38 research outputs found
A Stochastic Mean-Field Approach For Nuclear Dynamics
We propose a microscopic stochastic approach to improve description of
nuclear dynamics beyond the mean-field approximation at low energies. It is
shown that, for small amplitude fluctuations, the proposed model gives a result
for the dispersion of a one-body observable that is identical to the result
obtained previously through a variational approach. Furthermore, by projecting
the proposed stochastic mean-field evolution on a collective path, a
generalized Langevin equation is derived for collective variable, which
incorporate one-body dissipation and one-body fluctuation mechanism in
accordance with quantal fluctuation-dissipation relation.Comment: Paper is accepted for publication in Phys. Lett.
Stochastic quantum dynamics beyond mean-field
Mean-field approaches where a complex fermionic many-body problem is replaced
by an ensemble of independent particles in a self-consistent mean-field can
describe many static and dynamical aspects. It generally provides a rather good
approximation for the average properties of one-body degrees of freedom.
However, the mean-field approximation generally fails to produce quantum
fluctuations of collective motion. To overcome this difficulty, noise can be
added to the mean-field theory leading to a stochastic description of the
many-body problem. In the present work, we summarize recent progress in this
field and discuss approaches where fluctuations have been added either to the
initial time, like in the Stochastic Mean-Field theory or continuously in time
as in the Stochastic Time-Dependent Hartree-Fock. In some cases, the initial
problem can even be re-formulated exactly by introducing Quantum Monte-Carlo
methods in real-time. The possibility to describe superfluid systems is also
invoked. Successes and shortcomings of the different beyond mean-field theories
are discussed and illustrated.Comment: 34 pages, submitted to EPJA-Review sectio
Nucleus-nucleus potential, energy dissipation and mass dispersion in fusion and transfer reactions
The nucleus-nucleus potential and energy dissipation in fusion reactions are
obtained from microscopic mean-field dynamics. The deduced potentials nicely
reproduce the one extracted from experimental data. Energy dissipation shows a
universal behaviour between different reactions. Also, the dispersion of mass
distribution in transfer reaction is investigated in a stochastic mean-field
dynamics. By including initial fluctuations in collective space, the
description of the dispersion is much improved compared to that of mean field
only. The result is consistent with the macroscopic phenomenological analysis
of the experimental data.Comment: 4 pages, 4 figures. Proceedings of Second International Workshop on
Compound Nuclear Reactions and Related Topics (CNR*09), October 5-8, 2009,
Bordeaux, Franc
Collective response of nuclei: Comparison between experiments and extended mean-field calculations
The giant monopole, dipole and quadrupole responses in Ca, Zr,
Sn and Pb are investigated using linear response treatment
based on a stochastic one-body transport theory. Effects of the coupling to
low-lying surface modes (coherent mechanism) and the incoherent mechanism due
to nucleon-nucleon collisions are included beyond the usual mean-field
description. We emphasize the importance of both mechanism in the fragmentation
and damping of giant resonance. Calculated spectra are compared with experiment
in terms of percentage of Energy-Weighted Sum-Rules in various energy regions.
We obtained reasonable agreement in all cases. A special attention as been
given to the fragmentation of the Giant Quadrupole Resonance in calcium and
lead. In particular, the equal splitting of the in Ca is
correctly reproduced. In addition, the appearance of fine structure in the
response Pb is partly described by the calculations in which the
coherent mechanism play an important role.Comment: 44 pages, 8 figures, submitted to Physical Review
Quantal corrections to mean-field dynamics including pairing
Extending the stochastic mean-field model by including pairing, an approach
is proposed for describing evolutions of complex many-body systems in terms of
an ensemble of Time-Dependent Hartree-Fock Bogoliubov trajectories which is
determined by incorporating fluctuations in the initial state. Non-linear
evolution of the initial fluctuations provides an approximate description of
quantal correlations and fluctuations of collective observables. Since the
initial-state fluctuations break the particle-number symmetry, the dynamical
description in which pairing correlations play a crucial role is greatly
improved as compare to the mean-field evolution. The approach is illustrated
for a system of particles governed by a pairing Hamiltonian.Comment: 5 pages, 2 figures, To appear in Phys. Rev. C (Rapid communication
Finite Temperature Nuclear Response in Extended Random-Phase Approximation
The nuclear collective response at finite temperature is investigated for the
first time in the quantum framework of the small amplitude limit of the
extended TDHF approach, including a non-Markovian collision term. It is shown
that the collision width satisfies a secular equation. By employing a Skyrme
force, the isoscalar monopole, isovector dipole and isoscalar quadrupole
excitations in are calculated and important quantum features are
pointed out. The collisional damping due to decay into incoherent 2p-2h states
is small at low temperatures but increases rapidly at higher temperatures.Comment: 22 Latex pages including 9 figures. Phys. Rev. C (in press
A simplified BBGKY hierarchy for correlated fermionic systems from a Stochastic Mean-Field approach
The stochastic mean-field (SMF) approach allows to treat correlations beyond
mean-field using a set of independent mean-field trajectories with appropriate
choice of fluctuating initial conditions. We show here, that this approach is
equivalent to a simplified version of the Bogolyubov-Born-Green-Kirkwood-Yvon
(BBGKY) hierarchy between one-, two-, ..., N-body degrees of freedom. In this
simplified version, one-body degrees of freedom are coupled to fluctuations to
all orders while retaining only specific terms of the general BBGKY hierarchy.
The use of the simplified BBGKY is illustrated with the Lipkin-Meshkov-Glick
(LMG) model. We show that a truncated version of this hierarchy can be useful,
as an alternative to the SMF, especially in the weak coupling regime to get
physical insight in the effect beyond mean-field. In particular, it leads to
approximate analytical expressions for the quantum fluctuations both in the
weak and strong coupling regime. In the strong coupling regime, it can only be
used for short time evolution. In that case, it gives information on the
evolution time-scale close to a saddle point associated to a quantum
phase-transition. For long time evolution and strong coupling, we observed that
the simplified BBGKY hierarchy cannot be truncated and only the full SMF with
initial sampling leads to reasonable results.Comment: 10 pages, 4 figure