Time-dependent Density-matrix Theory Research Articles

Controlling Rotationally Resolved Two-Dimensional Infrared Spectra with Polarization.

Recent advancements in infrared frequency combs will enable facile recording of coherent two-dimensional infrared spectra of gas-phase molecules with rotational resolution (RR2DIR). Using time-dependent density-matrix perturbation theory and angular momentum algebra techniques, we derive new polarization conditions unique to freely rotating molecules and absent in the condensed phase. These polarization conditions can be used to suppress parts of 2DIR rovibrational response, clarifying complicated RR2DIR spectra. With the polarization control methods described here, RR2DIR spectroscopy can be a powerful tool for studying complex gas mixtures of polyatomic molecules.

Extended random-phase-approximation study of the fragmentation of the giant quadrupole resonance in O16

The damping of isoscalar giant quadrupole resonance in $^{16}\mathrm{O}$ is studied using extended random-phase-approximation approaches derived from the time-dependent density-matrix theory. It is pointed out that the effects of ground-state correlations bring strong fragmentation of quadrupole strength even if the number of two-particle--two-hole configurations is strongly limited.

Dynamics of molecular alignment steered by a few-cycle terahertz laser pulse

The field-free alignment of molecule ClCN is investigated by using a terahertz few-cycle pulse (THz FCP) based on the time-dependent density matrix theory. It is shown that a high degree of molecular alignment can be obtained by changing the matching number of the THz FCPs in the adiabatic regime and the non-adiabatic regime. The matching number can affect both the maximum value of the alignment and the time at which it is achieved. It is also found that a higher degree of alignment can be achieved by using the THz FCP at lower intensity and there exists an optimal threshold of molecular alignment with the increase of the field amplitude. Also found is the frequency sensitive region in which the degree of maximum alignment can be enhanced greatly by modulating the center frequencies of different THz FCPs. The investigation demonstrates that comparing with a THz single-cycle pulse, a better result of the field-free alignment can be created by a THz FCP at a constant rotational temperature of molecule.

Effects of ground-state correlations on the damping of giant dipole resonances in LS closed-shell nuclei

Abstract The effects of ground-state correlations on the damping of isovector giant dipole resonances in the LS closed-shell nuclei 16O and 40Ca are studied using extended random phase approximation (RPA) approaches derived from the time-dependent density matrix theory. It is pointed out that unconventional two-body amplitudes of one-particle–three-hole and three-particle–one-hole types that are neglected in most extended RPA theories play an important role in the fragmentation of isovector dipole strength.

Properties of Skyrme force as a residual interaction in beyond-mean-field theories

Abstract In an effort to find an effective interaction that can consistently be used for both the mean-field part and the residual part in beyond-mean-field theories, the properties of the Skyrme interactions as a residual interaction are investigated. The time-dependent density-matrix theory (TDDM) is used as a beyond-mean-field theory and the ground states of $^{16}$O and $^{40}$Ca are calculated using the five standard parametrizations of the Skyrme interaction, which differ in density and momentum dependence. It is found that the Skyrme interaction, which has strong density dependence and weak momentum dependence, induces substantial ground-state correlations comparable to the results of other theoretical calculations.

Applications of Time-Dependent Density-Matrix Approach

The equations of motion for reduced density matrices form a coupled chain known as the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy. To close the coupled chain at the two-body level, approximations for a three-body density matrix with one-body and two-body density matrices are needed. The time-dependent density-matrix theory (TDDM) assumes that the three-body density matrix is given by the antisymmetrized products of the one-body and two-body density matrices. In this review the truncation schemes of the BBGKY hierarchy beyond TDDM are discussed and a formulation for the study of excited states which is derived from the time-dependent approach is explained. The truncation schemes and the formulation for excited states are applied to the Lipkin model and the Hubbard model to corroborate their validity. Two realistic applications of the TDDM approaches are also presented. One is the dipole and quadrupole excitations of $^{40}$Ca and $^{48}$Ca and the other the fusion reactions of $^{16}$O + $^{16}$O.

Truncation scheme of time-dependent density-matrix approach III

The time-dependent density-matrix theory (TDDM) where the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy for reduced density matrices is truncated by approximating a three-body density matrix with one-body and two-body density matrices is applied to the Lipkin model. It is shown that in the large $N$ limit the ground state in TDDM approaches the exact solution. Various truncation schemes for the three-body density matrix are also tested for an extended three-level Lipkin model.

Effects of ground-state correlations on dipole and quadrupole excitations of 40Ca and 48Ca

The effects of ground-state correlations on the dipole and quadrupole excitations are studied for $^{40}$Ca and $^{48}$Ca using the extended random phase approximation (ERPA) derived from the time-dependent density-matrix theory. Large effects of the ground-state correlations are found in the fragmentation of the giant quadrupole resonance in $^{40}$Ca and in the low-lying dipole strength in $^{48}$Ca. It is discussed that the former is due to a mixing of different configurations in the ground state and the latter is from the partial occupation of the neutron single-particle states. The dipole and quadrupole strength distributions below 10 MeV calculated in ERPA are in qualitatively agreement with experiment.

