Abstract
A variational method is proposed to evaluate the generating functional {phi} which gives the multi-time correlation functions in equilibrium and non-equilibrium statistical mechanics or field theories. Its definition, {phi} = ln(Tr D A), involves the density operator D describing the initial state and an operator A depending on the observables of interest (in the Heisenberg picture), on the associated time-dependent sources and on the initial time. The example of interacting fermions in many-body physics is worked out by restricting the trial objects to exponentials of single-particle operators. This leads to an extended mean-field approximation for the generating functional associated with any set of observables using the variational approximation. The result incorporates both the static and dynamic Hartree-Fock equations as well as the associated RPA equations. It is free of several inconsistencies occurring in the conventional mean-field approximations. (K.A.) 21 refs.; 1 fig.
Balian, R;
[1]
Veneroni, M
- CEA Centre d`Etudes de Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique
Citation Formats
Balian, R, and Veneroni, M.
Variational approach to multi-time correlation functions.
France: N. p.,
1992.
Web.
Balian, R, & Veneroni, M.
Variational approach to multi-time correlation functions.
France.
Balian, R, and Veneroni, M.
1992.
"Variational approach to multi-time correlation functions."
France.
@misc{etde_10136897,
title = {Variational approach to multi-time correlation functions}
author = {Balian, R, and Veneroni, M}
abstractNote = {A variational method is proposed to evaluate the generating functional {phi} which gives the multi-time correlation functions in equilibrium and non-equilibrium statistical mechanics or field theories. Its definition, {phi} = ln(Tr D A), involves the density operator D describing the initial state and an operator A depending on the observables of interest (in the Heisenberg picture), on the associated time-dependent sources and on the initial time. The example of interacting fermions in many-body physics is worked out by restricting the trial objects to exponentials of single-particle operators. This leads to an extended mean-field approximation for the generating functional associated with any set of observables using the variational approximation. The result incorporates both the static and dynamic Hartree-Fock equations as well as the associated RPA equations. It is free of several inconsistencies occurring in the conventional mean-field approximations. (K.A.) 21 refs.; 1 fig.}
place = {France}
year = {1992}
month = {Dec}
}
title = {Variational approach to multi-time correlation functions}
author = {Balian, R, and Veneroni, M}
abstractNote = {A variational method is proposed to evaluate the generating functional {phi} which gives the multi-time correlation functions in equilibrium and non-equilibrium statistical mechanics or field theories. Its definition, {phi} = ln(Tr D A), involves the density operator D describing the initial state and an operator A depending on the observables of interest (in the Heisenberg picture), on the associated time-dependent sources and on the initial time. The example of interacting fermions in many-body physics is worked out by restricting the trial objects to exponentials of single-particle operators. This leads to an extended mean-field approximation for the generating functional associated with any set of observables using the variational approximation. The result incorporates both the static and dynamic Hartree-Fock equations as well as the associated RPA equations. It is free of several inconsistencies occurring in the conventional mean-field approximations. (K.A.) 21 refs.; 1 fig.}
place = {France}
year = {1992}
month = {Dec}
}