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

On the Simulation of Extended TDHF Theory

Denis Lacroix A, Ph. Chomaz, Sakir Ayik B

Published Feb 23, 1999• 8 citations
OpenAlex

Abstract

A novel method is presented for implementation of the extended mean-field theory incorporating two-body collisions. At a given time, stochastic imaginary time propagation of occupied states are used to generate a convenient basis. The quantal collision terms, including memory effects, is then computed by a backward mean-field propagation of these single-particle states. The method is illustrated in an exactly solvable model. Whereas the usual TDHF fails to reproduce the long time evolution, a good agreement is found between the extended TDHF and the exact solution. PACS: 05.30.-d, 24.10.Cn, 05.60.+w

Related papers

Quantal Extension of Mean-Field Dynamics

Denis Lacroix A, Ph. Chomaz, Sakir Ayik B

A method is presented for numerical implementation of the extended TDHF theory in which two-body correlations beyond the mean-field approximation are incorporated in the form of a quantal collision term. The method is tested in a model problem in which the exact solution can be obtained numerically. Whereas the usual TDHF fails to reproduce the long time evolution, a very good agreement is found between the extended TDHF and the exact solution.

arXiv:nucl-th/9810037•Oct 13, 1998•1 citation

Calculation of the propagation amplitude in the case of a Coulomb interaction via time-independent mean-field theory

Rabia Yekken, Feriel Mekideche

The exact study of many-body microscopic systems is impossible when the number of particles is large (N ≥ 3). Approximate methods are then used. The time-independent mean-field (TIMF) approximation has been proposed for the description of collisions in many-body systems. Collision amplitudes are derived by the use of a variational principle and the choice of trial functions as products of single-particle orbitals. Resulting mean-field equations with a nonvanishing right-hand side turn out to be a generalization of the traditional Hartree or Hatree–Fock type equations. These TIMF equations are successfully solved numerically for the case of short-range forces. In this paper, we test the validity of this theory for the Coulomb interaction between two particles, that is, a long-range interaction. A numerical comparison between the exact and the mean-field solutions is conducted PACS Nos.: 31.15.Ne, 31.15.Pf, 21.45.+v,25.10.-i

Canadian Journal of Physics•Jul 1, 2007•0 citations

Large amplitude motion with a stochastic mean-field approach

Denis Lacroix A, Sakir Ayik B, Bulent Yilmaz +1 more

In the stochastic mean-field approach, an ensemble of initial conditions is considered to incorporate correlations beyond the mean-field. Then each starting point is propagated separately using the Time-Dependent Hartree-Fock equation of motion. This approach provides a rather simple tool to better describe fluctuations compared to the standard TDHF. Several illustrations are presented showing that this theory can be rather effective to treat the dynamics close to a quantum phase transition. Applications to fusion and transfer reactions demonstrate the great improvement in the description of mass dispersion.

arXiv:1210.2519•EPJ Web of Conferences•Jan 1, 2012•0 citations

Dissipative dynamics within stochastic mean-field approach

Ibrahim Ulgen, Bulent Yilmaz

The time-dependent Hartree-Fock (TDHF) and density functional theory (DFT) are among the most useful approaches within mean-field theories for studying static and dynamic properties of complex many-body systems in different branches of physics. Despite the fact that they provide a good approximation for the average properties of one-body degrees of freedoms, they are known to fail to include quantal fluctuations of collective observables and they do not provide sufficient dissipation of collective motion. In order to incorporate these missing effects the stochastic mean-field (SMF) approach was proposed (Ayik 2008). In the SMF approach a set of stochastic initial one-body densities are evolved. Each stochastic one-body density matrix consists of a set of stochastic Gaussian random numbers that satisfy the first and second moments of collective one-body observables. Recent works indicate that the SMF approach provides a good description of the dynamics of the nuclear systems (Yilmaz et al. 2018; Ayik et al. 2019). In this work, the one-dimensional Fermi-Hubbard model is simulated with the SMF approach by using different distributions such as Gaussian, uniform, bimodal and two-point distributions. The dissipative dynamics are discussed and the predictive power of the SMF approach with different probability distributions are compared with each other and the exact dynamics. As a result it is shown that by considering different distributions, the predictive power of the SMF approach can be improved.

Bitlis Eren University Journal of Science and Technology•Dec 17, 2019•0 citations

Stability of mean-field solutions for collisions

S. Kessal, BERTRAND G. GIRAUD

The time-independent mean-field theory of collisions converts an intractable linear problem, namely, the calculation of the many-body propagator (E-H${)}^{\mathrm{\ensuremath{-}}1}$, into a numerically solvable problem, namely, the coupled calculation of single-particle propagators (\ensuremath{\eta}-h${)}^{\mathrm{\ensuremath{-}}1}$. The latter problem, however, reflects its nonlinearity through many solutions, out of which only one is nonspurious and gives a good approximation to the unique solution (off shell) of the former, linear problem. We prove the stability of this nonspurious solution in the special case of a four-body, one-dimensional collision. The experience thus gained is used to generate transition-shell models in the case of a realistic, three-dimensional, four-body elastic collision.

