Time-dependent Local Density Approximation Research Articles

4f photoabsorption in Pt+ to Pt4+

Detailed knowledge of the inner-shell atomic structure of lowly-ionised species is lacking for most elements along the sixth row of the periodic table, from hafnium to bismuth. This paper presents 4f-photoabsorption spectra of Pt+ to Pt4+ ions, recorded between 69 and 127 eV (9.8 nm and 18 nm) using the dual laser plasma method. Analysis of the spectra was supported by atomic structure calculations using the Cowan suite of codes, by relativistic time-dependent local-density approximation (RTDLDA) calculations, and by comparison along isoelectronic series, particularly with spectra of lowly-ionised gold plasmas. The RTDLDA calculations account for the influence of photoionisation and photoexcitation on the recorded spectra. The spectra show 4f 5d, 6d, and 7d transitions, broadened by autoionisation.

Photoionization and core resonances from range-separated density-functional theory: General formalism and example of the beryllium atom.

We explore the merits of linear-response range-separated time-dependent density-functional theory (TDDFT) for the calculation of photoionization spectra. We consider two variants of range-separated TDDFT, namely, the time-dependent range-separated hybrid (TDRSH) scheme, which uses a global range-separation parameter, and the time-dependent locally range-separated hybrid (TDLRSH), which uses a local range-separation parameter, and compare with standard time-dependent local-density approximation (TDLDA) and time-dependent Hartree-Fock (TDHF). We show how to calculate photoionization spectra with these methods using the Sternheimer approach formulated in a non-orthogonal B-spline basis set with appropriate frequency-dependent boundary conditions. We illustrate these methods on the photoionization spectrum of the Be atom, focusing, in particular, on the core resonances. Both the TDRSH and TDLRSH photoionization spectra are found to constitute a large improvement over the TDLDA photoionization spectrum and a more modest improvement over the TDHF photoionization spectrum.

Pairing dynamics and solitonic excitations in collisions of medium-mass, identical nuclei

We present results of collisions of $^{90}\mathrm{Zr}+^{90}\mathrm{Zr}$ and $^{96}\mathrm{Zr}+^{96}\mathrm{Zr}$ obtained within time-dependent density functional theory (TDDFT) extended to superfluid systems, known as the time-dependent superfluid local density approximation (TDSLDA). We discuss qualitatively new features occurring in collisions of two superfluid nuclei at energies in the vicinity of the Coulomb barrier. We show that a solitonic excitation---an abrupt pairing phase distortion---reported previously [P. Magierski et al., Phys. Rev. Lett. 119, 042501 (2017)] increases the barrier for capture, generating effective repulsion between colliding nuclei. Moreover we demonstrate that pairing field leads to qualitatively different dynamics at the Coulomb barrier which manifests itself in a slower evolution of deformation towards a compact shape. Last but not least, we show that magnitude of pairing correlations can be dynamically enhanced after collision. We interpret it as a dynamically induced $\text{U}(1)$ symmetry breaking, which leads to large-amplitude oscillations of pairing field and bears similarity to the pairing Higgs mechanism.

Quantum Dissipative Dynamics (QDD): A real-time real-space approach to far-off-equilibrium dynamics in finite electron systems

