Relaxation in time-dependent current-density-functional theory

We apply the time-dependent current-density-functional theory to the study of the relaxation of a closed many-electron system evolving from a nonequilibrium initial state. We show that the self-consistent unitary time evolution generated by the exchange-correlation vector potential irreversibly drives the system to equilibrium. We also show that the energy dissipated in the Kohn-Sham system, i.e., the noninteracting system whose particle and current densities coincide with those of the physical system under study, is related to the entropy production in the real system.     

Optical properties from time-dependent current-density-functional theory: the case of the alkali metals Na,K, Rb,and Cs

We present the optical conductivity as well as the electron-energy loss spectra of the alkali metals Na, K, Rb, and Cs calculated within time-dependent current-density functional theory. Our ab initio formulation describes from first principles both the Drude-tail and the interband absorption of these metals as well as the most dominant relativistic effects. We show that by using a recently derived current functional [Berger, Phys. Rev. Lett. 115, 137402 (2015)] we obtain an overall good agreement with experiment at a computational cost that is equivalent to the random-phase approximation. We also highlight the importance of the choice of the exchange-correlation potential of the ground state.     

Excitations in time-dependent density-functional theory

An approximate solution to the time-dependent density-functional theory response equations for finite systems is developed, yielding corrections to the single-pole approximation. These explain why allowed Kohn-Sham transition frequencies and oscillator strengths are usually good approximations to the true values, and why sometimes they are not. The approximation yields simple expressions for G?rling-Levy perturbation theory results, and a method for estimating expectation values of the unknown exchange-correlation kernel.     

Spin dynamics from time-dependent spin-density-functional theory

We derive the spin-wave dynamics of a magnetic material from the time-dependent spin-density-functional theory in the linear response regime. The equation of motion for the magnetization includes, besides the static spin stiffness, a "Berry curvature" correction and a damping term. A gradient expansion scheme based on the homogeneous spin-polarized electron gas is proposed for the latter two quantities, and the first few coefficients of the expansion are calculated to second order in the Coulomb interaction.     

Memory in time-dependent density functional theory

Exact time-dependent density functionals remember both the entire history of the density and the initial wave function. We show that the two effects are intimately related, and all history dependence can be written as initial-state dependence, including that of the exchange-correlation kernel. For states that can be evolved from a ground state, all initial-state dependence is a dependence on a pseudo-prehistory, providing a route to excited-state densities from time-dependent density functional theory.     

Derivative discontinuities in time-dependent density-functional theory

Based on the Runge-Gross theorem for ensembles we investigate the influence of particle-number-changes on the exchange-correlation potential in time-dependent density-functional theory. We show that the potential changes discontinuously when the particle number crosses an integer value. Real-time simulations of an atomic ionization process demonstrate that this discontinuity appears naturally in the theory of the time-dependent optimized effective potential. The importance of such a discontinuity for physical processes, even such ones in which the particle number is a constant, is discussed.     

Eigenstates of the time-dependent density-matrix theory

An extended time-dependent Hartree-Fock theory, known as the time-dependent density-matrix theory (TDDM), is solved as a time-independent eigenvalue problem for low-lying 2 ⁺ states in ²⁴O to understand the foundation of the rather successful time-dependent approach. It is found that the calculated strength distribution of the 2 ⁺ states has physically reasonable behavior and that the strength function is practically positive definite though the non-Hermitian Hamiltonian matrix obtained from TDDM does not guarantee it. A relation to an Extended RPA theory with hermiticity is also investigated. It is found that the density-matrix formalism is a good approximation to the Hermitian Extended RPA theory.Received: 26 May 2003, Revised: 30 October 2003, Published online: 26 January 2004PACS: 21.60.Jz Hartree-Fock and random-phase approximations - 21.10.Re Collective levels     

Stochastic time-dependent hartree-fock for heavy-ion collisions at fermi energies

We present the first application of Stochastic Time-Dependent Hartree-Fock for describing realistic heavy-ion collisions in the Fermi energy domain. We discuss the robustness of the collision scheme and show some examples of application. Presented by E. Suraud at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1997.     

Stochastic coupled cluster theory

We describe a stochastic coupled cluster theory which represents excitation amplitudes as discrete excitors in the space of excitation amplitudes. Reexpressing the coupled cluster (CC) equations as the dynamics of excitors in this space, we show that a simple set of rules suffices to evolve a distribution of excitors to sample the CC solution and correctly evaluate the CC energy. These rules are not truncation specific and this method can calculate CC solutions to an arbitrary level of truncation. We present results of calculation on the neon atom, and nitrogen and water molecules showing the ability to recover both truncated and full CC results.     

