Time-dependent Density-matrix Formalism Research Articles

Time-resolved optical conductivity and Higgs oscillations in two-band dirty superconductors

Recent studies have emphasized the importance of impurity scattering for the optical Higgs response of superconductors. In the dirty limit, an additional paramagnetic coupling of light to the superconducting condensate arises which drastically enhances excitation. So far, most work concentrated on the periodic driving with light, where the third-harmonic generation response of the Higgs mode was shown to be enhanced. In this work, we additionally calculate the time-resolved optical conductivity of single- and two-band superconductors in a two-pulse quench-probe setup, where we find good agreement with existing experimental results. We use the Mattis-Bardeen approach to incorporate impurity scattering and calculate explicitly the time-evolution of the system. Calculations are performed both in a diagrammatic picture derived from an effective action formalism and within a time-dependent density matrix formalism.

An exciton scattering model for carrier multiplication in semiconductor nanocrystals: Theory

The effect of carrier multiplication (CM) in semiconductor nanocrystals is systematically treated by employing an exciton scattering approach. Using projection operators, we reduce the Coulomb coupled multiexciton dynamics to scattering dynamics in the space spanning both single- and biexciton states. We derive a closed set of equations determining the scattering matrix elements. This allows us to interpret CM dynamics as a series of odd-order interband scattering events. Using the time-dependent density matrix formalism, we provide a rigorous description of the CM dynamics induced by a finite-time pump pulse. Within this approach, both processes of single- and biexciton photogeneration and the consequent population relaxation are treated on the same footing. This approach provides a framework for numerical calculations and for comparisons of the quantum efficiencies associated with each process. For applications, the limit of weak interband Coulomb coupling is considered. Finally, we demonstrate that three previously used theoretical models can be recovered as limiting cases of our exciton scattering model.

Quantum Study of a Trapped Dipolar Fermi Gas

Using the time-dependent Hartree–Fock theory (TDHF), we study the ground states of dipolar fermion gases in a spherical trap. It is found that deformed configurations which have prolate shape both in real and momentum space are energetically favored and that when the dipolar interaction is not very strong, the deformation of the gases shows a prominent shell structure at closed oscillator-shell configurations. The quadrupole and breathing modes are also studied in TDHF and it is found that these modes are little affected by the dipolar interaction when the gases have the closed-shell configurations. The effects of the two-body correlations on the ground-state properties and also on the damping of the quadrupole mode are also investigated using a time-dependent density-matrix formalism. It is found that the effects of the two-body correlations are not significant for the closed-shell configurations.

Mechanisms of holographic recording in rubidium vapor close to resonance

We investigate the nonlinear refraction and absorption related to holographic writing in rubidium vapor at resonance with 87Rb D2 transition. The numerical model based on time-dependent density matrix formalism is used. The theory adequately describes nonlinear optical rotation and absorption at light intensities in the 0.1-30 mW/cm2 range. The basic configurations for obtaining amplitude and phase gratings for nearly equal frequencies of writing beams are investigated experimentally, and the writing time is estimated.

Spurious modes in Extended RPA theories

Necessary conditions that the spurious state associated with the translational motion and its double-phonon state have zero excitation energy in extended RPA (ERPA) theories which include both one-body and two-body amplitudes are investigated using the small amplitude limit of the time-dependent density-matrix theory (STDDM). STDDM provides us with a quite general form of ERPA as compared with other similar theories in the sense that all components of one-body and two-body amplitudes are taken into account. Two conditions are found necessary to guarantee the above property of the single and double spurious states: The first is that no truncation in the single-particle space should be made. This condition is necessary for the closure relation to be used and is common for the single and double spurious states. The second depends on the mode. For the single spurious state all components of the one-body amplitudes must be included, and for the double spurious state all components of one-body and two-body amplitudes have to be included. It is also shown that the Kohn theorem and the continuity equations for transition densities and currents hold under the same conditions as the spurious states. ERPA theories formulated using the Hartree-Fock ground state have a non-hermiticity problem. A method for formulating ERPA with hermiticity is also proposed using the time-dependent density-matrix formalism.

