A variational principle for the average value and the dispersion of an operator ; application to mean field theory
| Autor: | H. Flocard |
|---|---|
| Přispěvatelé: | Institut de Physique Nucléaire d'Orsay (IPNO), Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Université Paris-Sud - Paris 11 (UP11), Goeke K. |
| Rok vydání: | 2008 |
| Předmět: |
Density matrix
[PHYS.NUCL]Physics [physics]/Nuclear Theory [nucl-th] Mathematical analysis Hartree–Fock method Measure (mathematics) symbols.namesake Operator (computer programming) Variational principle Quantum mechanics Luke's variational principle symbols Hamilton's principle Statistical dispersion Mathematics |
| Zdroj: | Time-Dependent Hartree-Fock and Beyond ISBN: 9783540119500 Time-Dependent Hartree-Fock and Beyond International Symposium On Time-Dependent Hartree-Fock And Beyond International Symposium On Time-Dependent Hartree-Fock And Beyond, Jun 1982, Bad Honnef, Germany. pp.99-110 |
| DOI: | 10.1007/3-540-11950-7_8 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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