Time-dependent Mean-field Approach Research Articles

Reexamining an extended-mean-field approach in heavy-ion collisions near the Fermi energy

Static and dynamical aspects of nuclear systems are described through an extended time-dependent mean-field approach. The foundations of the formalism are presented, with highlights on the estimation of average values and their corresponding dispersions. In contrast to semiclassical transport models, the particular interest of this description lies on its intrinsic quantal character. The reliability of this approach is discussed by means of stopping-sensitive observables analysis in heavy-ion collisions in the range of 20 to 120 MeV per nucleon.

Effect of long-range 1/r interactions on the Landau damping in a Bose-Fermi mixture

By using the time-dependent mean-field approach based on the Popov approximation, the Landau damping in a Bose-Fermi superfluid mixture in the presence of a long-range \( 1/r\) interaction between bosons at finite temperature is studied. For a homogeneous three-dimension (3D) gas, we will show, since both Bose-Fermi and the \( 1/r\) interactions contributions are exponentially suppressed, the contact interaction has the dominant role to the low-temperature behavior of the Landau damping and the temperature behavior of the damping rate due to the \( 1/r\) and Bose-Fermi interactions similar to contact interaction is linear at high temperatures. In a two-dimension (2D) system, we will also show that the damping rate in a gas with the \( 1/r\) interaction has a minor role in comparison with contact and dipole-dipole interactions at all ranges of temperatures, and the low-temperatures behavior of the damping rate due to both the \( 1/r\) and dipole-dipole interactions scales as \( e^{-1/T}\) while the contact contribution changes as \(T^{2}\) . Our results have important consequences for ongoing experiments and theoretical researches on ultracold gases with repulsive or attractive long-range \( 1/r\) interaction.

Transport coefficients for a slow Fermi-particle motion

The collective dynamics of a quantum gas of independent particles was studied for a slow collective motion within the nuclear model based on the time-dependent mean-field approach. Leading smooth semiclassical corrections to the friction and inertia coefficients for small multipole distortions of the infinitely deep square-well potential were obtained within the periodic orbit theory. The smooth inertia is mostly larger than its irrotational flow value.

Dynamical description of exotic structures at subnuclear densities

The dynamics of infinite nuclear matter in the conditions of density and temperature expected in the outermost layers of neutron stars is studied in the framework of a microscopic time-dependent mean-field approach around zero temperature. Dynamical processes in inhomogeneous nuclear matter are studied using a large number of nucleons in numerical simulations without any assumptions on the morphology of nuclear matter. The occurrence of exotic structures when varying internal conditions as densities, nuclear species and elementary cell symmetries is investigated. The corresponding structures are studied in terms of a phase diagram in density space evidencing some sensitivity to the isospin-dependent part of the equation of state.

A dynamical description of neutron star crusts

Neutron Stars are natural laboratories where fundamental properties of matter under extreme conditions can be explored. Modern nuclear physics input as well as many-body theories are valuable tools which may allow us to improve our understanding of the physics of those compact objects.In this work the occurrence of exotic structures in the outermost layers of neutron stars is investigated within the framework of a microscopic model. In this approach the nucleonic dynamics is described by a time-dependent mean field approach at around zero temperature. Starting from an initial crystalline lattice of nuclei at subnuclear densities the system evolves toward a manifold of self-organized structures with different shapes and similar energies. These structures are studied in terms of a phase diagram in density and the corresponding sensitivity to the isospin-dependent part of the equation of state and to the isotopic composition is investigated.

GROSS-SHELL EFFECTS IN THE DISSIPATIVE NUCLEAR DYNAMICS

The order-to-chaos transition in the dynamics of the quantum gas of independent particles was studied within the nuclear model based on the time-dependent mean-field approach. The excitation of the quantum gas in the Woods–Saxon potential with a small diffuseness of its surface rippled according to the Legendre polynomials P2 and P3 are obtained for a slow and small amplitude collective motion. We found strong correlations between time-derivatives of the excitation energies (one-body friction coefficients) and shell-correction energies as functions of the particle number. Semiclassical estimates of the friction coefficients were obtained within the periodic orbit theory by using the uniform approximation.

From crystalline to exotic arrangements of matter in neutron star crusts

We investigate the occurrence of exotic structures in the outermost layers of neutron stars within the framework of a microscopic model describing the nucleonic dynamics through a time-dependent mean field approach at around zero temperature. In this model starting from an initial crystalline lattice of nuclei at subnuclear densities the system evolves and self-organizes in various low-lying energy structures without assumption of final shapes. These structures are studied in terms of a density phase diagram. We investigate their sensitivity to the isotopic composition and to the symmetries of the lattice.

