Time-dependent Hartree-Fock Approximation Research Articles

Two-photon ionization of lithium in the time-dependent Hartree-Fock approximation

The two-photon ionization rate for the lithium atom is calculated in the time-dependent Hartree-Fock approximation for a variety of intensities and photon frequencies. The time-dependent equation for the valence Hartree-Fock orbital is solved on a two-dimensional cylindrical-coordinate lattice using both fixed and variable grid spacings. The nonperturbative results are compared with previous perturbation-theory results at photon energies near the 2s\ensuremath{\rightarrow}3p single-photon resonance.

Motion of solitons in one-dimensional spin density wave systems

The motion of charged solitons in spin-density-wave systems is numerically studied using the one-dimensional Hubbard model. The motion is induced by an electric filed, which is introduced into the model in terms of a time-dependent vector potential. Use is made of the time-dependent Hartree-Fock approximation, which reduces to the random-phase approximation in the small-amplitude fluctuation limit. Several interesting properties of the moving soliton are obtained. There is a maximum velocity above which the soliton cannot propagate. The maximum velocity is slightly lower than the Fermi velocity. As the soliton approaches the maximum velocity, it gets a remarkable contraction in its width and, in addition, emits longitudinal spin waves behind itself. The behavior of the energy is also studied. The effective mass of the soliton is also calculated.

Collective excitations of an electron Wigner lattice in double-quantum-well systems.

The time-dependent Hartree-Fock approximation is used to study the collective excitations of an electron Wigner solid state in a double quantum well under strong magnetic fields. The electronic tunneling between the two quantum wells is taken into account explicitly. The low-lying excitations consist of an intralevel acoustic phonon and an interlevel optical phonon. When the well separation is increased beyond a certain value, a soft mode is developed in the energy spectrum of the interlevel optical phonon, indicating that the system undergoes a phase transition to a new type of density wave state. We find that independent of the electronic filling factor \ensuremath{\nu}, the position at which the soft mode occurs is always located at the symmetry point J of the first Brillouin zone.

Spin-flip excitations from Landau levels in two dimensions.

Dispersion relations for the spin-flip modes, in which an electron is both promoted from one Landau level to the next and its spin reversed, are calculated in the time-dependent Hartree-Fock approximation and in the generalized single-mode approximation for integer and noninteger filling factors. The energy of these modes can be shifted substantially by electron-electron interactions at k=0. This is in contrast to the magnetoplasma and spin-wave modes, which are not shifted at k=0. The calculated dispersion relations are compared with the results of recent inelastic light-scattering experiments near filling factor ν=1, and predictions are made for other filling factors

Magnetorotons in quasi-one-dimensional electron systems in the absence of Kohn's theorem.

Using a time-dependent Hartree-Fock approximation we have investigated the inter-Landau-level collective excitation spectrum of quasi-one-dimensional electron gases where Kohn's theorem is violated. We find that the spectrum develops a roton minimum at finite wave vectors. In addition to the main magnetoroton, extra collective modes are found. Also we find that it is important to include both the Hartree and exchange local-field corrections in a calculation of the cyclotron resonance.

Magnetoplasmon excitation spectrum for integral filling factors in a two-dimensional electron system.

We present a theory of the magnetoplasmon excitation spectrum in a two-dimensional electron gas for integral filling factors, by calculating the dynamical structure factor within the framework of the time-dependent Hartree-Fock approximation. We include collisional-broadening effect in the dynamical polarizability function in a relaxation-time approximation. We find that to account for the experimentally observed light-scattering spectra, we must introduce a phenomenological breakdown of wave-vector conservation in the dynamical structure factor. For reasonable phenomenological models of the violation of wave-vector conservation (which, for example, may arise from impurities and disorder), we find good agreement with the experimental data. Our calculation resolves the origin of the asymmetric magnetoplasmon band in the Raman intensity spectra for filling factor \ensuremath{\nu}=1, whereas for \ensuremath{\nu}=2, it identifies the peak of the scattering intensity between the roton minimum and the maximum of the dispersion relation in low-mobility samples.

