Abstract
Using the Balian-Veneroni variational principle, we propose two consistent extensions of the time-dependent mean-field theory for many-boson systems. A first approximation, devised to take into account the effect of correlations, is obtained by means of a development of the optimal density operator suggested by the maximum entropy principle around a Gaussian operator. We discuss the relevance of the evolution equations and their possible generalizations. We present an application to an one-dimensional example. In a second type of approximation, to optimize the prediction of characteristic functions of one-body observables and of transition probabilities, we select for both, the variational observable and the density matrix, the class of exponential operators of quadratic forms. We obtain coupled evolution equations of an unusual kind called `two-point boundary value problem`. To solve them, we construct a suitable numerical algorithm. A test of the method is presented on two examples in one dimension. In a first case, we study the collision of a particle against a Gaussian barrier. The method improves significantly mean-field predictions relative to reflexion and transmission ratios. The study of the motion of a particle in a quartic well reveals the existence of several different solutions for the transition probabilities predicted by the
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Citation Formats
Benarous, M.
Variational extensions of the time-dependent mean-field theory; Extensions variationnelles de la methode du champ moyen dependant du temps.
France: N. p.,
1991.
Web.
Benarous, M.
Variational extensions of the time-dependent mean-field theory; Extensions variationnelles de la methode du champ moyen dependant du temps.
France.
Benarous, M.
1991.
"Variational extensions of the time-dependent mean-field theory; Extensions variationnelles de la methode du champ moyen dependant du temps."
France.
@misc{etde_10127911,
title = {Variational extensions of the time-dependent mean-field theory; Extensions variationnelles de la methode du champ moyen dependant du temps}
author = {Benarous, M}
abstractNote = {Using the Balian-Veneroni variational principle, we propose two consistent extensions of the time-dependent mean-field theory for many-boson systems. A first approximation, devised to take into account the effect of correlations, is obtained by means of a development of the optimal density operator suggested by the maximum entropy principle around a Gaussian operator. We discuss the relevance of the evolution equations and their possible generalizations. We present an application to an one-dimensional example. In a second type of approximation, to optimize the prediction of characteristic functions of one-body observables and of transition probabilities, we select for both, the variational observable and the density matrix, the class of exponential operators of quadratic forms. We obtain coupled evolution equations of an unusual kind called `two-point boundary value problem`. To solve them, we construct a suitable numerical algorithm. A test of the method is presented on two examples in one dimension. In a first case, we study the collision of a particle against a Gaussian barrier. The method improves significantly mean-field predictions relative to reflexion and transmission ratios. The study of the motion of a particle in a quartic well reveals the existence of several different solutions for the transition probabilities predicted by the Balian-Veneroni method.}
place = {France}
year = {1991}
month = {Oct}
}
title = {Variational extensions of the time-dependent mean-field theory; Extensions variationnelles de la methode du champ moyen dependant du temps}
author = {Benarous, M}
abstractNote = {Using the Balian-Veneroni variational principle, we propose two consistent extensions of the time-dependent mean-field theory for many-boson systems. A first approximation, devised to take into account the effect of correlations, is obtained by means of a development of the optimal density operator suggested by the maximum entropy principle around a Gaussian operator. We discuss the relevance of the evolution equations and their possible generalizations. We present an application to an one-dimensional example. In a second type of approximation, to optimize the prediction of characteristic functions of one-body observables and of transition probabilities, we select for both, the variational observable and the density matrix, the class of exponential operators of quadratic forms. We obtain coupled evolution equations of an unusual kind called `two-point boundary value problem`. To solve them, we construct a suitable numerical algorithm. A test of the method is presented on two examples in one dimension. In a first case, we study the collision of a particle against a Gaussian barrier. The method improves significantly mean-field predictions relative to reflexion and transmission ratios. The study of the motion of a particle in a quartic well reveals the existence of several different solutions for the transition probabilities predicted by the Balian-Veneroni method.}
place = {France}
year = {1991}
month = {Oct}
}