A variational principle for the average value and the dispersion of an operator ; application to mean field theory
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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.
KeywordsDensity Matrix Variational Principle Gauge Transformation Variational Space Exact Equation
- (1).R. BALIAN, M. VENERONI, Phys. Rev. Let. 47 (1981) 1353.Google Scholar