Frequency-dependent conductivity of a pinned Wigner crystal

We have evaluated the frequency-dependent conductivity of the electron crystal state which occurs in two-dimensional systems in a strong magnetic field and studied its dependence on the strength of a commensurate pinning potential. We find that, in contrast to the zero-field case, the pinning frequency is linearly proportional to the strength of the pinning potential and point out that, even in the absence of pinning, poles in the frequency-dependent conductivity do not occur at magnetophonon frequencies. Our calculations are based on a time-dependent Hartree-Fock approximation which allows for arbitrarily large anharmonicities in the electron crystal and can be used to justify a “two-fluid” model in which the system consists of a thermally excited gas of interstitial electrons and an essentially classical electron crystal.

Collective modes of the two-dimensional Wigner crystal in a strong magnetic field.

We present a calculation of the dispersion relation of the intra-Landau-level and inter-Landau-level collective modes of the two-dimensional Wigner crystal in a strong magnetic field. Our analysis is based on the time-dependent Hartree-Fock approximation (TDHFA) for the density-density response function and allows for an arbitrary large degree of anharmonicity. We derive the density-density response function from an equation-of-motion approach that uses identities valid in the strong-field limit. The TDHFA response function is shown to depend only on the ground-state density as calculated in the Hartree-Fock approximation. The intra-Landau-level collective excitation and the excitation near the cyclotron frequency are shown to correspond, respectively, to the low- and high-energy branches of the harmonic phonon spectrum. Additional collective-excitation branches occur near larger multiples of the cyclotron frequency. In contrast with the Hartree-Fock approximation, the TDHFA excitation spectrum does not contain transitions between the Landau-level subbands created by the self-consistent Hartree-Fock potential in the electron lattice.

Simulation of correlated electron tunneling and a Coulomb blockade in a quantum-dot diode.

We investigate the effects of electron exchange and Coulomb correlations on resonant tunneling in a quantum-dot diode by numerically solving the two-electron time-dependent Schr\"odinger equation. Electron-electron interaction effects for spin-parallel and spin-antiparallel electrons give rise to specific peaks in the transmission probability. These features resemble the observed fine structure in the I-V curves. The results of two-electron simulations are used to assess the validity of theoretical approaches such as the Hartree-Fock approximation and the local-spin-density approximation (LSDA), with and without the self-interaction correction, in the density-functional theory. Unlike the LSDA, the time-dependent Hartree-Fock approximation and the self-interaction-corrected LSDA work well for a quantum-confined electron pair. The implications of these simulation results on the many-electron transport in ultrasmall devices is also discussed.

Optical harmonic generation in atomic and molecular hydrogen

We compare calculated optical harmonic spectra for the hydrogen molecule and the hydrogen atom in an intense, linearly polarized laser field. The hydrogen atom calculations use an exact, time-dependent method and the hydrogen molecule calculations are performed in a time-dependent Hartree-Fock approximation. In both cases, the laser-matter interaction is treated completely non-perturbatively. We show that if the H 2 bond length is stretched so that H 2 has the same ionization potential as H, both systems produce remarkably similar harmonic spectra when irradiated with a 1064 nm laser at 1 × 10 14 or 2 × 10 13 W/cm 2.

Phonons as collective modes: The case of a two-dimensional Wigner crystal in a strong magnetic field.

We present a fully quantum-mechanical theory for the phonon modes of a two-dimensional Wigner crystal in the strong-magnetic-field limit. Our theory is based on a time-dependent Hartree-Fock approximation for the density-density response function χ which is exact in the harmonic limit but allows for arbitrarily large anharmonicity. Our calculation is facilitated by identities, valid in the strong-magnetic-field-limit, which allow χ to be expressed solely in terms of the ground-state electron density

Truncation of time-dependent many-body theories

We investigate truncation schemes for the many-body dynamics of finite fermion systems beyond the time-dependent Hartree-Fock (TDHF) approximation. One approach starts from the quantum Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY-)hierarchy of equations of motion for density matrices. It is shown that simple truncation of higher correlations within this scheme is inconsistent because essential exchange correlations are lost. As an alternative, we study the (extended) exp(S) or coupled-cluster formalism. It provides a wider range of applicability. But it also runs into problems with non-unitary propagation after truncation.

Stress and the van hove singularities of hole magnetoplasmons

The hole magnetoplasmon dispersion of GaAs/AlGaAs heterostructures is calculated in the presence of uniaxial stress using a time-dependent Hartree-Fock approximation which becomes exact in the limit of large Landau level separations. We find that the stress affects both the magnitude of cyclotron resonance positions shifted by hole-hole interactions and the sharpness of the Van Hove singularities present in the density of states of hole magnetoplasmons. Both results are consequences of strong heavy and light hole mixing, and differ from the case of an electron gas, where cyclotron resonance position shifts are forbidden by Kohn's theorem. The dependence of the singularities on the applied uniaxial stress should provide a test of our theory.