Excitation dynamics in a lattice Bose gas within the time-dependent Gutzwiller mean-field approach

The dynamics of the collective excitations of a lattice Bose gas at zero temperature is systematically investigated using the time-dependent Gutzwiller mean-field approach. The excitation modes are determined within the framework of the linear-response theory as solutions of the generalized Bogoliubov--de Gennes equations valid in the superfluid and Mott-insulator phases at arbitrary values of parameters. The expression for the sound velocity derived in this approach coincides with the hydrodynamic relation. We calculate the transition amplitudes for the excitations in the Bragg scattering process and show that the higher excitation modes make significant contributions. We simulate the dynamics of the density perturbations and show that their propagation velocity in the limit of week perturbation is satisfactorily described by the predictions of the linear-response analysis.

THE INTERNAL EXCITATION OF THE GAS OF INDEPENDENT PARTICLES IN A TIME DEPENDENT POTENTIAL

The order-to-chaos transition in the dynamics of independent classical and quantum gas of particles was studied by means of the computer simulations within the nuclear model based on the time-dependent mean-field approach. The excitation of the classical gas for containers whose surfaces are rippled according to Legendre polynomials P2, P3 is followed for twenty periods of oscillations. For different vibration frequencies of small amplitude vibrations of such a container near the spherical equilibrium shape we obtained for the classical gas much smaller excitation energies than those predicted by the wall formula. With increasing equilibrium deformation they become significantly larger and for P3 vibrations they are close to the wall formula limit. Notable shell effects were found in the excitation energies of the quantum gas in the Woods-Saxon potential with the corresponding relatively sharp (diffuseness equals to 0.1 fm) moving surfaces for small-amplitude slow vibrations.

Microscopic description of nuclear fission dynamics

We discuss possible avenues to study fission dynamics starting from a time-dependent mean-field approach. Previous attempts to study fission dynamics using the time-dependent Hartree–Fock (TDHF) theory are analyzed. We argue that different initial conditions may be needed to describe fission dynamics depending on the specifics of the fission phenomenon and propose various approaches toward this goal. In particular, we provide preliminary calculations for studying fission following a heavy-ion reaction using TDHF with a density constraint. Regarding prompt muon-induced fission, we also suggest a new approach for combining the time evolution of the muonic wavefunction with a microscopic treatment of fission dynamics via TDHF.

Nonequilibrium pairing instability in ultracold Fermi gases with population imbalance

We present detailed numerical and analytical investigations of the nonequilibrium dynamics of spin-polarized ultracold Fermi gases following a sudden switching on of the atom-atom pairing coupling strength. Within a time-dependent mean-field approach we show that on increasing the imbalance it takes longer for pairing to develop, the period of the nonlinear oscillations lengthens, and the maximum value of the pairing amplitude decreases. As expected, dynamical pairing is suppressed by the increase of the imbalance. Eventually, for a critical value of the imbalance the nonlinear oscillations do not even develop. Finally, we point out an interesting temperature-reentrant behavior of the exponent characterizing the initial instability.

Mean-field dynamics of the superfluid-insulator phase transition in a gas of ultracold atoms

A large scale dynamical simulation of the superfluid to Mott insulator transition in the gas of ultra cold atoms placed in an optical lattice is performed using the time dependent Gutzwiller mean field approach. This approximate treatment allows us to take into account most of the details of the recent experiment [Nature 415, 39 (2002)] where by changing the depth of the lattice potential an adiabatic transition from a superfluid to a Mott insulator state has been reported. Our simulations reveal a significant excitation of the system with a transition to insulator in restricted regions of the trap.

Quantum soliton dynamics in vibrational chains: Comparison of fully correlated, mean field, and classical dynamics

The dynamics of a chain of vibrational bonds which develop a classical solitary compression wave is simulated. A converged fully correlated quantum mechanical calculation is compared with a time dependent mean field approach (TDSCF) and with a classical simulation. The dynamics were all generated from the same Hamiltonian. The TDSCF and classical calculations show a fully developed solitary wave with the expected dependence of group velocity on amplitude. The full quantum calculations show a solitary-like wave which propagates for a while but then degrades. The robustness of the compression wave depends on the initial preparation. Evidence of partial recurrence of the wave has also been observed.