In this paper, we present “QDD” (Quantum Dissipative Dynamics), a code package for simulating the dynamics of electrons and ions in finite electron systems (atoms, molecules, clusters) under the influence of external electromagnetic fields. Electron emission is properly accounted for. The novel feature of the present code is that it also covers the description of dissipative dynamics induced by dynamical correlations generated by electron-electron collisions.The paper reviews the underlying theoretical as well as numerical methods and demonstrates the code's capabilities on a selection of typical examples. Program summaryProgram Title: QDDCPC Library link to program files:https://doi.org/10.17632/jpwzm9knmb.1Licensing provisions: GPLv3Programming language: Fortran 90 (with Fortran 2008 standard)Supplementary material: User Manual, input and output filesNature of problem: The QDD code serves to simulate the dynamics of finite electron systems (atoms, molecules, clusters) excited by strong electromagnetic fields as delivered by lasers or highly charged ions. Basis of the description is Time-Dependent Density Functional Theory (TDDFT) at the level of the Time-Dependent Local-Density Approximation (TDLDA) augmented by an approximate Self-Interaction Correction (SIC), the latter being crucial for proper description of electron emission. The novel feature of the present code is that it allows one to track the dissipative dynamics induced by dynamical correlations from the earliest times of excitation on. This is done here at a fully quantum mechanical level within the Relaxation-Time Approximation (RTA). Electron dynamics is also coupled to ionic motion treated by classical molecular dynamics.Solution method: The numerical representation uses a 3D coordinate-space grid for electronic wave functions and fields. The kinetic energy operator is evaluated in momentum space connected by a Fast Fourier Transform (FFT). Standard schemes for electronic ground state, ionic ground state, and propagation of TDLDA in real time as well as ionic dynamics are used. Electron emission is enabled by absorbing boundary conditions using a mask function near the boundaries. The time evolution of dissipation (by RTA) is evaluated in a large space of occupied and unoccupied single-electron states.Additional comments including restrictions and unusual features: Only the actual computing hardware (RAM, number of nodes on board) limits the system size which can be treated. The code package allows sequential and parallel (OpenMP) computation. The simulation can be continued from a previously saved dynamical configuration.

The LISE package: Solvers for static and time-dependent superfluid local density approximation equations in three dimensions

Nuclear implementation of the density functional theory (DFT) is at present the only microscopic framework applicable to the whole nuclear landscape. The extension of DFT to superfluid systems in the spirit of the Kohn-Sham approach, the superfluid local density approximation (SLDA) and its extension to time-dependent situations, time-dependent superfluid local density approximation (TDSLDA), have been extensively used to describe various static and dynamical problems in nuclear physics, neutron star crust, and cold atom systems. In this paper, we present the codes that solve the static and time-dependent SLDA equations in three-dimensional coordinate space without any symmetry restriction. These codes are fully parallelized with the message passing interface (MPI) library and the time-dependent code takes advantage of graphic processing units (GPU) for accelerating execution. The dynamic code has checkpoint/restart capabilities and for initial conditions one can use any generalized Slater determinant type of wave function. By generating the appropriate initial quasi-particle wave-functions in a static calculation only, the time-dependent code can describe a large number of physical problems: nuclear fission, collisions of heavy ions, the interaction of quantized vortices with nuclei in the nuclear star crust, excitation of superfluid fermion systems by time dependent external fields, quantum shock waves, domain wall generation and propagation, the dynamics of the Anderson-Bogoliubov-Higgs mode, dynamics of fragmented condensates, vortex rings dynamics, generation and dynamics of quantized vortices, their crossing and recombinations and the incipient phases of quantum turbulence. Program summaryProgram title: LISECPC library link to program files:https://doi.org/10.17632/mwr7rsxpjw.1Licensing provisions: BSD 3-ClauseProgramming language: C, CUDANature of problem: The description of nuclear fission and nuclear reactions within the mean field approximation in real time within the extension of the density functional theory to superfluid systems is an extremely computationally demanding problem, which requires the solutions of a very large system of nonlinear coupled complex partial differential equations in 3+1 coordinates. Similar problems also appear in the case of cold atoms and in the dynamics of the neutron star crust, which have been tackled within the same framework with the same codes, using appropriate initial quasi-particle wave functions and/or an appropriate time-dependent external potential.Solution method: The evolution equations are discretized on a 3-dimensional spatial lattice and propagated in time. Spatial derivatives are evaluated using the fast Fourier transform technique. The propagation in time is performed using a predictor-modifier-corrector algorithm due to Adams-Bashforth-Milne, which requires only two evaluations of the right hand side of the equations per time step. The numerical accuracy of the time integration is ∼O(Δt)6. This method has a low truncation error, excellent numerical stability, and low roundoff errors.Additional comments including restrictions and unusual features: The code has been implemented on a variety of supercomputers (Jaguar, Titan, Piz Daint, Tsubame, Summit, Sierra) and demonstrates excellent scaling properties. The strong scaling capabilities can be significantly affected if a very large number of GPUs is used, when the communication time between processes overtakes the computation time as the dominant run time cost.

