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

Benarous, M.

doi:10.1006/aphy.1998.5844

Cited by 6 publications

(16 citation statements)

References 18 publications

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“…This last quantity turns out to be of no interest in our particular case but it may play a major role in other situations especially when one intends to calculate correlation functions [11,12].…”

Section: Introductionmentioning

confidence: 96%

BEC from a time-dependent variational point of view

Benarous¹

2005

Annals of Physics

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Section: Introductionmentioning

confidence: 96%

BEC from a time-dependent variational point of view

Benarous¹

2005

Annals of Physics

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“…The BV variational principle has been applied to various quantum problems including heavy ion reactions [46], quantum fields out of equilibrium [47] attempts to go beyond the Gaussian approximation for fermion systems [48]. Therefore, the BV principle has been used to provide the best approximation to the generating functional for two and multi-time correlation functions of a set of bosonic and fermionic observables [49][50][51][52]. More recently, it was used to derive a set of equations governing the dynamics of trapped Bose gases [53,54].…”

Section: Introductionmentioning

confidence: 99%

Anomalous density for Bose gases at finite temperature

Boudjemâa¹,

Benarous²

2011

Phys. Rev. A

102

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We analyze the behavior of the anomalous density as function of the radial distance at different temperatures in a variational framework. We show that the temperature dependence of the anomalous density agrees with the Hartree-Fock-Bogoliubov (HFB) calculations. Comparisons between the normal and the anomalous fractions at low temperature show that the latter remains higher and consequently the neglect of the anomalous density may destabilize the condensate. These results are compatible with those of Yukalov. Surprisingly, the study of the anomalous density in terms of the interaction parameter shows that the dip in the central density is destroyed for sufficiently weak interactions. We explain this effect.

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“…In agreement with the boundary conditions (13) and (14) relating the sectors τ and t, equations (15) and (18) for D should be solved forward in time, with τ running from 0 to β and t running from t i to ∞, whereas Eqs. (17) and (16) for A should be solved backward. We obtain the stationary value of Ψ as…”

Section: The Variational Principlementioning

confidence: 99%

“…The variational procedure has duplicated the dynamical equations, introducing Eqs. (16) and (18), besides the approximate Bloch equation (15) and the approximate equation (17) for the generating operator A(t). While the formalism was set up in the Heisenberg picture, the stationarity condition (18) reduces, in the absence of sources and for unrestricted variations of A(t) and D(t), to the Liouville-von Neumann equation…”

Section: The Variational Principlementioning

confidence: 99%

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Correlation functions from a unified variational principle: Trial Lie groups

Balian

Vénéroni

2015

Annals of Physics

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Time-dependent expectation values and correlation functions for many-body quantum systems are evaluated by means of a unified variational principle. It optimizes a generating functional depending on sources associated with the observables of interest. It is built by imposing through Lagrange multipliers constraints that account for the initial state (at equilibrium or off equilibrium) and for the backward Heisenberg evolution of the observables. The trial objects are respectively akin to a density operator and to an operator involving the observables of interest and the sources. We work out here the case where trial spaces constitute Lie groups. This choice reduces the original degrees of freedom to those of the underlying Lie algebra, consisting of simple observables; the resulting objects are labeled by the indices of a basis of this algebra. Explicit results are obtained by expanding in powers of the sources. Zeroth and first orders provide thermodynamic quantities and expectation values in the form of mean-field approximations, with dynamical equations having a classical Lie-Poisson structure. At second order, the variational expression for two-time correlation functions separates-as does its exact counterpart-the approximate dynamics of the observables from the approximate correlations in the initial state. Two building blocks are involved: (i) a commutation matrix which stems from the structure constants of the Lie algebra; and (ii) the second-derivative matrix of a free-energy function. The diagonalization of both matrices, required for practical calculations, is worked out, in a way analogous to the standard RPA. The ensuing structure of the variational formulae is the same as for a system of non-interacting bosons (or of harmonic oscillators) plus, at non-zero temperature, classical gaussian variables. This property is explained by mapping the original Lie algebra onto a simpler Lie algebra. The results, valid for any trial Lie group, fulfill consistency properties and encompass several special cases: linear responses, static and time-dependent fluctuations, zero-and high-temperature limits, static and dynamic stability of small deviations.

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

Cited by 6 publications

References 18 publications

BEC from a time-dependent variational point of view

BEC from a time-dependent variational point of view

Anomalous density for Bose gases at finite temperature

Correlation functions from a unified variational principle: Trial Lie groups

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