Stochastic climate dynamics: Random attractors and time-dependent invariant measures

This article attempts a unification of the two approaches that have dominated theoretical climate dynamics since its inception in the 1960s: the nonlinear deterministic and the linear stochastic one. This unification, via the theory of random dynamical systems (RDS), allows one to consider the detailed geometric structure of the random attractors associated with nonlinear, stochastically perturbed systems. We report on high-resolution numerical studies of two idealized models of fundamental interest for climate dynamics. The first of the two is a stochastically forced version of the classical Lorenz model. The second one is a low-dimensional, nonlinear stochastic model of the El Niño-Southern Oscillation (ENSO). These studies provide a good approximation of the two models’ global random attractors, as well as of the time-dependent invariant measures supported by these attractors; the latter are shown to have an intuitive physical interpretation as random versions of Sinaï-Ruelle-Bowen (SRB) measures.     

Adiabatic approximation in nonperturbative time-dependent density-functional theory

We construct the exact exchange-correlation potential of time-dependent density-functional theory and the approximation to it that is adiabatic but exact otherwise. For the strong-field double ionization of the Helium atom these two potentials are virtually identical. Thus, memory effects play a negligible role in this paradigm process of nonlinear, nonperturbative electron dynamics. We identify the regime of high-frequency excitations where the adiabatic approximation breaks down and explicitly calculate the nonadiabatic contribution to the exchange-correlation potential.     

Giant quadrupole resonances in time-dependent density-matrix theory

Damping of an isoscalar giant quadrupole resonance (GQR) in ⁴⁰Ca is studied using an extended version of the time-dependent Hartree-Fock theory known as the time-dependent density-matrix theory (TDDM). The Skyrme III force is used as an effective interaction for the calculation of both a mean-field potential and a two-body correlation function, and a correlated state is used as the ground state on which GQR is built. It is found that the calculated strength of GQR is split into a major component and a minor component. The spreading width of the major component is found small as compared with experimental data. A double giant quadrupole resonance (DGQR) is also studied in TDDM, and it is found that DGQR given in TDDM has properties of the double phonon state of GQR calculated in the random phase approximation.     

Some remarks on the time-dependent Thomas-Fermi theory

We investigate the Thomas Fermi limit (?=0) of the density operator in phase space for a system of noninteracting fermions evolving from the ground state in a time dependent potential. The semiclassical calculations for model situations in one spatial dimension are compared with the solution of the time dependent Schrödinger equation. The role of time dependent invariants and the relation to the hydrodynamical formulation of quantum mechanics is pointed out.     

Relativistic multiconfiguration time-dependent self-consistent-field theory for molecules

A relativistic multiconfiguration time-dependent self-consistent-field theory is constructed for molecules. Equations are derived for relativistic response functions, and their solutions are found in general form for multielectron molecules. Within the adopted approach, the equivalence of the results of relativistic calculations of the oscillator strengths in the molecules is demonstrated by using equations in length and velocity. A relativistic formalism is formulated for the Liouville-Dirac-Fock self-consistent field; this formalism may be very effective in molecular calculations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, 29–34, October, 1991.     

Generalized time-dependent density-functional theory including core polarization

A generalization of the time-dependent density-functional-theory for metal clusters which treats both valence and core polarization on the same microscopic basis is presented. The selfconsistency between valence and core responses is taken into account by means of a modified kernel and external field in the linearized response equations. The general case of an arbitrary external field and cluster structure, with given specific atomic positions, is presented. Presented by Ll. Serra at the International Conference on “Atomic Nuclei and Metallic Clusters”, Prague, September 1–5, 1997.     

Stochastic theory of ignition processes

We consider a closed gaseous system immersed in a heat bath undergoing a thermal explosion. The effects of instantaneous fluctuations in the temperature on the heat removal mechanism and on the reaction rate are considered. The intensity of the fluctuations in situations far from equilibrium is determined by calculating the temperature self-correlation. This quantity scales with the inverse of an effective volume obtained from generalized fluctuation-dissipation theory. This determines a virtual system corresponding to the localized ignition process, possibly leading to a global runaway. The induction period is identified with the Kramers mean passage time for diffusion across a kinetic barrier. The induction period is thus shown to be dependent on the fluctuation volume . The diffusion process is hastened by the critical fluctuations. The explosive decomposition of ethyl azide was selected to test the theory and the results exhibit very good agreement with experimental data. Our treatment resolves the previous discrepancy between the predictions rooted in the classical Frank-Kamenetsky treatment and the premature ignition observed experimentally.