Emission and collisional correlation in far-off equilibrium quantum systems

We propose a scheme to describe dynamical correlations in finite fermion systems which are open in the sense that they can lose particles, electrons in the present case. It is built as an extension of recently developed schemes to describe dissipative dynamics in finite fermion systems, namely stochastic time-dependent adiabatic local-density approximation (STDLDA) and its averaged version, ASTDLDA, so far being applied only in closed systems. STDLDA and ASTDLDA are based on real-time real-space dynamics in terms of time-dependent density functional theory and add dynamical two-body collisions in a stochastic manner. The extension to systems that can emit electrons is achieved by complementing the complete (numerical) description of wave functions in “inner” space (inside the computation box) through a global description in “outer” space (outside the computation box) and a careful bookkeeping of flow between inner and outer regions. We test the method in a 1D model system, mimicking simple molecules or clusters. Two test cases are investigated: a metal-like system excited by an instantaneous dipole boost, and a covalent-like system excited by an instantaneous one-particle–one-hole transition. The dynamics is analyzed in terms of one-body observables (dipole moment, ionization, entropy). STDLDA and ASTDLDA exhibit clearly dissipative features at variance with mean-field dynamics. Unlike the pattern in closed systems, differences between STDLDA and ASTDLDA show up for ionization. They can be attributed to significantly larger fluctuations of the mean field in STDLDA.

Fission in a microscopic framework: From basic science to support for applications

Recent developments, both in theoretical modeling and computational power, have allowed us to make progress on a goal not fully achieved yet in nuclear theory: a microscopic theory of nuclear fission. Even if the complete microscopic description remains a computationally demanding task, the information that can be provided by current calculations can be extremely useful to guide and constrain more phenomenological approaches, which are simpler to implement. First, a microscopic model that describes the real-time dynamics of the fissioning system can justify or rule out some of the approximations. Second, the microscopic approach can be used to obtain trends, e.g., with increasing excitation energy of the fissioning system, or even to compute observables that cannot be otherwise calculated in phenomenological approaches or that can be hindered by the limitations of the method. We briefly present in this contribution the time-dependent superfluid local density approximation (TDSLDA) approach to nuclear fission, approach that has become a very successful theoretical model in many areas of many-body research. The TDSLDA incorporates the effects of the continuum, the dynamics of the pairing field, and the numerical solution is implemented with controlled approximations and negligible numerical errors. The main part of the current contribution will be dedicated to discussing the method, and recent results concerning the fission dynamics. In addition, we present results on the excitation energy sharing between the fragments, which are in agreement with a qualitative conclusions extracted from a limited number of experimental measurements of properties of prompt neutrons.

Multiplicity of scision neutrons from density functional scission dynamics

The time evolution of the nuclear density of the fissioning system 240Pu during the scission process is obtained from the time-dependent superfluid local-density approximation (TDSLDA) to the density functional theory. A nuclear energy density functional based on the Skyrme force Skm* is used. The duration of the scission process Δt as well as the neck radius (rmin) of the ‘just-before scission’ configuration and the minimum separation (dmin) of the inner surfaces of the fragments in the ’immediately-after scission’ configuration were extracted in order to calculate the multiplicity of the scission neutrons (Vsc) using a phenomenological dynamical scission model (DSM). We find that Vsc=1.347, i.e. half of the prompt fission neutrons measured in the reaction 239Pu(nth; f) are released at scission. After scission, the fragments are left excited and with some extra deformation energy (mainly the heavy one). In this way we can account for the evaporation of the other half and for the emission of γ rays.