Quadrupole resonances in unstable oxygen isotopes in time-dependent density-matrix formalism

The strength functions of quadrupole modes in the unstable oxygen isotopes 22O and 24O are calculated using an extended version of the time-dependent Hartree–Fock theory known as the time-dependent density-matrix theory (TDDM). It is found that TDDM gives the lowest quadrupole states which are energetically shifted upward and become significantly collective due to the coupling to two-body configurations. It is pointed out that these features of the lowest quadrupole states are similar to those obtained in the quasi-particle random phase approximation.

Stationary Solution of a Time Dependent Density Matrix Formalism

Stationary Solution of a Time Dependent Density Matrix Formalism

Stationary Solution of a Time Dependent Density Matrix Formalism

A stationary solution of a time-dependent density-matrix formalism, which is an extension of the time-dependent Hartree-Fock theory to include the effects of two-body correlations, is obtained for the Lipkin model hamiltonian, using an adiabatic treatment of the two-body interaction. It is found that the obtained result is a reasonable approximation for the exact solution of the model. We have recently reported realistic calculations for the damping of giant reso­ nances1>-3> and for low-energy heavy-ion collisions, 4 > based on an extended version of the time-dependent Hartree-Fock theory. The ETDHF theory called the time­ dependent density-matrix theory (TDDM) determines the time evolution of both one-body and two-body density matrices and allows us to consistently treat the effects of the nuclear mean field and two-body correlations. Although the obtained results are quite encouraging, these numerical calculations contain an inconsistency in the treatment of the ground state: the Hartree-Fock (HF) ground state, which clearly is not a stationary solution of TDDM, is used as the initial ground state. In our previous paper 5 > we tried to find a correlated stationary solution of TDDM using the stationary limit of the TDDM equations and the constraints on reduced density matrices derived from general relations among them. The obtained results for the Lipkin model, 6 > however, were not quite satisfactory and the problem of finding the ·reasonable stationary solutions of TDDM has not been settled yet. In this paper we demonstrate that a better stationary solutions of TDDM can be obtained through an adiabatic treatment of two-body interactions. The TDDM equations have been derived from the truncation scheme, proposed by Wang and Cassing,7), 8 > of the well-known BBGKY hierarchy 9 > for reduced density

Approximate ground state of the Lipkin model hamiltonian in density-matrix formalism

A method for finding the ground state of a many-body system, which is consistent with the truncation scheme used in the time-dependent density-matrix formalism of Wang and Cassing, is presented and applied to the Lipkin model. It is found that the method gives better ground states than the Hartree-Fock approximation. However, they significantly differ from the exact ground states.

Landau's collision term in time-dependent density matrix formalism

Landau's expression for the spreading widths of giant resonances is derived, based on the small-amplitude limit of the time-dependent density-matrix theory. It is pointed out that a consistent treatment of the groundstate correlations is essential to obtain the expression.

Application of a time-dependent density-matrix formalism

An extended time-dependent Hartree-Fock theory which includes the effects of nucleon-nucleon collisions is presented and applied to the small-amplitude quadrupole motions of16O and40Ca. The collision term of the theory includes not only the Born term but also higher-order terms. It is found that the higher-order terms are essential to the damping of the motions.

Phase effects in bichromatic field interactions with a two-level atom.

Phase-dependent resonance transitions induced in two-level atoms by a bichromatic field are reported. Strong phase effects are observed in the interaction of a fast atomic beam with a standing-wave rf field. In the atomic rest frame, this field consists of two components with different frequencies and a controlled initial phase difference. Numerical calculations including well-defined phase factors are performed in the time-dependent density matrix formalism. The observed effects are in excellent agreement with this theory.