Abstract
The calculational techniques developed around the notion of clustering in the preceding chapter are obviously powerful, particularly as applied to the virial series. But, just as with methods of statistical analysis in general, no calculational scheme is likely to be universally optimal. Cluster-related techniques appear most efficient at moderate to high temperatures, although they certainly can be extended to the study of low-temperature phenomena, as already demonstrated.
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References
Adhikari, S.K., and R.D. Amado: 1971, ‘Low-Temperature Behavior of the Quantum Cluster Coefficients’,Phys. Rev. Letters 27, 485.
Alers, G.A., and J.R. Neighbours: 1959, ‘Comparison of the Debye ө Determined from ElasticConstants and Calorimetry’, Rev. Mod. Phys. 31, 675.
Bogoliubov, N.N.: 1947, ‘On the Theory of Superfluidity’, J. Phys. U.S.S.R.) 11, 23.
Born, M., and Th. von Karman: 1912, ‘Uber Schwingungen in Raumgittern’, Phys. Z. 13, 297
Brueckner, K.A.: 1955, ‘Many-Body Problem for Strongly Interacting Particles.II. Linked ClusterExpansion’, Phys. Rev. 100, 36.
Carr, W.J., Jr., R.A. Coldwell-Horsfall, and A.E. Fein: 1961, ‘Anharmonic Contribution to the Energy of a Dilute Electron Gas— Interpolation for the Correlation Energy’, Phys. Rev. 124, 747.
Carr, W. J., Jr., and A.A. Maradudin: 1964, ‘Ground-State Energy of a High-Density Electron Gas’, Phys. Rev. 133, A371.
Chandrasekhar, S.: 1931, ‘The Highly Collapsed Configurations of a Stellar Mass’, Mon. Not. Roy.Astron. Soc. 91, 456.
Debye, P.: 1912, ‘Zur Theorie der spezifischen Wärme’, Ann. d. Phys. 39, 789.
Debye, P., and E. Hückel: 1923, ‘Zur Theorie der Elektrolyte’, Phys. Z. 24, 185, 305.
DuBois, D.F.: 1959, ‘Electron Int er act ions. Part I. Field Theory of a Degenerate Electron Gas’,Ann. Phys. (N.Y.) 7, 174.
Dyson, F.J., and A. Lenard: 1967, ‘Stability of Matter.I’, J. Math. Phys. 8, 423.
Efimov, V.N., and M.Ya. Amus’ya: 1964, ‘Ground State of a Rarefied Fermi Gas of Rigid Spheres’, J. Exptl Theor. Phys. (U.S.S.R.) 47, 581 [English translation, 1965: Sov. Phys. JETP 20, 388.].
Einstein, A.: 1907, ‘Die Plancksche Theorie der Strahlung und die Theorie der spezifischen Wärme’, Ann.d. Phys. 22, 180.
Fetter, A.L., and J.D. Walecka: 1971, Quantum Theory of Many-Particle Systems, McGraw-Hill, New York.
Fine, P.C.: 1939, ‘The Normal Modes of Vibration of a Body-Centered Cubic Lattice’, Phys. Rev. 56, 355.
Fisher, M.E., and D. Ruelle: 1966, ‘The Stability of Many-Particle Systems’, J. Math. Phys. 7, 260.
Fock, V.: 1930, ‘Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems’, Z. Phys. 61, 126.
Fock, V.: 1932, ‘Konfigurationsraum und zweite Quantelung’, Z. Phys. 75, 622.
Gell-Mann, M.: 1957, ‘Specific Heat of a Degenerate Electron Gas at High Density’, Phys. Rev. 106, 369.
Gell-Mann, M., and K.A. Brueckner: 1957, ‘Correlation Energy of an Electron Gas at High Density’, Phys. Rev. 106, 364.
Ginibre, J.: 1968, ‘On the Asymptotic Exactness of the Bogoliubov Approximation for Many BosonSystems’, Commun. Math. Phys. 8, 26.
Ginibre, J., and G. Velo: 1968, ‘On the Bogoliubov Approximation for Many-Boson Systems’, Phys. Letters 26A, 517.
Goldstone, J.: 1957, ‘Derivation of the Brueckner Many-Body Theory’, Proc. Roy. Soc. (London) A239, 267.
Grandy, W.T., Jr.: 1970, ‘Intrinsic Quantum Behavior of the Fully Ionized Gas’, Nuovo Cimento 65B, 73.
Grandy, W.T., Jr., and F. Mohling: 1965, ‘Quantum Statistics of Fully Ionized Gases’, Ann. Phys. (N.Y.) 34, 424.
