Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:hep-th/9505031 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Variational approximation for two-time correlation functions in Φ4 theory: Optimization of the dynamics

Cécile Martin

Published Dec 15, 1995• 17 citations
arXivHTMLPDF

Abstract

We apply the time-dependent variational principle of Balian and V\'en\'eroni to ${\mathrm{\ensuremath{\Phi}}}^{4}$ theory. An appropriate parametrization for the variational objects allows us to write coupled dynamical equations from which we derive approximations for the two-time correlation functions involving two, three, or four field operators. \textcopyright{} 1995 The American Physical Society.

DOI
10.1103/physrevd.52.7121

Related papers

Variational approximations for correlation functions in quantum field theories

Cécile Martin

Applying the time-dependent variational principle of Balian and Vénéroni, we derive variational approximations for multi-time correlation functions in characterized by a density operator equal to a Gaussian density matrix. Then, we study the more realistic situation where only a few expectation values are given at the initial time and we perform an optimization with respect to the initial state. We calculate explicitly the two-time correlation functions with two and four field operators at equilibrium in the symmetric phase.

•Jan 1, 1999•4 citations

Variational Multi-Time Green’s Functions for Nonequilibrium Quantum Fields

Mohamed Benarous

The time-dependent variational principle proposed by Balian and Vénéroni is used to provide the best approximation to the generating functional for multi-time Green’s functions of a set of (bosonic) observables Qµ. By suitably restricting the trial spaces, the computation of the two-time Green’s function, obtained by a second order expansion in the sources, is considerably simplified. This leads to a tractable formalism suited to quantum fields out of equilibrium. We propose an illustration on the finite temperature Φ4-theory in curved space and coupled to gravity.

•Jan 1, 2008•5 citations

Various variational approximations of quantum dynamics

Caroline Lasser, Chunmei Su

We investigate variational principles for the approximation of quantum dynamics that apply for approximation manifolds that do not have complex linear tangent spaces. The first one, dating back to McLachlan [Mol. Phys. 8, 39–44 (1964)], minimizes the residuum of the time-dependent Schrödinger equation, while the second one, originating from the lecture notes of Kramer and Saraceno [Geometry of the Time-Dependent Variational Principle in Quantum Mechanics, Lecture Notes in Physics Vol. 140 (Springer, Berlin, 1981)], imposes the stationarity of an action functional. We characterize both principles in terms of metric and symplectic orthogonality conditions, consider their conservation properties, and derive an elementary a posteriori error estimate. As an application, we revisit the time-dependent Hartree approximation and frozen Gaussian wave packets.

arXiv:2103.11783•Journal of Mathematical Physics•Jul 1, 2022•12 citations

Dynamics of Gaussian Wigner functions derived from a time-dependent variational principle

Jens Aage Poulsen, S. Karl-Mikael Svensson, Gunnar Nyman

By using a time-dependent variational principle formulated for Wigner phase-space functions, we obtain the optimal time-evolution for two classes of Gaussian Wigner functions, namely those of either thawed real-valued or frozen but complex Gaussians. It is shown that tunneling effects are approximately included in both schemes.

AIP Advances•Nov 1, 2017•4 citations

Time-dependent variational principle and the effective action in density-functional theory and Berry’s phase

A. K. Rajagopal

An alternative form of the variational principle is set up by defining an action functional which takes explicit account of the time path and thus is different from that used traditionally in time-dependent density-functional theory. This has the attractive feature of not having the formal difficulties in defining the effective potential and the effective interaction as its functional derivatives. Also, the Berry phase, not explicitly found at first sight in a time-dependent density-functional theory, is shown to reside in this action functional. It lies buried as the sum over the individual phases of the occupied states associated with the time-dependent Kohn-Sham orbitals. Some recent work on superconductivity and ferroelectricity in the literature are cited as examples of the Berry-phase considerations developed here. \textcopyright{} 1996 The American Physical Society.

Physical Review A•Nov 1, 1996•29 citations

Study of molecular dynamics with the Balian-Vénéroni variational principle

A. A. Karlson, Michel Godefroid, Jacques Liévin +1 more

info:eu-repo/semantics/nonPublished

•Jun 7, 1996•0 citations
We apply the time-dependent variational principle of Balian and V'en'eroni to \ensuremathΦ4{\mathrm{\ensuremath{\Phi}}}^{4}\ensuremathΦ4 theory. An appropriate parametrization for the variational objects allows us to write coupled dynamical equations from which we derive approximations for the two-time correlation functions involving two, three, or four field operators. \textcopyright{} 1995 The American Physical Society.
Applying the time-dependent variational principle of Balian and Vénéroni, we derive variational approximations for multi-time correlation functions in characterized by a density operator equal to a Gaussian density matrix. Then, we study the more realistic situation where only a few expectation values are given at the initial time and we perform an optimization with respect to the initial state. We calculate explicitly the two-time correlation functions with two and four field operators at equilibrium in the symmetric phase.
The time-dependent variational principle proposed by Balian and Vénéroni is used to provide the best approximation to the generating functional for multi-time Green’s functions of a set of (bosonic) observables Qµ. By suitably restricting the trial spaces, the computation of the two-time Green’s function, obtained by a second order expansion in the sources, is considerably simplified. This leads to a tractable formalism suited to quantum fields out of equilibrium. We propose an illustration on the finite temperature Φ4-theory in curved space and coupled to gravity.
We investigate variational principles for the approximation of quantum dynamics that apply for approximation manifolds that do not have complex linear tangent spaces. The first one, dating back to McLachlan [Mol. Phys. 8, 39–44 (1964)], minimizes the residuum of the time-dependent Schrödinger equation, while the second one, originating from the lecture notes of Kramer and Saraceno [Geometry of the Time-Dependent Variational Principle in Quantum Mechanics, Lecture Notes in Physics Vol. 140 (Springer, Berlin, 1981)], imposes the stationarity of an action functional. We characterize both principles in terms of metric and symplectic orthogonality conditions, consider their conservation properties, and derive an elementary a posteriori error estimate. As an application, we revisit the time-dependent Hartree approximation and frozen Gaussian wave packets.
An alternative form of the variational principle is set up by defining an action functional which takes explicit account of the time path and thus is different from that used traditionally in time-dependent density-functional theory. This has the attractive feature of not having the formal difficulties in defining the effective potential and the effective interaction as its functional derivatives. Also, the Berry phase, not explicitly found at first sight in a time-dependent density-functional theory, is shown to reside in this action functional. It lies buried as the sum over the individual phases of the occupied states associated with the time-dependent Kohn-Sham orbitals. Some recent work on superconductivity and ferroelectricity in the literature are cited as examples of the Berry-phase considerations developed here. \textcopyright{} 1996 The American Physical Society.