Spin response and neutrino mean free path in neutron matter

The longitudinal and transverse density- and spin-density response functions in pure neutron matter (PNM) are derived over a wide range of densities within the time dependent local spin density approximation. The underlying density functional was derived from an Auxiliary Field Diffusion Monte Carlo computation of the equation of state of unpolarized and fully spin polarized PNM. In order to assess the dependence of the results on the specific underlying nucleon–nucleon Hamiltonian, we used both the phenomenological Argonne AV8 + UIX force, and local chiral forces up to next-to-next-to-leading-order (N2LO). The resulting response function has then been applied to the study of the neutrino mean free path in PNM.

Photoionization of neutral magnesium and sodium anion in C60 versus C240

SynopsisWe investigate the effects of confinement and electron correlation on the photoemission properties of Mg and Na− endohedrally sequestered in C60 versus C240. Cross sections and Wigner-Smith time delays for emissions from various electronic levels are computed and analyzed in time-dependent local density approximation.

Assessing density functional theory in real-time and real-space as a tool for studying bacteriochlorophylls and the light-harvesting complex 2

We use real-time density functional theory on a real-space grid to calculate electronic excitations of bacteriochlorophyll chromophores of the light-harvesting complex 2 (LH2). Comparison with Gaussian basis set calculations allows us to assess the numerical trust range for computing electron dynamics in coupled chromophores with both types of techniques. Tuned range-separated hybrid calculations for one bacteriochlorophyll as well as two coupled ones are used as a reference against which we compare results from the adiabatic time-dependent local density approximation (TDLDA). The tuned range-separated hybrid calculations lead to a qualitatively correct description of the electronic excitations and couplings. They allow us to identify spurious charge-transfer excitations that are obtained with the TDLDA. When we take into account the environment that the LH2 protein complex forms for the bacteriochlorophylls, we find that it substantially shifts the energy of the spurious charge-transfer excitations, restoring a qualitatively correct electronic coupling of the dominant excitations also for TDLDA.

On the inclusion of dissipation on top of mean-field approaches

We discuss extensions of time-dependent mean-field theories such as time-dependent local density approximation (TDLDA) in order to include incoherent dynamical correlations, which are known to play a key role in far-off equilibrium dynamics. We focus here on the case of irradiation dynamics in clusters and molecules. The field, still largely unexplored, requires quantum approaches which represents a major formal and computational effort. We present several approaches we have investigated to address such an issue. We start with time-dependent current-density functional theory (TDCDFT), known to provide damping in the linear regime and explore its capability far-off equilibrium. We observe difficulties with the scaling of relaxation times with deposited energy. We next briefly discuss semi-classical approaches which deliver kinetic equations applicable at sufficiently large excitation energies. We then consider a first quantum kinetic equation at the level of a simplified, though rather elaborate in its content, relaxation time approximation (RTA). Thanks to its sophistication, the method allows us to address numerous realistic irradiation scenarios beyond the usual domain of reliability of such theories. We demonstrate in particular the key role played by dense spectral regions in the impact of dissipation in the response of the irradiated system. RTA nevertheless remains a phenomenological approach which calls for more fundamental descriptions. This is achieved by a stochastic extension of mean field theory, coined stochastic time dependent Hartree–Fock (STDHF), which provides an ensemble description of far-off equilibrium dynamics. The method is equivalent to a quantum kinetic equation complemented by a stochastic collision term. STDHF clearly leads to proper thermalization behaviors in 1D test systems considered here. It remains limited by its ensemble nature which requires possibly huge ensembles to properly sample small transition rates. An alternative approach, coined average STDHF (ASTDHF), consists in overlooking mean field fluctuations of STDHF. ASTDHF provides a robust tool, properly matching STDHF when possible and allowing extension to realistic dynamical scenarios in full 3D. It can also be used in open systems to explore, as done in RTA, the competition between ionization and dissipation.

Attosecond Time Delay in Photoionization of Noble-Gas and Halogen Atoms

Ultrafast processes are now accessible on the attosecond time scale due to the availability of ultrashort XUV laser pulses. Noble-gas and halogen atoms remain important targets due to their giant dipole resonance and Cooper minimum. Here, we calculate photoionization cross section, asymmetry parameter and Wigner time delay using the time-dependent local-density approximation (TDLDA), which includes the electron correlation effects. Our results are consistent with experimental data and other theoretical calculations. The asymmetry parameter provides an extra layer of access to the phase information of the photoionization processes. We find that halogen atoms bear a strong resemblance on cross section, asymmetry parameter and time delay to their noble-gas neighbors. Our predicted time delay should provide a guidance for future experiments on those atoms and related molecules.

