Václav Špička

Kinetic equation for strongly interacting dense fermi systems.

We review the non-relativistic Greens-function approach to the kinetic equations for Fermi liquids far from equilibrium. The emphasis is on the consistent treatment of the off-shell motion between collisions and on the non-instant and non-local picture of binary collisions.
The resulting kinetic equation is of the Boltzmann type, and it represents an interpolation between the theory of transport in metals and the theory of moderately dense gases. The free motion of particles is renormalised by various mean field and mass corrections in the spirit of Landaus quasiparticles in metals. The collisions are non-local in the spirit of Enskogs theory of non-ideal gases. The collisions are moreover non-instant, a feature which is absent in the theory of gases, but which is shown to be important for dense Fermi systems.
In spite of its formal complexity, the presented theory has a simple implementation within the Monte-Carlo simulation schemes. Applications in nuclear physics are given for heavy-ion reactions and the results are compared with the former theory and recent experimental data.
The effect of the off-shell motion and the non-local and non-instant collisions on the dynamics of the system can be characterised in terms of thermodynamic functions such as the energy density or the pressure tensor. Non-equilibrium counterparts of these functions and the corresponding balance equations are derived and discussed from two points of view. Firstly, they are used to prove the conservation laws. Secondly, the role of individual microscopic mechanisms in fluxes of particles and momenta and in transformations of the energy is clarified.

NONLOCAL CORRECTIONS TO THE BOLTZMANN EQUATION FOR DENSE FERMI SYSTEMS

Abstract A kinetic equation which combines the quasiparticle drift of Landaus equation with a dissipation governed by a nonlocal and noninstant scattering integral in the spirit of Sniders equation for gases is derived. Consequent balance equations for the density, momentum and energy include quasiparticle contributions and the second-order quantum virial corrections. The medium effects on binary collisions are shown to mediate the latent heat, i.e. an energy conversion between correlation and thermal energy. An implementation to heavy ion collisions is discussed.A kinetic equation which combines the quasiparticle drift of Landaus equation with a dissipation governed by a nonlocal and noninstant scattering integral in the spirit of Sniders equation for gases is derived. Consequent balance equations for the density, momentum and energy include quasiparticle contributions and the second order quantum virial corrections. The medium effects on binary collisions are shown to mediate the latent heat, i.e., an energy conversion between correlation and thermal energy. An implementation to heavy ion collisions is discussed.

QUASIPARTICLE TRANSPORT EQUATION WITH COLLISION DELAY. II. MICROSCOPIC THEORY

For a system of noninteracting electrons scattered by neutral impurities, we derive a modified Boltzmann equation that includes quasiparticle and virial corrections. We start from a quasiclassical transport equation for nonequilibrium Green`s functions and apply a limit of small scattering rates. The resulting transport equation for quasiparticles has gradient corrections to scattering integrals. These gradient corrections are rearranged into a form characteristic for virial corrections. {copyright} {ital 1997} {ital The American Physical Society}

Duration and nonlocality of a nucleon-nucleon collision

For a set of realistic nucleon-nucleon potentials we evaluate microscopic parameters of binary collisions: a time duration of the scattering state, a mean distance and a rotation of nucleons during a collision. These parameters enter the kinetic equation as non-instantaneous and non-local corrections of the scattering integral, i.e., they can be experimentally tested. Being proportional to off-shell derivatives of the scattering T-matrix, non-instantaneous and non-local corrections make it possible to compare the off-shell behavior of different potentials in a vicinity of the energy shell. The Bonn one-Boson-exchange (A-C) and Paris potentials are found to yield very close results, while the separable Paris potential differs.

Formation of binary correlations in strongly coupled plasmas

Abstract Employing quantum kinetic equations we study the formation of binary correlations in plasma at short time scales. It is shown that this formation is much faster than dissipation due to collisions, and in hot (dense) plasma the correlations form on the timescale of inverse plasma frequency (Fermi energy). This hierarchy of characteristic times is used to derive analytical formulae for the time dependence of the potential energy of binary interactions which measures the extent of correlations. We discuss the dynamical formation of screening and compare this with the static screened result. Comparisons are made with molecular dynamic simulations. In the low temperature limit we find an analytical expression for the formation of correlation which is general for any binary interaction. It can be applied in nuclear situations as well as for dense metals.

Retarded versus Time-Nonlocal Quantum Kinetic Equations

Abstract The finite duration of the collisions in Fermionic systems as expressed by the retardation time in non-Markovian Levinson-type kinetic equations is discussed in the quasiclassical limit. We separate individual contributions included in the memory effect resulting in (i) off-shell tails of the Wigner distribution, (ii) renormalization of scattering rates, (iii) renormalization of the single-particle energy, (iv) collision delay, and (v) related nonlocal corrections to the scattering integral. In this way we transform the Levinson equation into the Landau–Silin equation extended by the nonlocal corrections known from the theory of dense gases. The derived nonlocal kinetic equation unifies the Landau theory of quasiparticle transport with the classical kinetic theory of dense gases. The space-time symmetry is discussed versus particle-hole symmetry and a solution is proposed which transforms these two exclusive pictures into each other.

Chaotic scattering on surfaces and collisional damping of collective modes

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 A3/2p of the centroid energy. @S0556-2813~99!00710-4#

Formation of Binary Correlations in Plasma

The characteristic time of formation of correlations at high temperature limit is given by the inverse plasma frequency \( \tau _C \approx \frac{1} {{\omega _p }} = \frac{{\sqrt 2 }} {{\upsilon _{th} \kappa }} \) . The inverse plasma frequency indicates that the dominant role play the long range fluctuation. On the other hand, we also see that the correlation time is found to be given by the time a particle needs to travel through the range of the potential with a thermal velocity υth. This confirms the numerical finding of [12] that the correlation or memory time is proportional to the range of interaction. In the low temperature region, i.e., in highly degenerated system μ 》 T one finds a differentpicture. From (3) we can calculate the formationofcorrelationsaswell. 13,14 Unlike in the classical case, the equilibrium limit of the degenerated case is rapidly built up and then oscillates around the equilibrium value. We can define the build up time τ C as the time where the correlation energy reaches its first maximum, \( \tau _C = 1.0\frac{\hbar } {\mu } \) . Note that τ C is in agreement with the quasiparticle formation time known as Landau’s criterion for is the Fermi energy. Indeed, the quasiparticle formation and the build up of correlations are two alternative views of the same phenomena. The formation of binary correlations is very fast on the time scale of dissipative process. Under extremely fast external perturbations, like the massive femto second laser pulses, the dynamics of binary correlations will hopefully become experimentally accessible. Even if related measurement will not reveal any unexpected features, the experimental justification of basic concepts of the non-equilibrium many-body physics is very desirable.

Quasiparticle picture of friction between two coupled two-dimensional metals at zero temperature

A current induced by the van der Waals interaction between two parallel two-dimensional metals is reinterpreted in the quasiparticle picture. It is shown that in the presence of a dissipation, this current vanishes due to an effect of the van der Waals interaction on scattering processes.

NONLOCAL KINETIC THEORY

The short time behavior of a disturbed system is influenced by off-shell motion and characterized by the reduced density matrix possessing high energetic tails. After this short time regime the time evolution is controlled by small gradients. This leads to a nonlocal Boltzmann equation for the quasiparticle distribution and a functional relating the latter one to the reduced density matrix. The nonlocalities are presented as time and space shifts arising from gradient expansion and are leading to virial corrections in the thermodynamical limit.