Scattering between composite particles composed of Fermions in the one-dimensional delta-force model

The general explicit formula of the exact amplitude of the composite particle scattering in the one-dimensional delta-force model is derived. The composite particles are composed of Fermions with an arbitrary SU h internal symmetry. The derivation is made by the use of the recoupling technique of the unitary group and by setting up the recurrence relation with respect to the Fermion number. The exact equivalent local potential which reproduces the exact scattering amplitude is constructed by the use of the soliton solutions of the Kortewegde Vries equation. In most cases the potential is energy-dependent. The accuracy of the time-dependent Hartree-Fock (TDHF) approximation for the composite particle scattering is investigated by comparing the TDHF scattering amplitude with the exact scattering amplitude. While at low energy limit the approximation is not good for small Fermion numbers, at high energy it is good for all Fermion numbers.

Regular and irregular behavior of trajectories in the time-dependent Hartree-Fock approximation.

We investigate the validity of the time-dependent Hartree-Fock (TDHF) approximation for a finite fermion model system. With the help of coherent states we derive equations of motion for the one-particle density, which are of classical Hamiltonian form and can be interpreted in terms of generalized coordinates and momenta. The corresponding trajectories in phase space show transitions between regular and chaotic regimes depending on the parameters of the model. A chaotic behavior indicates a failure of the TDHF approximation because the exact solutions are always regular due to the linearity of the Schr\"odinger equation.

Time-dependent Hartree-Fock theory and residual interactions

In the time-dependent Hartree-Fock approximation (TDHF), the nucleons are assumed to interact only through the mean-field generated by the effective interactions and collisions between particles are neglected. The effect of two body collisions due to the residual interactions is added to the mean-field description of low energy heavy-ion collisions. A collision term from which one may express the collisional results is obtained.

AB initio linear response calculations of the dipole polarizability of the acetylene molecule

The static and dynamic dipole polarizabilities of C 2H 2 molecule are calculated using the time-dependent Hartree-Fock (TDHF) scheme and its multiconfiguration extension, the MCTDHF method. These methods provide the correct linear response to optimized single configuration and multiconfiguration wavefunctions, respectively. Hence, MCTDHF includes correlation effects for the polarizability. For the static polarizability we find α ∥ (0) = 31.37 au and α − (0) = 19.34 au in the TDHF approximation and for an initial MCTDHF calculation including in the complete active space only the 2σ g, 2σ u, 3σ g, 3σ u, 1π u and 1π g orbitals α ∥ (0) =28.75 au and α − (0) = 17.44 au.

Time-dependent Hartree-Fock calculation of the escape width of the giant monopole resonance in 16O.

The damping of the giant monopole resonance in $^{16}\mathrm{O}$ is calculated within the framework of the time-dependent Hartree-Fock approximation. The strength function contains two peaks, centered at around 25 and 33 MeV, with escape widths of \ensuremath{\sim}11 and \ensuremath{\sim}2 MeV, associated with the 1p(0p${)}^{\mathrm{\ensuremath{-}}1}$ and 1s(0s${)}^{\mathrm{\ensuremath{-}}1}$ configurations, respectively.

Collective excitations of closed shell nuclei in heavy ion grazing collisions

Abstract The single and multiple excitations of giant resonances in heavy ion reactions is investigated in the framework of a microscopic model. The scattering process is treated semi-classically as in the Copenhagen model but the target response is constructed from a microscopic RPA calculation using Skyrme forces. The importance of an accurate description of excitation operators and transition form factors is stressed. The connection with other approaches (time-dependent Hartree-Fock approximation, boson expansion method, second RPA) is discussed. The model is applied to reactions involving 208 Pb and 40 Ca nuclei. We conclude that, under near-grazing conditions, with medium or heavy projectiles and for incident energies around 30 MeV/nucleon, there is a substantial probability of observing multiphonon states built on 2 7z.xl;hω giant resonances.

Systematic procedure for going beyond the time-dependent Hartree-Fock approximation.

A systematic procedure that allows for corrections of arbitrary order to the time-dependent Hartree-Fock approach is presented and illustrated with reference to an exactly solvable U(3) model. Substantial improvements over the uncorrelated picture are obtained.