Hartree, D.R.: 1928, ‘The Wave Mechanics of an Atom with a Non-Coulomb Central Field.Part I.Theory and Methods’, Proc. Camb. Phil Soc. 24, 89.
Henshaw, D.G., and A.D.B. Woods: 1961, ‘Modes of Atomic Motions in Liquid Helium by InelasticScattering of Neutrons’, Phys. Rev. 121, 1266.
Hertel, P., and W. Thirring: 1971, ‘Free Energy of Gravitating Fermions’, Commun. Math. Phys. 24, 22.
Hwang, I.-K., and W.T. Grandy, Jr.: 1969, ‘Theory of Photons in a Fully Ionized Gas.I. PhotonMomentum Distribution’, Phys. Rev. 177, 359.
Jordan, P., and E.P. Wigner: 1928, ‘Über das Paulische Äquivalenzverbot’, Z. Phys. 47, 631
Kawasaki, K., and I. Oppenheim: 1965, ‘Logarithmic Term in the Density Expansion of TransportCoefficients’, Phys. Rev. 139, A1763.
Keller, W.E.: 1969, Helium-3 and Helium-4, Plenum Press, New York.
Landau, L.D.: 1941, ‘The Theory of Superfluidity of Helium II’, J. Phys. (U.S.S.R.) 5, 71.
Landau, L.D.: 1944, ‘On the Hydrodynamics of He II’, J.Phys. (U.S.S.R.) 8, 1.
Landau, L.D.: 1947, ‘On the Theory of Superfluidity of Helium II’, J.Phys. (U.S.S.R.) 11, 91.[Landau's Russian articles are translated into English in: D. ter Haar (ed.), Collected Papers of L.D. Landau, Gordon and Breach, New York, 1965.]
Leighton, R.B.: 1948, ‘The Vibrational Spectrum and Specific Heat of a Face-Centered CubicCrystal’, Rev. Mod. Phys. 20, 165.
Lenard, A., and F.J. Dyson: 1968, ‘Stability of Matter,II’, J. Math. Phys. 9, 698.
Levy-Leblond, J.-M.: 1969, ‘Nonsaturation of Gravitational Forces’, J. Math. Phys. 10, 806.
Lynden-Bell, D., and R. Wood: 1968, ‘The Gravo-Thermal Catastrophe in Isothermal Spheres and the Onset of Red-Giant Structure for Stellar Systems’, Mon. Not. Roy. Astron. Soc. 138, 495.
Macke, W.: 1950, ‘Uber die Wechselwirkungen im Fermi-Gas’, Z. Naturforsch. 5a, 192.
Mohling, F., and W.T. Grandy, Jr.: 1965, ‘Quantum Statistics of Multicomponent Systems’, J. Math. Phys. 6, 348.
Rice, S.A., and P. Gray: 1965, The Statistical Mechanics of Simple Liquids, Interscience (Wiley), New York, p.22.
Salzberg, A.M.: 1965, ‘Exact Statistical Thermodynamics of Gravitational Interactions in One andTwo Dimensions’, J. Math. Phys. 6, 158.
Schick, M., and T.M. Wu: 1969, ‘Charged Bose Gas’, Phys. Rev. 177, 313.
Spruch, L.: 1986, ‘Retarded, or Casimir, Long-Range Potentials’, Physics Today, November, p.37.
Thirring, W.: 1970, ‘Systems with Negative Specific Heat’, Z. Phys. 235, 339.
Thouless, D.J.: 1972, The Quantum Mechanics of Many-Body Systems,2nd ed., Academic Press, New York.
Wick, G.C.: 1950, ‘The Evaluation of the Collision Matrix’, Phys. Rev. 80, 268.
Wigner, E.: 1934, ‘On the Interaction of Electrons in Metals’, Phys. Rev. 46, 1002.
Wigner, E.P.: 1938, ‘Effects of the Electron Interaction on the Energy Levels of Electrons in Metals’,Trans. Faraday Soc. 34, 678.
Wigner, E.P.: 1960, ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences’,Commun. Pure Appl. Math. 13, 1
Wu, T.T.: 1959, ‘Ground State of a Bose System of Hard Spheres’, Phys. Rev. 115, 1390.
Wilks, J.: 1967, The Properties of Liquid and Solid Helium, Clarendon Press, Oxford.
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Grandy, W.T. (1987). Interacting Particles, II: Fock Space Formulation. In: Foundations of Statistical Mechanics. Fundamental Theories of Physics, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3867-0_8
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