Accuracy of Fission Dynamics Within the Time-dependent Superfluid Local Density Approximation

We discuss properties of the method based on time dependent superfluid local density approximation (TDSLDA) within an application to induced fission of 240Pu and surrounding nuclei. Various issues related to accuracy of time evolution and the determination of the properties of fission fragments are discussed.

Pairing Dynamics and Time-dependent Density Functional Theory

We discuss issues related to pairing dynamics in nuclear large amplitude collective motion. The examples of effects which are not properly described within BCS theory are presented. In the second part we review properties of TDDFT and in particular we discuss the time-dependent local density approximation (TDSLDA) starting from the stationary action principle.

Surface Plasmon Resonance Damping in Spheroidal Metal Particles: Quantum Confinement, Shape, and Polarization Dependences

A key parameter for optimizing nanosized optical devices involving small metal particles is the spectral width of their localized surface plasmon resonances (LSPR). In the small size range the homogeneous LSPR line width is to a large extent ruled by the spatial confinement-induced broadening contribution which, within a classical description, underlies the popular phenomenological limited mean free path model. This unavoidable contribution to the LSPR line width is basically a quantum finite-size effect rooted in the finite extent of the electronic wave functions. This broadening reflects the surface-induced decay of the coherent collective plasmon excitations into particle–hole (p–h) excitations (Landau damping), the signature of which is a size-dependent fragmented LSPR band pattern which is clearly evidenced in absorption spectra computed within the time-dependent local density approximation (TDLDA). In this work we analyze the spatial confinement-induced LSPR damping contribution in the framework on ...

Towards quantum turbulence in cold atomic fermionic superfluids

Fermionic superfluids provide a new realization of quantum turbulence, accessible to both experiment and theory, yet relevant to phenomena from both cold atoms to nuclear astrophysics. In particular, the strongly interacting Fermi gas realized in cold-atom experiments is closely related to dilute neutron matter in neutron star crusts. Unlike the liquid superfluids 4He (bosons) and 3He (fermions), where quantum turbulence has been studied in laboratory for decades, superfluid Fermi gases stand apart for a number of reasons. They admit a rather reliable theoretical description based on density functional theory called the time-dependent superfluid local density approximation that describes both static and dynamic phenomena. Cold atom experiments demonstrate exquisite control over particle number, spin polarization, density, temperature, and interaction strength. Topological defects such as domain walls and quantized vortices, which lie at the heart of quantum turbulence, can be created and manipulated with time-dependent external potentials, and agree with the time-dependent theoretical techniques. While similar experimental and theoretical control exists for weakly interacting Bose gases, the unitary Fermi gas is strongly interacting. The resulting vortex line density is extremely high, and quantum turbulence may thus be realized in small systems where classical turbulence is suppressed. Fermi gases also permit the study of exotic superfluid phenomena such as the Larkin–Ovchinnikov–Fulde–Ferrell pairing mechanism for polarized superfluids which may give rise to 3D supersolids, and a pseudo-gap at finite temperatures that might affect the regime of classical turbulence. The dynamics associated with these phenomena has only started to be explored. Finally, superfluid mixtures have recently been realized, providing experimental access to phenomena like Andreev–Bashkin entrainment predicted decades ago. Superfluid Fermi gases thus provide a rich forum for addressing phenomena related to quantum turbulence with applications ranging from terrestrial superfluidity to astrophysical dynamics in neutron stars.

