Nonzero Temperatures

  • Gerald D. Mahan
Part of the Physics of Solids and Liquids book series (PSLI)


Experiments are done at nonzero temperatures. Since one goal of many-body theory is to explain experiments (another is to predict them), the theories should be done at nonzero temperatures too. It is often unnecessary if the temperature is small compared to other energies in the problem. But often temperature is important, and here it will be incorporated into Green’s functions. The nonzero temperature formalism was originated by Matsubara (1955). It will actually be easier to use than the zero-temperature theory of Chapter 2, so that the Matsubara method will be used throughout the remainder of the book. The zero-temperature result is always easily obtained from the nonzero-temperature result by just setting T = 0.


Spectral Function Nonzero Temperature Kubo Formula Wigner Distribution Function Retarded Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abrikosov, A. A., L. P. Gorkov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics ( Prentice-Hall, Englewood Cliffs, N.J., 1963 ).zbMATHGoogle Scholar
  2. Barnard, R. D., Thermoelectricity in Metals and Alloys ( Taylor and Francis, London, 1972 ).Google Scholar
  3. Brandt, W, and A. Dupasquier, editors of Positron Solid State Physics, Int. School “Enrico Fermi” ( Varenna, Italy, 1981 ).Google Scholar
  4. Brout, R., and P. Carruthers, Lectures on the many-Electron Problem ( Wiley-Interscience, New York, 1963 ).Google Scholar
  5. De Groot, S. R., Thermodynamics of Irreversible Processes ( North-Holland, Amsterdam, 1952 ).Google Scholar
  6. De Groot, S. R., and P. Mazur, Non-Equilibrium Thermodynamics ( North-Holland, Amsterdam, 1962 ).Google Scholar
  7. Dunn, D., Can. J. Phys. 53, 321 (1975).ADSCrossRefGoogle Scholar
  8. Green, M. S., J. Chem. Phys. 20, 1281 (1952)MathSciNetADSCrossRefGoogle Scholar
  9. Green, M. S., J. Chem. Phys. 22, 398 (1954).MathSciNetADSCrossRefGoogle Scholar
  10. Korn, W, and J. M. Luttinger, Phys. Rev. 118, 41 (1960).MathSciNetADSCrossRefGoogle Scholar
  11. Kubo, R., Lectures in Theoretical Physics, Vol. I (Boulder) (Wiley-Interscience, New York, 1959), pp. 120–203; J. Phys. Soc. Japan 12, 570 (1957).MathSciNetGoogle Scholar
  12. Langreth, D., in NATO Advanced Study Institute on Linear and Nonlinear Transport, ed. J. T. Devreese, V E. van Doren ( Plenum, New York, 1976 ), p. 3.Google Scholar
  13. Lehmann, H., Nuovo Cimento 11, 342 (1954).MathSciNetzbMATHCrossRefGoogle Scholar
  14. Luttinger, J. M., Phys. Rev. 135, A1505 (1964).MathSciNetADSCrossRefGoogle Scholar
  15. Luttinger, J. M., and J. C. Ward, Phys. Rev. 118, 1417 (1960).MathSciNetADSzbMATHCrossRefGoogle Scholar
  16. Mahan, G. D., Phys. Rev. B 11, 4814 (1975).ADSCrossRefGoogle Scholar
  17. Matsubara, T., Prog. Theor. Phys. (Kyoto) 14, 351 (1955).MathSciNetADSzbMATHCrossRefGoogle Scholar
  18. Mills, A. P., W. S. Crane, and K. F. Canter, editors of Positron Studies of Solids, Surfaces, Atoms ( World Scientific, Singapore, 1986 ).Google Scholar
  19. Taylor, P. L., A Quantum Approach to the Solid State ( Prentice-Hall, Englewood Cliffs, N.J., 1970 ).Google Scholar
  20. Tomonaga, S., Prog. Theor. Phys. (Kyoto) 2, 6 (1947).ADSCrossRefGoogle Scholar
  21. Wigner, E., Phys. Rev. 40, 749 (1932).ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Gerald D. Mahan
    • 1
    • 2
  1. 1.University of TennesseeKnoxvilleUSA
  2. 2.Oak Ridge National LaboratoryUSA

Personalised recommendations