A variational principle for the average value and the dispersion of an operator ; application to mean field theory

  • H. Flocard
II. Correlations and Dispersions
Part of the Lecture Notes in Physics book series (LNP, volume 171)


We propose a variational principle which can be used to extract successively the optimal average value and dispersion associated with the measure of a given operator at a final time t1 on a system whose density matrix is known at some initial time t0. For the most general variations the exact equations of motion are recovered. In addition, the stationary values of the actions are equal to the quantities of interest, namely the average value and the dispersion measured in the variational space of the trial density matrices. We have derived the equations for the case of one-body operators and uncorrelated density matrices and showed how the time-dependent Hartree-Fock equations should be modified in order to evaluate a dispersion. Application to the Lipkin model is in progress.


Density Matrix Variational Principle Gauge Transformation Variational Space Exact Equation 
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  1. (1).
    R. BALIAN, M. VENERONI, Phys. Rev. Let. 47 (1981) 1353.Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • H. Flocard
    • 1
  1. 1.Division de Physique ThéoriqueInstitut de Physique NucléaireOrsay

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