Role of small-norm components in extended random-phase approximation

The role of the small-norm amplitudes in extended RPA theories such as the particle-particle and hole-hole components of one-body amplitudes and the two-body amplitudes other than two particle - two holes components are investigated for the one-dimensional Hubbard model using an extended RPA derived from the time-dependent density-matrix theory. It is found that these amplitudes cannot be neglected in strongly interacting regions where the effects of ground-state correlations are significant.

Two-body dissipation effects on the synthesis of superheavy elements

To investigate the two-body dissipation effects on the synthesis of superheavy elements, we calculate low-energy collisions of the $N=50$ isotones ($^{82}$Ge, $^{84}$Se, $^{86}$Kr and $^{88}$Sr) on $^{208}$Pb using the time-dependent density-matrix theory (TDDM). TDDM is an extension of the time-dependent Hartree-Fock (TDHF) theory and can determine the time evolution of one-body and two-body density matrices. Thus TDDM describes both one-body and two-body dissipation of collective energies. It is shown that the two-body dissipation may increase fusion cross sections and enhance the synthesis of superheavy elements.

Time-dependent density-matrix functional theory for trion excitations: Application to monolayerMoS2and other transition-metal dichalcogenides

To examine optically excited bound states, excitons and trions, in monolayer ${\mathrm{MoS}}_{2}$, ${\mathrm{MoSe}}_{2}$, and ${\mathrm{WSe}}_{2}$, we have formulated and applied a generalized time-dependent density-matrix functional theory approach. Three different types of exchange-correlation (XC) kernels were used and their validity was evaluated through comparison with available experimental data. For excitons, we find that the local kernels, from the local density approximation and its gradient-corrected form, lead to much smaller binding energy than that extracted from experimental data, while those based on long-range (LR) interactions fare much better. The same is the case for the trion binding energy once screening effects are taken into account. Our results suggest that for both excitons and trions, the LR form of the XC kernel is necessary to describe bound states. These results confirm information from experimental data on single-layer dichalcogenides that their exciton and trion binding energies are of the order of hundreds (excitons) and tens (trions) of milli-electron volts, a result that may suggest technological application of these materials at room temperature. The proposed methodology can be straightforwardly extended to bound states with a larger number of electrons and holes than considered here.

Application of extended random-phase approximation with ground-state correlations to collective excitations of 16O

The ground-state correlation effects on the octupole excitation of 16O are studied using the extended random phase approximation (ERPA) derived from the time-dependent density-matrix theory. ERPA includes the effects of ground-state correlations through the fractional occupation of single-particle states and a correlated two-body density matrix. The coupling to two particle – two hole configurations is also included in ERPA. It is found that the first 3− state calculated in the random phase approximation (RPA) is shifted upward when the self-energy contributions due to ground-state correlations are included in particle – hole pairs and that the coupling to two particle – two hole states plays a role in shifting the first 3− state down to the right position.

Effects of ground-state correlations on collective excitations of16O

The effects of the correlations in the ground state of $^{16}$O on the octupole and dipole excitations are studied using the extended random phase approximation (ERPA) derived from the time-dependent density-matrix theory. It is found that the ground-state correlation effects are significant especially in the octupole excitation. It is shown that the first $3^-$ state calculated in the random phase approximation (RPA) is shifted upward when the self-energy contributions are included in particle - hole pairs. The coupling to the two particle - two hole states plays a role in shifting the first $3^-$ state down to the right position. It is also found that the dipole strength is fragmented due to the partial occupation of the single-particle states and that the peak position of the giant dipole resonance calculated in ERPA is little changed from that in RPA due to the above-mentioned competing effects: the increase in particle - hole energy and the coupling to two particle - two hole configurations.

Odd particle number random-phase approximation and extensions: Applications to particle and hole states around16O

The hole-state random phase approximation (hRPA) and the particle-state random phase approximation (pRPA) for systems like odd $A$ nuclei are discussed. These hRPA and pRPA are formulated based on the Hartree-Fock ground state. An extension of hRPA and pRPA based on a correlated ground state is given using time-dependent density-matrix theory. Applications to the single-particle states around $^{16}$O are presented. It is shown that inclusion of ground-state correlation affects appreciably the results of hRPA and pRPA. The question of the coupling of the center of mass motion of the core to the particle (hole) is also discussed.

