Exchange and correlation in finite-temperature TDDFT

We discuss the finite-temperature generalization of time-dependent density functional theory (TDDFT). The theory is directly analogous to that at temperature T = 0. For example, the finite-T TDDFT exchange-correlation kernel f_xc(T, n) in the local density approximation can again be expressed as a density derivative of the exchange correlation potential f_xc(T, n) = [?v_xc(T, n)∕?n]δ(r ? r′), where n = N∕V is the electron number density. An approximation for the kernel f_xc(T, n) is obtained from the finite-T generalization of the retarded cumulant expansion applied to the homogeneous electron gas. Results for f_xc and the loss function are presented for a wide range of temperatures and densities including the warm dense matter regime, where T ≈ T_F, the electron degeneracy temperature. The theory also permits a physical interpretation of the exchange and correlation contributions to the theory.     

Higher order parabolic approximations of the reduced wave equation

Asymptotic solutions of order k⁻ⁿ are developed for the reduced wave equation. Here k is a dimensionless wave number and n is the arbitrary order of the approximation. These approximations are an extension of geometric acoustics theory and provide corrections to that theory in the form of multiplicative functions which satisfy parabolic partial differential equations. These corrections account for the diffraction effects caused by variation of the field normal to the ray path and the interaction of these transverse variations with the variation of the field along the ray. The theory is applied to the example of radiation from a piston, and it is demonstrated that the higher order approximations are more accurate for decreasing values of k.     

Models and approximations for the momentum distribution in nuclear matter

As a step toward development of a framework for phenomenological analysis of nuclear momentum distributions in terms of dynamical interparticle correlations, the momentum distribution n(k) of symmetrical nuclear matter described by a Jastrow wave function is studied within a variety of approximation schemes. In particular, two simple low-cluster-order approximations are proposed, one of which may be readily adapted to finite nuclei. For two choices of pair correlations tailored respectively to soft and moderately stiff repulsive cores, the results based on these approximations compare favorably with the standards set by Fermi-hypernetted-chain evaluation and (for the kinetic energy) by Monte Carlo integration — even at densities somewhat beyond the empirical equilibrium density of nuclear matter. The crucial role played by the Jastrow wound parameter, as a determinant of the overall behavior of n(k), emerges clearly from these calculations.     

Nonperturbative Renormalization in Light-Front Dynamics and Applications

We present a general framework to calculate the properties of relativistic compound systems from the knowledge of an elementary Hamiltonian. Our framework provides a well-controlled nonperturbative calculational scheme which can be systematically improved. The state vector of a physical system is calculated in light-front dynamics. From the general properties of this form of dynamics, the state vector can be further decomposed in well-defined Fock components. In order to control the convergence of this expansion, we advocate the use of the covariant formulation of light-front dynamics. In this formulation, the state vector is projected on an arbitrary light-front plane ω·x =  0 defined by a light-like four-vector ω. This enables us to control any violation of rotational invariance due to the truncation of the Fock expansion. We then present a general nonperturbative renormalization scheme in order to avoid field-theoretical divergences which may remain uncancelled due to this truncation. This general framework has been applied to a large variety of models. As a starting point, we consider QED for the two-body Fock space truncation and calculate the anomalous magnetic moment of the electron. We show that it coincides, in this approximation, with the well-known Schwinger term. Then we investigate the properties of a purely scalar system in the three-body approximation, where we highlight the role of antiparticle degrees of freedom. As a non-trivial example of our framework, we calculate the structure of a physical fermion in the Yukawa model, for the three-body Fock space truncation (but still without antifermion contributions). We finally show why our approach is also well-suited to describe effective field theories like chiral perturbation theory in the baryonic sector.     

SUPER AND COMBINATORIAL HARMONIC RESPONSE OF FLEXIBLE ELASTIC CABLES WITH SMALL SAG

The paper deals with the analysis of cables in stayed bridges and TV-towers, where the excitation is caused by harmonically varying in-plane motions of the upper support point with the amplitude U. Such cables are characterized by a sag-to-chord-length ratio below &0uml;02, which means that the lowest circular eigenfrequencies for in-plane and out-of-plane eigenvibrations, ω₁and ω₂, are closely separated. The dynamic analysis is performed by a two-degree-of-freedom modal decomposition in the lowest in-plane and out-of-plane eigenmodes. Modal parameters are evaluated based on the eigenmodes for the parabolic approximation to the equilibrium suspension. Superharmonic components of the ordern , supported by the parametric terms of the excitation and the non-linear coupling terms, are registered in the response for circular frequency ω?ω₁/n. At moderate U, the cable response takes place entirely in the static equilibrium plane. At larger amplitudes the in-plane response becomes unstable and a coupled whirling superharmonic component occurs. In the paper a first order perturbation solution to the superharmonic response is performed based on the averaging method. For ω?(m/n)ω₁, m<n, the geometrical non-linear restoring forces gives rise to a substantial combinatorial harmonic component with the circular frequency (n/m)ω. Both entirely in-plane and coupled in-plane and out-of-plane responses occur. Based on an initial frequency analysis of the response, an analytical model for these vibrations is formulated with emphasis on superharmonics of the order n=3 and combinatorial harmonics of the order (n, m)=(3,2). All analytical solutions have been verified by direct numerical integration of the modal equations of motion.     

