Advertisement

Sharp Spectral Asymptotics for Dirac Energy

  • Victor Ivrii
Part of the International Mathematical Series book series (IMAT, volume 10)

I derive sharp semiclassical asymptotics of \(\int {|e_h } \left( {x,y,0} \right)|^2 \omega \left( {x,y} \right)dxdy\) where e h (x, y, τ) is the Schwartz kernel of the spectral projector and ω(x, y) is singular as x = y. I also consider asymptotics of more general expressions.

Keywords

Ground State Energy Scalar Operator Spectral Projector Smooth Case Nondegeneracy Condition 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bronstein, M., Ivrii, V.: Sharp Spectral Asymptotics for Operators with Irregular coefficients. Pushing the limits. Commun. Partial Differ. Equ. 28, no. 1–2, 99–123 (2003)MathSciNetGoogle Scholar
  2. 2.
    Ivrii, V.: Semiclassical asymptotics for exchange energy. Séminaire sur les Équations aux Dérivées Partielles, 1993 –1994, Exp. No. XX, 12 pp., Ecole Polytech., Palaiseau (1994)Google Scholar
  3. 3.
    Ivrii, V.: Asymptotics of the ground state energy of heavy molecules in the strong magnetic field. I. Russian J. Math. Phys. 4, no 1, 29–74 (1996)MATHMathSciNetGoogle Scholar
  4. 4.
    Ivrii, V.: Heavy molecules in the strong magnetic field. Russian J. Math. Phys. 4, no 4, 449–456 (1996)MATHMathSciNetGoogle Scholar
  5. 5.
    Ivrii, V.: Asymptotics of the ground state energy of heavy molecules in the strong magnetic field. II. Russian J. Math. Phys. 5, no 3, 321–354 (1997)MATHMathSciNetGoogle Scholar
  6. 6.
    Ivrii, V.: Microlocal Analysis and Precise Spectral Asymptotics. Springer-Verlag (1998)Google Scholar
  7. 7.
    Ivrii, V., Sigal, I.M.: Asymptotics of the ground state energies of large Coulomb systems. Ann. Math. 138, 243 –335 (1993)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Victor Ivrii
    • 1
  1. 1.University of TorontoTorontoCanada

Personalised recommendations