Spin-orbit coupling and its effects in organic solids

We present a detailed analysis of spin-orbit coupling (SOC) in $\ensuremath{\pi}$-conjugated organic materials and its effects on spin characteristics including the spin-relaxation time, spin-diffusion length, and $g$ factor. While $\ensuremath{\pi}$ electrons are responsible for low-energy electrical and optical processes in $\ensuremath{\pi}$-conjugated organic solids, $\ensuremath{\sigma}$ electrons must be explicitly included to properly describe the SOC. The SOC mixes up- and down-spin states and, in the context of spintronics, can be quantified by an admixture parameter in the electron and hole polaron states in $\ensuremath{\pi}$-conjugated organics. Molecular geometry fluctuations such as ring torsion, which are common in soft organic materials and may depend on sample preparation, are found to have a strong effect on the spin mixing. The SOC-induced spin mixing leads to spin flips as polarons hop from one molecule to another, giving rise to spin relaxation and diffusion, which are examined by the time-dependent perturbation theory and density-matrix theory. The spin-relaxation rate is found to be proportional to the carrier hopping rate, or equivalently, carrier mobility. The spin-diffusion length depends on the spin mixing and hopping distance but is insensitive to the carrier mobility. An applied electric field causes spin drift and gives rise to upstream and downstream spin-diffusion lengths in the hopping-conduction regime. The SOC influences the $g$ factor of the polaron state and makes it deviate from the free-electron value. The deviation is due to the mixing of different orbitals in the polaron state, which does not include the spin mixing within the same orbital, and therefore underestimates the SOC strength. In particular, the $g$ factor is not sensitive to the molecular geometry fluctuations, where the spin mixing within the same orbital is dominant. The SOCs in tris-(8-hydroxyquinoline) aluminum (Alq${}_{3}$) and in copper phthalocyanine (CuPc) are particularly strong, due to the orthogonal arrangement of the three ligands in the former and Cu $3d$ orbitals in the latter. The theory quantitatively explains the recent measured spin-diffusion lengths in Alq${}_{3}$ from muon spin rotation and in CuPc from spin-polarized two-photon photoemission.

Time-dependent density-matrix functional theory for biexcitonic phenomena

We formulate a time-dependent density-matrix functional theory (TDDMFT) approach for higher-order correlation effects like biexcitons in optical processes in solids based on a reduced two-particle density-matrix formalism within the normal orbital representation. A TDDMFT version of the Schr\"odinger equation for biexcitons in terms of one- and two-body reduced density matrices is derived, which leads to finite biexcitonic binding energies already with an adiabatic approximation. Biexcitonic binding energies for several bulk semiconductors are calculated using a contact biexciton model.

Damping of collective states in an extended random-phase approximation with ground-state correlations

Applications of an extended version of the Hartree-Fock theory and the random-phase approximation derived from the time-dependent density-matrix theory (TDDM) are presented. In this TDDM-based theory, the ground state is given as a stationary solution of the TDDM equations and the excited states are calculated using the small-amplitude limit of TDDM. The first application presented is an extended Lipkin model in which an interaction term describing a particle scattering is added to the original Hamiltonian so that the damping of a collective state is taken into account. It is found that the TDDM-based theory well reproduces the ground state and excited states of the extended Lipkin model. The quadrupole excitation of the oxygen isotopes $^{16,20,22}\mathrm{O}$ is also studied as realistic applications of the TDDM-based theory. It is found that large fragmentation of the giant quadrupole resonance in $^{16}\mathrm{O}$ is reproduced, and it is pointed out that the effects of ground-state correlations are quite important for fragmentation. It is also found that the quadrupole states in neutron-rich oxygen isotopes have small spreading widths.

Comparison of Density-Matrix Theory and Pairing Theory

The ground states and the first 2 + states of 20 O and 22 O are derived using two schemes, one consisting of the Hartree-Fock-Bogoliubov theory (HFB) plus the quasi-particle random phase approximation (QRPA) and the other consisting of the stationary solution and the small amplitude limit of the time-dependent density-matrix theory (TDDM). It is found that although the two schemes give similar results for the ground state of 20 O, there are differences between the results obtained with the two methods for the first 2 + state of 20 O and the ground state of 22 O: The first 2 + state of 20 O derived with TDDM has a larger collectivity, and TDDM induces a long-range correlation in the ground state of 22 O, which cannot be obtained with the HFB calculation. The origins of the differences are discussed.

Extended RPA with ground-state correlations in a solvable model

The ground states and excited states of the Lipkin model hamiltonian are calculated using a new theoretical approach which has been derived from an extended time-dependent Hartree-Fock theory known as the time-dependent density-matrix theory (TDDM). TDDM enables us to calculate correlated ground states, and its small amplitude limit (STDDM), which is a version of extended RPA theories based on a correlated ground state, can be used to calculate excited states. It is found that this TDDM plus STDDM approach gives much better results for both the ground states and the excited states than the Hartree-Fock ground state plus RPA approach.

Relation between Density-Matrix Theory and Pairing Theory

The time-dependent density-matrix theory (TDDM) gives a correlated ground state as a stationary solution of the time-dependent equations for one-body and two-body density matrices. The small amplitude limit of TDDM (STDDM) is a version of extended RPA theories which include the effects of ground state correlations. It is shown that the solutions of the Hartree-Fock Bogoliubov theory and the quasi-particle RPA satisfy the TDDM and STDDM equations, respectively, when only pairing-type correlations are taken into account in TDDM and STDDM.