Linearizing the appropriate kinetic equation we derive general response functions including selfconsistent mean fields or density functionals and collisional dissipative contributions. The latter ones are considered in relaxation time approximation conserving successively different balance equations. The effect of collisions is represented by correlation functions which are possible to calculate with the help of the finite temperature Lindhard RPA expression. The presented results are applicable to finite temperature response of interacting quantum systems if the quasiparticle or mean field energy is parameterized within Skyrme -type of functionals including density, current and energy dependencies which can be considered alternatively as density functionals. By this way we allow to share correlations between density functional and collisional dissipative contributions appropriate for the special treatment. We present results for collective modes like the plasmon in plasma systems and the giant resonance in nuclei. The collisions lead in general to an enhanced damping of collective modes. If the collision frequency is close to the frequency of the collective mode, resonance occurs and the collective mode is enhanced showing a collisional narrowing.

Starting from a nonmarkovian conserving relaxation time approximation for collisions we derive coupled dispersion relations for asymmetric nuclear matter. The isovector and isoscalar modes are coupled due to asymmetric nuclear meanfield acting on neutrons and protons differently. A further coupling is observed by collisional correlations. The latter one leads to the appearance of a new soft mode besides isoscalar and isovector modes in the system. We suggest that this mode might be observable in asymmetric systems. This soft mode approaches the isovector mode for high temperatures. At the same time the isovector mode remains finite and approaches a constant value at higher temperatures showing a transition from zero sound like damping to first sound. The damping of the new soft mode is first sound like at all temperatures.The investigation of collective excitations in asymmetric nuclear matter is of current interest for experiments with nuclei far from β-stability, [1] and citations therein. We consider here a Fermi gas model consisting of a number of different species (neutrons, protons, etc) interacting with the own specie and with other ones. The interaction between different sorts of particles is important to consider if we want to include friction between different streams of isospin components. Especially the isospin current may not be conserved by this way. We neglect explicitly shell effects and concentrate only on bulk matter properties. Let us start with a set of coupled quantum kinetic equations for the reduced density operator ρ a for the specie awhere E = P 2 /2m denotes the kinetic energy operator and U the mean field operator and the external field which is assumed to be a nonlinear function of the density. We have approximated the collision integral by a non-Markovian relaxation time [8]. The memory effects condensed in the frequency dependent relaxation time turned out to be necessary to reproduce damping of zero sound [2,3]. It accounts for the fact that during a two particle collision a collective mode can couple to the scattering process. Consequently, the dynamical relaxation time represents the physical content of a hidden three particle process and is equivalent to the memory effects.We have further assumed the relaxation with respect to the local equilibriumρ b of any specie in the system. The relaxation of the actual distribution of specie a is driven by the local equilibrium of all the other components. The cross coupling is realized by nondiagonal relaxation times τ ab . We specify the local equilibrium by a small deviation of the chemical potential of specie a [4] compared with the global equilibrium (2) with < k|E|k ′ >= ǫ(k). The equilibrium distributions < k|ρ 0 a |k ′ >= f a (k)δ kk ′ are the corresponding Fermi functions with chemical potential µ a and the normalization to density n a = 2 dp (2π) 3 f a (p). The local equilibrium specified by δµ a is determined if we impose the density balance to be fulfilled separately for each specie current J a which reads in Wigner coordinat...

The damping rate of hot giant dipole resonances (GDR) is investigated. Besides Landau damping we consider collisions and density fluctuations as contributions to the damping of GDR. Within the non-equilibrium Green's function method we derive a non-Markovian kinetic equation. The linearization of the latter one leads to complex dispersion relations. The complex solution provides the centroid energy and the damping width of giant resonances. The experimental damping widths are the full width half maximum (FWHM) and can be reproduced by the full width of the structure function. Within simple finite size scaling we give a relation between the minimal interaction strength which is required for a collective oscillation and the clustersize. We investigate the damping of giant dipole resonances within a Skyrme type of interaction. Different collision integrals are compared with each other in order to incorporate correlations. The inclusion of a conserving relaxation time approximation allows to find the T 2 -dependence of the damping rate with a temperature known from the Fermi-liquid theory. However, memory effects turn out to be essential for a proper treatment of the damping of collective modes. We derive a Landau like formula for the one-particle relaxation time similar to the damping of zero sound. 21.30.Fe,21.60.Ev, 24.30.Cz, 24.60.Ky

We reanalyze the recently derived response function for interacting systems in relaxation time approximation respecting density, momentum and energy conservation. We find that momentum conservation leads exactly to the local field corrections for both cases respecting only density conservation and respecting density and energy conservation. This rewriting simplifies the former formulae dramatically. We discuss the small wave vector expansion and find that the response function shows a high frequency dependence of ω −5 which allows to fulfill higher order sum rules. The momentum conservation also resolves a puzzle about the conductivity which should only be finite in multicomponent systems. 05.30.Fk,21.60.Ev, 24.30.Cz, 24.60.Ky Recently the improvement of the response function in interacting quantum systems has regained much interest [1,2]. This quantity is important in a variety of fields and describes the induced density variation if the system is externally perturbed: δn = χV ext . As an example for an interacting system with potential V the conductivity can be calculated from the response function viaOne of the most fruitful concepts to improve the response functions including correlations are the local field correc-see [1,3,4] and references therein. On the other hand there exists an extremely useful form of the response function when the interactions are abbreviated in the relaxation time approximation τ respecting density conservation [5]. One of the advantages of the resulting Mermin formula (9) is that it leads to the Drude -like form of the dielectric function in the long wavelength limitwith the plasma frequency ω p for the Coulomb potential V from which follows the conductivityHowever one should note that this formula is valid only for the extension to a multicomponent system [6] (at least a two-component system) since it makes no sense to speak of conductivity in a single component system where the conductivity should be infinite. Clearly the Mermin formula does not distinguish these cases and cannot be sufficient to describe the response. Therefore we will show that the inclusion of additional momentum conservation will repair this defect (22) and will lead to a conductivitywhich shows indeed for the static limit a diverging behavior in contrast to (4). There are two distinguishable cases, the single component case where we have to include momentum conservation and obtain divergent conductivity and the multicomponent case where we should expect Mermin-like formulae in order to render the conductivity finite. In order to bring these two extreme cases together the response function for multicomponent systems should be considered [6].In this letter we want to restrict to the one -component situation. In [2] we have derived the density, current and energy response χ, χ J , χ E of an interacting quantum systemto the external perturbation V ext provided the density, momentum and energy are conserved. The interacting system has been described by the quantum kinetic equation for the density operator in r...

The damping of hot giant dipole resonances is investigated. The contribution of surface scattering is compared with the contribution from interparticle collisions. A unified response function is presented which includes surface damping as well as collisional damping. The surface damping enters the response via the Lyapunov exponent and the collisional damping via the relaxation time. The former is calculated for different shape deformations of quadrupole and octupole type. The surface as well as the collisional contribution each reproduce almost the experimental value, and therefore we propose a proper weighting between both contributions related to their relative occurrence due to collision frequencies between particles and of particles with the surface. We find that for low and high temperatures the collisional contribution dominates whereas the surface damping is dominant around the temperatures ͱ3/2 of the centroid energy. ͓S0556-2813͑99͒00710-4͔