Connection between the Dielectric and the Ballistic Treatment of Collisional Absorption

I this work two important models of treating collisional absorption in a laser driven plasma are compared, the dielectric and the ballistic model. We will see that there exists a remarkable connection between these basic approaches which could give a hint how to overcome the inherent limitations. The approximations made in the models are not identical and lead to different advantages and disadvantages. We notice that the dieletric model is able to handle screening in a selfconsistent manner, but is limited to first order in the electron‐ion interaction. The ballistic model calculates the electron‐ion collision exactly in each order of the interaction, but has to introduce a cut‐off to incorporate screening effects. This means in the context of kinetic theory that the electron‐ion correlation has to be calculated either in random phase or in ladder approximation, or, in other words, the linearized Lenard‐Balescu or Boltzmann collision term has to be used.     

Localization in one-dimensional Soukoulis-Economou model with incommensurate potentials

The localization of one-dimensional Soukoulis- Economou model with incommensurate potentials ε_n=1.9 [cos(2πωn)+1/3cos(4πωn)], where ω=σ≡(√5?1)/2 is studied by the use of two methods: the scaling analysis of bandwidth in successively periodic approximation, and the mutlifractal analysis of wave functions. A mobility edge is found in a gap of the fifth subband. We found that all the states at higher energies are localized while all those at lower energies are extended. These results are different from those given in previous works.     

Correlation effects in the theory of combined doppler and pressure broadening—I. Classical theory

A classical Fourier amplitude theory of combined Doppler and pressure broadening in the impact approximation is developed which treats phase changes changes due ti translation and collision on an equal basis. Radiator motion is accounted for properly by including speed dependence in the collision frequency and velocity dependence in the distribution function for phase shifts and final velocities as the result of a collision. The resulting theory is shown to be equivalent to a previous kinetic equation formulation of the problem. The one-perturber and classical analogue of the quantum one-interacting-level approximations are derived. In the latter case, a simple expression for the line shape in terms of speed dependent width and shift functions is obtained without approximation. Correlation effects are investigated by means of model speed dependent width and shift functions calculated for an inverse power interaction using straight line trajectories. The model shows no departure from a Voigt profile for the r^-3 interaction and for the r^-6 and r^-12 interactions the resulting profile is narrower in the core than the Voigt and in general asymmetric. Analysis of correlated profiles as Voigt profiles is shown under some conditions to lead to non-linear density dependence in the width and shifts resulting in extra- polation anomalies and to significant errors in temperatures inferred from Doppler widths. Results are compared with previous work.     

Variational principles and linked-cluster exp S expansions for static and dynamic many-body problems

The exp S formalism for the ground state of a many-body system is derived from a variational principle. An energy functional is constructed using certain n-body linked-cluster amplitudes with respect to which the functional is required to be stationary. By using two different sets of amplitudes one either recovers the normal exp S method or obtains a new scheme called the extended exp S method. The same functional can be used also to obtain the average values of any operators as well as the linear response to static perturbations. The theory is extended to treat dynamical phenomena by introducing time dependence to the cluster amplitudes. This allows the calculation of both nonlinear dynamical behaviour and of dynamical linear response and Green's functions. Practical approximation schemes are considered. In a SUB n approximation the m-body amplitudes are restricted to the order $\text{m ? n}$ and the energy functional is a finite-order multinomial in the amplitudes to be variationally determined. It is shown that the solution corresponds to summing well-defined subsets of Goldstone diagrams. These subsets are conveniently specificed in terms of tree structures, the normal or extended generalized time ordering g.t.o. trees. The extended exp S method is in the SUB n approximation able to sum, in addition to the normal SUB n diagrams, a set which contains m-body cluster amplitudes of arbitrarily high order (m > n) in the ordinary sense. The article also discusses how the SUB n truncation schemes must be modified to be able to treat a system with a strong repulsive core in the two-body interaction. The method is formulated for the general cases of Bose and Fermi systems which may or may not conserve total particle number. It is shown that the simplest approximation, SUB 1, in the extended exp S method agrees with the mean field theory, which is the coherent-state approximation in the boson case or the Hartree-Fock approximation in the fermion case. It is argued that the extended exp S method already in low-order approximations can realistically treat a great variety of diverse many-body problems, even including systems which may undergo ground-state phase transitions. A few applications are described in more detail. The Bose liquid is treated in the extended SUB 2 approximation. It is shown that the ground-state results in the uniform limit are exact and agree with the hypernetted-chain approximation. The modifications due to hard-core interactions and the non-linear equations of motion are also discussed in this case. For Fermi systems it is shown that the supercondictive phase transition of the BCS model Hamiltonian and the deformation phase transition of the Lipkin model are properly obtained by the extended exp S method in a low-order approximation.     

Kinetic parameters in the nuclear Fermi gas model at finite temperatures

The validity of the dilute Fermi gas model for the evaluation of transport parameters in nuclear matter is examined in the framework of quantal kinetic theory. The consistency of the approximations involved in the calculations of the collision rate between weakly interacting nucleons is analyzed, considering several ways of representing the residual interaction, namely via zero-range, medium-range, and short-momentum-spread forces. The theoretical mean free path is derived, with a proper handling of the collision kernel in a nuclear kinetic equation, and computed as a function of temperature and single-particle energy for the interactions in the weak-coupling approximation. The competition among interaction range and quantal and kinetic length scales is discussed.     

Optical properties of SiC nanocages: ab initio study

The structural, electronic and optical properties of Si _n C _n (n=12,16,20,30,35 and 60) nanocages were studied using different approximations of density functional theory, i.e. local density approximation (LDA), generalized gradient approximation (GGA) and density functional theory based tight binding approximation (DFTB). The highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbitals (LUMO) energy gaps were calculated for all nanocages. Time-dependent density functional theory (TD-DFT) was also applied for estimating of the optical excitation and exciton binding energies of the nanocages and the results compared with pure DFT calculations.     

Electron impact excitation of the resonance transitions of highly ionized atoms of the Be-, Mg-, and Zn-isoelectronic sequences

Electron impact excitation collision strengths for the ns²¹S - nsnp¹P resonance transitions of highly ionized Be, Mg, and Zn-like ions have been computed in the distorted wave approximation, including the effects of exchange and target state correlation. Good agreement is observed between these data and collision strengths computed in the Coulomb-Born and Born approximations at high incident energies. Analytic fits to the distorted wave data are presented.     

Higher-order approximations for the particle-particle propagator

A new type of approximations for many-body Green's functions proposed recently is applied to the particle-particle (pp) propagator for anN-particle fermion system. The new approach which is referred to as the algebraic diagrammatic construction (ADC) is based on an exact resummation of the perturbation series for the pp-propagator in terms of a simple algebraic form introducing energy-independent effective interaction matrix elements and transition amplitudes. These effective quantities are represented by perturbation expansions and can be determined consistently through a given ordern of perturbation theory by comparing the algebraic form with the diagrammatic perturbation series of the pp-propagator through ordern. By this procedure one obtaines a systematic set of approximation schemes (ADC(n)) that represent infinite partial summations for the pp-propagator being complete throughnth order of perturbation theory. The explicit ADC equations forn=1 and 2 are presented and discussed. Comparison is made with the particle-particle random phase approximation (RPA). It is demonstrated that the second-order ADC scheme constitutes an essential step beyond the RPA which is consistent only through first order.     

Theory of the local field correction in an electron gas

The wave-vector- and frequency-dependent dielectric function ?(k,ω) of an electron gas can be expressed in terms of Lindhard's function and a complex local field correctionG(k,ω) which incorporates all the effects of dynamic exchange and correlation in the system. The general properties ofG(k,ω) are discussed, in particular the static and high-frequency limits. It is shown that for smallk, bothG(k, 0) andG(k, ∞) vary ask ², with different coefficients, but both determined by the average kinetic and potential energies per particle. For largek,G(k, ∞) varies again ask ² and it is argued that the same holds true forG(k, 0), with both coefficients (though different) determined by the average kinetic energy per particle. General formulas for the plasma dispersion relation and damping, involving, respectively, the real and imaginary parts ofG(k,ω), are given. The term in the plasma frequency which is proportional tok ² is given directly in terms of the average kinetic and potential energies per particle, a result true at all temperatures. A calculation of the frequency dependence ofG(k,ω), starting from the exact equation of motion for the particle-hole operator and employing a decoupling approximation introduced previously by Toigo and Woodruff, is presented. Explicit results forG(k,ω) are obtained for smallk and allω. The complete expressions forG(k, 0) andG(k, ∞) in this approximation have been obtained and are plotted.     

Exact renormalization group and Φ-derivable approximations

We show that the so-called Φ-derivable approximations can be combined with the exact renormalization group to provide efficient non-perturbative approximation schemes. On the one hand, the Φ-derivable approximations allow for a simple truncation of the infinite hierarchy of the renormalization group flow equations. On the other hand, the flow equations turn the non-linear equations that derive from the Φ-derivable approximations into an initial value problem, offering new practical ways to solve these equations.     

Intramolecular vibrational energy transfer in mixtures of anthraquinone with foreign gases

Properties of collision transfer of vibrational energy in the vibrational quasi-continuum of mixed singlet-triplet levels of anthraquinone are studied by the method of time-resolved delayed fluorescence. The two-exponential fluorescence decay is analyzed in the kinetic approximation. It is shown that dependences of the intensities and decay rates of the fast and slow components on pressure can be used for estimating the rates of the establishment of the vibrational (V-V) and thermal (V-T) equilibrium. The efficiency β and the average energy 〈ΔE〉 transferred in collisions are estimated for these processes. It is found that the V-V process is characterized by high values of β, which, however, are lower in the quasi-continuum of mixed singlet-triplet states than the gas-kinetic values (β < 0.2). The transformation of the vibrational energy to the translational energy occurs with the low efficiency (10^?2 > β > 10^?5). The average energy 〈ΔE〉 transferred during a collision in the V-V process is comparable with the energy predicted by the statistical theory of ergodic transfer. The correlation between experimental and theoretical values improves when the time resolution of the experiment is sufficient for the separation of the V-V and V-T processes.     

Renormalized Kinetic Theory of Classical Fluids in and out of Equilibrium

We present a theory for the construction of renormalized kinetic equations to describe the dynamics of classical systems of particles in or out of equilibrium. A closed, self-consistent set of evolution equations is derived for the single-particle phase-space distribution function f, the correlation function C=〈δfδf〉, the retarded and advanced density response functions χ ^R,A =δf/δφ to an external potential φ, and the associated memory functions Σ ^R,A,C . The basis of the theory is an effective action functional Ω of external potentials φ that contains all information about the dynamical properties of the system. In particular, its functional derivatives generate successively the single-particle phase-space density f and all the correlation and density response functions, which are coupled through an infinite hierarchy of evolution equations. Traditional renormalization techniques (involving Legendre transform and vertex functions) are then used to perform the closure of the hierarchy through memory functions. The latter satisfy functional equations that can be used to devise systematic approximations that automatically imply the conservation laws of mass, momentum and energy. The present formulation can be equally regarded as (i) a generalization to dynamical problems of the density functional theory of fluids in equilibrium and (ii) as the classical mechanical counterpart of the theory of non-equilibrium Green’s functions in quantum field theory. It unifies and encompasses previous results for classical Hamiltonian systems with any initial conditions. For equilibrium states, the theory reduces to the equilibrium memory function approach used in the kinetic theory of fluids in thermal equilibrium. For non-equilibrium fluids, popular closures of the BBGKY hierarchy (e.g. Landau, Boltzmann, Lenard-Balescu-Guernsey) are simply recovered and we discuss the correspondence with the seminal approaches of Martin-Siggia-Rose and of Rose and we discuss the correspondence with the seminal approaches of Martin-Siggia-Rose and of Rose.     

A stochastic approach to the kinetic theory of gases

A theory of fluctuations in non-equilibrium diluted gases is presented. The velocity distribution function is treated as a stochastic variable and a master equation for its probability is derived. This evolution equation is based on two processes: binary hard sphere collisions and free flow. A mean-field approximation leads to a non-linear master equation containing explicitly a parameter which represents the spatial correlation length of the fluctuations. An infinite hierarchy of equations for the successive moments is found. If the correlation length is sufficiently short a truncation after the first equation is possible and this leads to the Boltzmann kinetic equation. The associated probability distribution is Poissonian. As to the fluctuation of the macroscopic quantities, an approximation scheme permits to recover the Langevin approach of fluctuating hydrodynamics near equilibrium and its fluctuation-dissipation relations.     

The self-consistent determination of HF electroconductivity of strongly coupled plasmas

Here is presented the calculation of the dynamic electrical conductivity of fully ionized, strongly coupled plasmas as a function of the external electric field frequency ω. The calculations are based on the formula for the energy-dependent collision frequency which is determined by means of the Green function theory methods, as a sum over the Matsubara frequencies. The domain of extremely high electron density: ¹⁰²¹?ne?¹⁰²⁴ cm−3, and for the temperature varying from 10 kK to 1000 kK was examined. The real and imaginary parts of the conductivity for every electron density are presented in the generalized Drude-like form as a two-parameter function of the frequency ω in the region 0<ω<0.5ωp, where ωp is the plasma frequency. A good agreement between the obtained results and the existing theoretical and computing simulation data is shown.