Time-dependent mean-field theory of the superfluid-insulator phase transition

We develop a time-dependent mean field approach, within the time-dependent variational principle, to describe the Superfluid-Insulator quantum phase transition. We construct the zero temperature phase diagram both of the Bose-Hubbard model (BHM), and of a spin-S Heisenberg model (SHM) with the XXZ anisotropy. The phase diagram of the BHM indicates a phase transition from a Mott insulator to a compressibile superfluid phase, and shows the expected lobe-like structure. The SHM phase diagram displays a quantum phase transition between a paramagnetic and a canted phases showing as well a lobe-like structure. We show how the BHM and Quantum Phase model (QPM) can be rigorously derived from the SHM. Based on such results, the phase boundaries of the SHM are mapped to the BHM ones, while the phase diagram of the QPM is related to that of the SHM. The QPM's phase diagram obtained through the application of our approach to the SHM, describes the known onset of the macroscopic phase coherence from the Coulomb blockade regime for increasing Josephson coupling constant. The BHM and the QPM phase diagrams are in good agreement with Quantum Monte Carlo results, and with the third order strong coupling perturbative expansion.

Even-odd anomalous tunneling effect.

The analysis of the interacting fermion models with the SU(2) symmetry indicates the different behavior of the splittings of opposite-parity lowest-energy eigenstates for even and odd numbers of fermions. The imaginary time-dependent mean-field approach reproduces the average results only. For the odd particle numbers, an introduction of the universal logarithmic term to the action integral is needed. The even-odd effect appears in a wide class of models with the SU(2) symmetry and is connected with the crossing of the energy surfaces of opposite-parity states for an odd number of fermions.

Aspects of quantum chaos

We briefly review some quantum aspects of classically chaotic systems. Their relevance in the context of nuclear physics is illustrated by the time dependent mean field approach and its application to a schematic nuclear shell model.

Solutions of optical Bloch equations for highly excited direct gap semiconductors in a time-dependent mean-field approach

The time-dependent mean-field (TDMF) Bloch equations which describe the near band edge dynamics of a laser excited semiconductor in the athermal stage are solved as coupled integro-differential equations by a numerical procedure. The pseudo-spin vector Sk(t), containing both the complex interband current expectation values Sk± = Skx ± iSky and the inversion Skz, is cast out for resonant as well as nonresonant pump frequencies of the laser pulse. The results for the parameter values of bulk GaAs are drawn in 3d-plots vs. the absolute value of the k-vector and the time. They exhibit in a cleft mountains structure Rabi oscillations near resonant |k|-values as well as adiabatic following far away from the resonance sphere in the k-space. For nonresonant excitations Rabi oscillations are observed in the TDMF approach up to a large detuning of nearly 10 exciton Rydbergs below the fundamental gap.

Time-dependent mean-field approach to molecule-surface scattering at finite temperatures

Theories are presented for the phonon inelastic scattering of molecules from surfaces. Both the molecule and the surface and bulk vibrations of the solid are treated in a fully quantum mechanical fashion. The models can include one- or multiphonon interactions and are thus applicable to both heavy and light gas species at both high and low beam energies. The method is a mean-field approach in that both the molecule and the bath are evolved simultaneously and self-consistently. The result is that the molecular wavefunction obeys a Schrödinger-like equation, but propagates on a gas-surface interaction potential which is both time- and temperature-dependent. The theory is easily implemented using spectral grid or semiclassical time-dependent scattering techniques, with only a small increase in computer requirements. The model is extended to the specific cases of atom- and diatom-metal scattering. Results are presented for H 2, HD, D 2, He, Ne and Ar scattered from metal surfaces.

On the validity of the adiabatic approach to the tunneling phenomenon

The imaginary time-dependent mean-field approach to the tunneling phenomenon is tested in a simple, exactly solvable model. An important role of nonadiabatic effects is found in the region where the approach works well. This is the case of small penetration probability which corresponds to high barriers. Thus, the applicability of the usual cranked mean-field approximation is questionable in this case.

Variational extension of the time-dependent mean-field approach

We investigate an application of the variational principle of Balian and Vénéroni for density operators and observables. Our choice for the trial spaces incorporates correlations in the density operator. It allows one to calculate the expectation values of both one-body and two-body observables. We derive a set of coupled equations which extends the TDHF formalism and determines the evolution of the partition function, the one-body density, and the second cumulant (it corresponds also to a truncation of the quantal counterpart of the BBKGY equations). By restricting further the trial space for the two-body observables, the variational principle generates simpler equations which still include the effects of a selected class of correlations on the evolution of the one-body density.