Skip to main content

Nonlinear Response Theory

  • Chapter

Part of the book series: NATO Advanced Study Institutes Series ((NSSB,volume 35))

Abstract

In recent years there has been significant progress in the molecular derivations of transport equations describing the time dependences of macroscopic variables in non-equilibrium systems. One of the most powerful approaches has been linear response theory which has been developed and extensively applied by Kubo (1) and by others (2,3). The aims of this theory, as well as those of the other molecular approaches, are the following: to obtain the form of the macroscopic equations; to obtain explicit molecular expressions for the coefficients appearing in these equations usually in the form of correlation functions; to determine the range of validity of the equations; to extend the range of validity of the equations to more complicated situations; and to compare the transport equations with those obtained phenomenologically using hydrodynamics, thermodynamics of irreversible processes, etc.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Kubo, J.Phys.Soc.Japan 12 (1957) 570

    Article  MathSciNet  ADS  Google Scholar 

  2. R. Kubo, M. Yokota and S. Nakajima, J.Phys.Soc.Japan 12 (1957) 1203.

    Article  MathSciNet  ADS  Google Scholar 

  3. L.P. Kadanoff and P.C. Martin, Ann.Physics 24 (1963) 419.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. P.A. Selwyn and I. Oppenheim, Physica 54 (1971) 161.

    Article  ADS  Google Scholar 

  5. N.G. Van Kampen, Physica Norwegica 5 (1971) 10.

    Google Scholar 

  6. J.H. Weare and I. Oppenheim, Physica 72 (1974) 1, 20.

    ADS  Google Scholar 

  7. I. Oppenheim, in Topics in Statistical Mechanics and Biophysics: A Memorial to J.L. Jackson, R.A. Piccirelli, ed. (A.I.P., New York, 1976) p. 111.

    Google Scholar 

  8. D. Ronis and I. Oppenheim, Physics 86A (1977) 475.

    MathSciNet  ADS  Google Scholar 

  9. For a discussion of ergodic theory and the choice of ensemble, see: A.I. Khinchin, Mathematical Foundations of Statistical Mechanics, chapter II (Dover Publ., New York, 1949).

    Google Scholar 

  10. J.L. Lebowitz, Hamiltonian Flows and Rigorous Results in Non-Equilibrium Statistical Mechanics, in The Proc.I.U.P.A.P. Conference on Statistical Mechanics, S.A. Rice, K.F. Freed and J.C. Light, eds. (Univ. of Chicago Press, 1972).

    Google Scholar 

  11. Ja.G. Sinai, Ergodicity of Boltzmann’s Gas Model, in Proc. I.U.P.A.P. Meeting, Copenhagen, 1966, T.A. Bak, ed. (Benjamin, New York, 1967) p. 559.

    Google Scholar 

  12. J.L. Lebowitz and J.K. Percus, Phys.Rev., 122 (1961) 1675.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. T. Keyes and I. Oppenheim, Phys.Rev., A7 (1973) 522

    Google Scholar 

  14. I.A. Michaels and I. Oppenheim, Physica 81A (1975) 522.

    ADS  Google Scholar 

  15. S.R. De Groot and P. Mazur, Non-Equilibrium Thermodynamics (North-Holland Publ.Comp., Amsterdam 1962).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1978 Plenum Press, New York

About this chapter

Cite this chapter

Oppenheim, I. (1978). Nonlinear Response Theory. In: Halley, J.W. (eds) Correlation Functions and Quasiparticle Interactions in Condensed Matter. NATO Advanced Study Institutes Series, vol 35. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-3360-9_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-3360-9_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-3362-3

  • Online ISBN: 978-1-4684-3360-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics