Skip to main content

Non-Commutative Large Deviations and Applications

  • Chapter
Instabilities and Nonequilibrium Structures III

Part of the book series: Mathematics and Its Applications ((MAIA,volume 64))

  • 253 Accesses

Abstract

Results on equilibrium statistical mechanics of inhomogeneous quantum mean-field systems are described. These can be seen as non-commutative extensions of classical large deviation theory.

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

Access this chapter

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
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Varadhan, S.R.S.:Asymptotic probabilities and differential equations.Commun. Pure Appl. Math.19, 261–286 (1966).

    MathSciNet  MATH  Google Scholar 

  2. Varadhan, S.R.S.:Large DeviationsandApplications.Philadelphia: Society for Industrial and Applied Mathematics 1984.

    Book  Google Scholar 

  3. Ellis, R.S.:Entropy Large Deviations and Statistical Mechanics. New York, Berlin, Heidelberg, Tokio: Springer 1985.

    MATH  Google Scholar 

  4. Berg, M. van den, Lewis, J.T., and Pulé, J.V.:The Large Deviation Principle and some models ofan interactingBose gas.Commun. Math. Phys.118, 61–85 (1988).

    Article  MATH  Google Scholar 

  5. Dorlas, T.C., Lewis, J.T., and Pulé, J.V.:The Yang-Yang thermodynamic formalismandlarge deviations.Commun. Math. Phys. (1990) ?.

    Google Scholar 

  6. Araki, H.:Relative hamiltonian for faithful normal states of a von Neumann algebra.Publ. Res. Inst. Math. Sci,9, 165–209 (1973).

    MathSciNet  MATH  Google Scholar 

  7. Petz, D.:A variational expression for the relative entropy.Commun. Math. Phys.114, 345–349 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  8. ArakiH.:Relative entropy of states of von Neumann algebras I & Il.Publ. Res. Inst. Math. Sci. 11, 809–833 (1976) & 13, 173–192 (1977).

    Google Scholar 

  9. Cramér, H.:On a new limit theorem in the theory of probability.In: Colloq. on the Theory of Probability. Paris: Hermann 1937.

    Google Scholar 

  10. Petz, D., Raggio, G.A., and Verbeure, A.:Asymtpotics of VaradhanType and the Gibbs Variational Principle. Commun. Math. Phys.121271–282 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  11. Reggio, G.A., and Werner, R.F:Quantumstatisticalmechanics of ge-neral mean field systems.Helvet. Phys. Acta.62, 980–1003 (1989).

    Google Scholar 

  12. Reggio, G.A., and Werner, R.F:The Gibbs Variational Principle for inhomogeneous mean-field systems.Preprint DIAS, March 1990.

    Google Scholar 

  13. Duffield, N.G, and Pule, J.V.:Thermodynamics and phase transitions in the Overhauser model.J. Stat. Phys.54, 449–475 (1989).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Raggio, G.A. (1991). Non-Commutative Large Deviations and Applications. In: Tirapegui, E., Zeller, W. (eds) Instabilities and Nonequilibrium Structures III. Mathematics and Its Applications, vol 64. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3442-2_8

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-3442-2_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5522-2

  • Online ISBN: 978-94-011-3442-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics