Skip to main content
SpringerLink
Log in

Metastable states of molecules

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

We define metastable states to be density matrices which are at local minima of a certain non-linear functional, and investigate their general properties, proving in particular that the metastable states are not necessarily unique but are “modified Gibbs states”. The case of an atom in an external electric field is investigated in some detail.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Capocaccia, D., Cassandro, M., Olivieri, E.: A study of metastability in the Ising model. Commun. Math. Phys.39, 185–205 (1974)

    Google Scholar 

  2. Davies, E.B.: Symmetry breaking for a non-linear Schrödinger equation. Commun. Math. Phys.64, 191–210 (1979)

    Google Scholar 

  3. Herbst, I.: Dilation analyticity in constant electric field. I. The two body problem. Commun. Math. Phys.64, 279–298 (1979)

    Google Scholar 

  4. Herbst, I., Simon, B.: The Stark effect revisited. Phys. Rev. Lett.41, 67–69 (1978)

    Google Scholar 

  5. Hunziker, W.: Schrödinger operators with electric or magnetic fields. Proc. Int. Conf. Math. Phys., Lausanne, 1979 (to appear)

  6. Lavine, R.: Spectral density and sojourn times. Proc. London Ontario Conf. on Atomic Scattering, 1979 (to appear)

  7. Lindblad, G.: Expectations and entropy inequalities for finite quantum systems. Commun. Math. Phys.39, 111–119 (1974)

    Google Scholar 

  8. Penrose, O., Lebowitz, J.L.: Towards a rigorous molecular theory of metastability. In: Fluctuation phenomena, studies in statistical mechanics (eds. J.L. Lebowitz, E.W. Montroll). Amsterdam: North-Holland 1979

    Google Scholar 

  9. Reed, M., Simon, B.: Methods of modern mathematical physics, Vol. 4. Analysis of operators. London, New York: Academic Press 1978

    Google Scholar 

  10. Rockafellar, R.T.: Convex analysis. Princeton, NJ: Princeton University Press 1970

    Google Scholar 

  11. Sewell, G.L.: Stability, equilibrium, and metastability in statistical mechanics. Phys. Rep.57, 307–342 (1980)

    Google Scholar 

  12. Simon, B.: Pointwise bounds on eigenfunctions and wave packets inN-body quantum systems. II. Proc. Am. Math. Soc.45, 454–456 (1974)

    Google Scholar 

  13. Wehrl, A.: General properties of entropy. Rev. Mod. Phys.50, 221–260 (1978)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St. John's College, OX1 3JP, Oxford, England

    E. B. Davies

Authors
  1. E. B. Davies
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by J. Ginibre

Rights and permissions

Reprints and permissions

About this article

Cite this article

Davies, E.B. Metastable states of molecules. Commun.Math. Phys. 75, 263–283 (1980). https://doi.org/10.1007/BF01212712

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01212712

Keywords

Search

Navigation