Scattering Theory, Wiley, New York, p.310.

    Google Scholar 

  • Ternov, I.M., V.G. Bagrov, V.A. Bordovitzin, and O.F. Dorofeev: 1969, ‘Concerning the Anomalous Magnetic Moment of the Electron’, Sov. Phys. JETP 28, 1206.

    ADS  Google Scholar 

  • Titchmarsh, E.C.: 1930, Theory of the Riemann Zeta Function, Cambridge Univ. Press, Cambridge.

    Google Scholar 

  • Trugman, S.A.: 1986, ‘A General Theory of Inhomogeneous Systems, Based on Maximum Entropy’, Phys. Rev. Letters 57, 607.

    Article  ADS  Google Scholar 

  • van Leeuwen, H.-J.: 1919, ‘Problèmes de la Théorie Electronique du Magnétisme’, Ph.D thesis, Leiden [J. de Phys. et Le Radium 2, 361(1921)]

    Google Scholar 

  • Watson, G.N.: 1918, ‘The Diffraction of Electric Waves by the Earth’, Proc.Roy. Soc. (London) A95, 83.

    ADS  Google Scholar 

  • Widom, A.: 1968a, ‘Statistical Mechanics of Rotating Quantum Liquids’, Phys. Rev. 168, 150.

    Article  ADS  Google Scholar 

  • Widom, A.: 1968b, ‘Superfluid Phase Transitions in One and Two Dimensions’, Phys. Rev. 176, 254.

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of Wyoming, USA

    Walter T. Grandy Jr.

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  1. Walter T. Grandy Jr.
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© 1987 D. Reidel Publishing Company, Dordrecht, Holland

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Grandy, W.T. (1987). External Fields. In: Foundations of Statistical Mechanics. Fundamental Theories of Physics, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3867-0_6

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  • DOI: https://doi.org/10.1007/978-94-009-3867-0_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8219-8

  • Online ISBN: 978-94-009-3867-0

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