Physical Review A•May 1, 1989•0 citations

Simulating Quantum Dynamics with Entanglement Mean Field Theory

Aditi Sen, Ujjwal Sen

Exactly solvable many-body systems are few and far between, and the utility of approximate methods cannot be overestimated. Entanglement mean field theory is an approximate method to handle such systems. While mean field theories reduce the many-body system to an effective single-body one, entanglement mean field theory reduces it to a two-body system. And in contrast to mean field theories where the self-consistency equations are in terms of single-site physical parameters, those in entanglement mean field theory are in terms of both single- and two-site parameters. Hitherto, the theory has been applied to predict properties of the static states, like ground and thermal states, of many-body systems. Here we give a method to employ it to predict properties of time-evolved states. The predictions are then compared with known results of paradigmatic spin Hamiltonians.

arXiv:1105.2382•Journal of Physics Conference Series•May 1, 2011•2 citations
A novel method is presented for implementation of the extended mean-field theory incorporating two-body collisions. At a given time, stochastic imaginary time propagation of occupied states are used to generate a convenient basis. The quantal collision terms, including memory effects, is then computed by a backward mean-field propagation of these single-particle states. The method is illustrated in an exactly solvable model. Whereas the usual TDHF fails to reproduce the long time evolution, a good agreement is found between the extended TDHF and the exact solution. PACS: 05.30.-d, 24.10.Cn, 05.60.+w
The exact study of many-body microscopic systems is impossible when the number of particles is large (N ≥ 3). Approximate methods are then used. The time-independent mean-field (TIMF) approximation has been proposed for the description of collisions in many-body systems. Collision amplitudes are derived by the use of a variational principle and the choice of trial functions as products of single-particle orbitals. Resulting mean-field equations with a nonvanishing right-hand side turn out to be a generalization of the traditional Hartree or Hatree–Fock type equations. These TIMF equations are successfully solved numerically for the case of short-range forces. In this paper, we test the validity of this theory for the Coulomb interaction between two particles, that is, a long-range interaction. A numerical comparison between the exact and the mean-field solutions is conducted PACS Nos.: 31.15.Ne, 31.15.Pf, 21.45.+v,25.10.-i
In the stochastic mean-field approach, an ensemble of initial conditions is considered to incorporate correlations beyond the mean-field. Then each starting point is propagated separately using the Time-Dependent Hartree-Fock equation of motion. This approach provides a rather simple tool to better describe fluctuations compared to the standard TDHF. Several illustrations are presented showing that this theory can be rather effective to treat the dynamics close to a quantum phase transition. Applications to fusion and transfer reactions demonstrate the great improvement in the description of mass dispersion.
The time-dependent Hartree-Fock (TDHF) and density functional theory (DFT) are among the most useful approaches within mean-field theories for studying static and dynamic properties of complex many-body systems in different branches of physics. Despite the fact that they provide a good approximation for the average properties of one-body degrees of freedoms, they are known to fail to include quantal fluctuations of collective observables and they do not provide sufficient dissipation of collective motion. In order to incorporate these missing effects the stochastic mean-field (SMF) approach was proposed (Ayik 2008). In the SMF approach a set of stochastic initial one-body densities are evolved. Each stochastic one-body density matrix consists of a set of stochastic Gaussian random numbers that satisfy the first and second moments of collective one-body observables. Recent works indicate that the SMF approach provides a good description of the dynamics of the nuclear systems (Yilmaz et al. 2018; Ayik et al. 2019). In this work, the one-dimensional Fermi-Hubbard model is simulated with the SMF approach by using different distributions such as Gaussian, uniform, bimodal and two-point distributions. The dissipative dynamics are discussed and the predictive power of the SMF approach with different probability distributions are compared with each other and the exact dynamics. As a result it is shown that by considering different distributions, the predictive power of the SMF approach can be improved.
The time-independent mean-field theory of collisions converts an intractable linear problem, namely, the calculation of the many-body propagator (E-H${)}^{\mathrm{\ensuremath{-}}1}$, into a numerically solvable problem, namely, the coupled calculation of single-particle propagators (\ensuremath{\eta}-h${)}^{\mathrm{\ensuremath{-}}1}$. The latter problem, however, reflects its nonlinearity through many solutions, out of which only one is nonspurious and gives a good approximation to the unique solution (off shell) of the former, linear problem. We prove the stability of this nonspurious solution in the special case of a four-body, one-dimensional collision. The experience thus gained is used to generate transition-shell models in the case of a realistic, three-dimensional, four-body elastic collision.
Exactly solvable many-body systems are few and far between, and the utility of approximate methods cannot be overestimated. Entanglement mean field theory is an approximate method to handle such systems. While mean field theories reduce the many-body system to an effective single-body one, entanglement mean field theory reduces it to a two-body system. And in contrast to mean field theories where the self-consistency equations are in terms of single-site physical parameters, those in entanglement mean field theory are in terms of both single- and two-site parameters. Hitherto, the theory has been applied to predict properties of the static states, like ground and thermal states, of many-body systems. Here we give a method to employ it to predict properties of time-evolved states. The predictions are then compared with known results of paradigmatic spin Hamiltonians.