Transverse isospin response function of asymmetric nuclear matter from a local isospin density functional

The time dependent local isospin density approximation (TDLIDA) has been extended to the study of the transverse isospin response function in nuclear matter with an arbitrary neutron-proton asymmetry parameter $\ensuremath{\xi}$. The energy density functional has been chosen in order to fit existing accurate quantum Monte Carlo calculations with a density dependent potential. The evolution of the response with $\ensuremath{\xi}$ in the $\mathrm{\ensuremath{\Delta}}{T}_{z}=\ifmmode\pm\else\textpm\fi{}1$ channels is quite different. While the strength of the $\mathrm{\ensuremath{\Delta}}{T}_{z}=+1$ channel disappears rather quickly by increasing the asymmetry, the $\mathrm{\ensuremath{\Delta}}{T}_{z}=\ensuremath{-}1$ channel develops a stronger and stronger collective mode that in the regime typical of neutron star matter at $\ensuremath{\beta}$ equilibrium almost completely exhausts the excitation spectrum of the system. The neutrino mean free paths obtained from the TDLIDA responses are strongly dependent on $\ensuremath{\xi}$ and on the presence of collective modes, leading to a sizable difference with respect to the prediction of the Fermi gas model.

Dynamics of water trimer in femtosecond laser pulses

With the help of the time-dependent local-density approximation (TDLDA) coupled non-adiabatically to molecular dynamics (MD), we studied both the static properties and irradiation dynamics of water trimer subject to the short and intense femtosecond laser field. It is shown that the optimized geometry and the optical absorption strength of the water trimer accord well with results in literature. Three typical possible irradiated scenarios of water trimer which are “normal oscillation”, “dissociation and formation” and “pure OH dissociation” are exhibited by investigating the ionization and the level depletion related to electrons as well as the OH bonds, proton-transfer, the intermolecular distance and the kinetic energy connected with ions. In three scenarios, the behaviors of water trimer can be attributed to the sequential combination of responses of the electrons emission, the proton-transfer, OH vibration and rotation, OH dissociation and hydroxyl formation, respectively. The relevant time scales of the first proton-transfer and OH dissociation are identified as 13 fs and 10–20 fs, respectively. The study of kinetic energies of ions show that the kinetic energies of the remaining ions are all below 4.5 eV and outgoing hydrogen ions carry a kinetic energy about 5–12 eV. Furthermore, it is found that in the tunneling ionization situations the depletion is fairly shared between the various levels except the most deep occupied electronic level while in the multiphotonic ionization case the electron loss comes from all single-electron levels and the HOMO level contributes the most.

Plasmon-resonant Raman spectroscopy in metallic nanoparticles: Surface-enhanced scattering by electronic excitations

Since the discovery of surface-enhanced Raman scattering (SERS) 40 years ago, the origin of the ``background'' that is systematically observed in SERS spectra has remained questionable. To deeply analyze this phenomenon, plasmon-resonant Raman scattering was recorded under specific experimental conditions on a panel of composite multilayer samples containing noble metal (Ag and Au) nanoparticles. Stokes, anti-Stokes, and wide, including very low, frequency ranges have been explored. The effects of temperature, size (in the nm range), embedding medium (${\text{SiO}}_{\text{2}}, {\text{Si}}_{\text{3}}{\text{N}}_{\text{4}}$, or ${\text{TiO}}_{\text{2}}$) or ligands have been successively analyzed. Both lattice (Lamb modes and bulk phonons) and electron (plasmon mode and electron-hole excitations) dynamics have been investigated. This work confirms that in Ag-based nanoplasmonics composite layers, only Raman scattering by single-particle electronic excitations accounts for the background. This latter appears as an intrinsic phenomenon independently of the presence of molecules on the metallic surface. Its spectral shape is well described by revisiting a model developed in the 1990s for analyzing electron scattering in dirty metals, and used later in superconductors. The ${g}_{s}$ factor, that determines the effective mean-free path of free carriers, is evaluated, ${g}_{s}^{\mathrm{expt}}=0.33\ifmmode\pm\else\textpm\fi{}0.04$, in good agreement with a recent evaluation based on time-dependent local density approximation ${g}_{s}^{\mathrm{theor}}=0.32$. Confinement and interface roughness effects at the nanometer range thus appear crucial to understand and control SERS enhancement and more generally plasmon-enhanced processes on metallic surfaces.