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Variational Approach to Quantum Statistical Mechanics

  • Riccardo Giachetti
  • Valerio Tognetti
  • Ruggero Vaia
Part of the NATO ASI Series book series (NSSB, volume 218)

Abstract

The path-integral formulation of quantum statistical mechanics has been accomplished several years ago by Feynman [1], who extended his treatment of quantum mechanics propagator to imaginary times, in order to give the expression for the density operator in the coordinate representation. This approach gives useful tools to reduce quantum statistical mechanics calculations to classical ones, in order to use again the configurational integral and eventually the phase-space integral for the evaluation of the partition function. This turns out to be useful expecially for numerical applications and can be alternative with the Wigner [2] expansion.

Keywords

Partition Function Effective Potential Continuum Limit Quantum Fluctuation Imaginary Time 
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References

  1. 1.
    R.P. Feynman, ”Statistical Mechanics”, Benjamin, Reading MA (1972).R.P. Feynman and A.R. Hibbs, ”Quantum Mechanics and Path-Integrals”, Mc Graw Hill, New York (1965).Google Scholar
  2. 2.
    M.Hillery, R.F. O’Connell, M.O. Scully and E.P. Wigner, Phys. Rep. 106, 122 (1984).MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    R.Giachetti and V. Tognetti, Phys. Rev. Lett. 55, 912 (1985) and Phys. Rev. B33, 7647 (1986) and B36, 5512 (1987).MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    R.Giachetti, V. Tognetti and R. Vaia, Variational approach to quantum statistical mechanics, in ”The Path Integral Method with Applications”, eds. A. Ranfagni, V. Sa-Yakanit and L. Schulman, World Scientific, Singapore (1988); Phys. Rev. A37, 2165 (1988); Phys.Rev. A38, 1521 and 1638 (1988).Google Scholar
  5. 5.
    R.P. Feynman and H. Kleinert, Phys. Rev. A34, 5080 (1986). W. Janke, in ”Path Integrals from meV to MeV”, eds. V. Sa-Yakanit and L. Schulman, World Scientific, Singapore (1989).MathSciNetADSGoogle Scholar
  6. 6.
    R.Giachetti, V. Tognetti and R. Vaia, in ”Path Integrals from meV to MeV”, eds. V. Sa-Yakanit and L. Schulman, World Scientific, Singapore (1989).Google Scholar
  7. 7.
    K.Maki and H. Takayama, Phys. Rev. B20, 3223 and 5009 (1979).ADSGoogle Scholar
  8. 8.
    R.F.Dashen, B. Hasslacher and A. Neveu, Phys. Rev. D10, 4114 and 4130 (1974) and D11, 3424 (1975).ADSGoogle Scholar
  9. 9.
    K.Sasaki, Progr. Theor. Phys. 68, 411 (1982) and 71, 1169 (1984). K. Sasaki and T. Tsuzuki, J. Mag. Mag. Mat. 31–34, 1283 (1983). Progr. Theor. Phys. (Suppl. N.94), (1988). T. Tsuzuki, Progr. Theor. Phys. 70, 975 (1983)ADSCrossRefGoogle Scholar
  10. 10.
    T.Schneider and E. Stoll, Phys. Rev. B22. 5317 (1980).MathSciNetADSGoogle Scholar
  11. 11.
    S.Wouters and H. De Raedt, in ”Magnetic Excitations and Fluctuations II”, eds. U. Balucani, S.W. Lovesey, M. Rasetti and V. Tognetti, XXIII Springer Proceedings in Physics, Springer Verlag, Berlin (1987).Google Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • Riccardo Giachetti
    • 1
  • Valerio Tognetti
    • 2
  • Ruggero Vaia
    • 3
  1. 1.Dipartimento di MatematicaUniversitá di CagliariCagliariItaly
  2. 2.Dipartimento di FisicaUniversitá di FirenzeFirenzeItaly
  3. 3.Istituto di Elettronica QuantisticaCNRFirenzeItaly

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