Pavel Lipavský

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.

Virial Corrections to Simulations of Heavy Ion Reactions

Within quantum molecular dynamics (QMD) simulations we demonstrate the effect of virial corrections on heavy ion reactions. Unlike in standard codes, the binary collisions are treated as nonlocal so that the contribution of the collision flux to the reaction dynamics is covered. A comparison with standard QMD simulations shows that the virial corrections lead to a broader proton distribution bringing theoretical spectra closer towards experimental values. Complementary Boltzmann-Uehling-Uhlenbeck simulations reveal that the nonlocality enhances the collision rate in the early stage of the reaction. It suggests that the broader distribution appears due to an enhanced preequilibrium emission of particles. [S0031-9007(99)09104-8] The Boltzmann equation including the Pauli blocking [the Boltzmann-Uehling-Uhlenbeck (BUU) equation [1]] and the closely related method of quantum molecular dynamics (QMD) [2,3] are extensively used to interpret experimental data from heavy ion reactions. Because of their quasiclassical character, they offer a transparent picture of the internal dynamics of reactions and allow one to link observed particle spectra with individual stages of reactions. The expectation to cover the heavy ion reactions within experimental errors has been recently set back by a failure of BUU simulations to describe the energy and angular distribution of neutrons and protons in the energy domain #200 MeVyA [4‐6]. Indeed, the Boltzmann equation does not contain all of the relevant physics. As noticed in numerical studies of hard sphere cascades by Halbert [7] and, more generally, by Malfliet [8], it is unfortunate that all dynamical models rely more or less on the use of the space- and time-local approximation of binary collisions inherited from the Boltzmann equation. This approximation neglects a contribution of the collision flux to the compressibility and the shear viscosity which control the hydrodynamic motion during the reaction. In order to include the collision flux and other virial corrections, the nonlocal character of binary collisions has to be accounted for. Malfliet also demonstrated that nonlocal collisions can be easily incorporated into BUU simulation codes.

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.

Ginzburg-Landau theory of superconducting surfaces under the influence of electric fields

A boundary condition for the Ginzburg-Landau wave function at surfaces biased by a strong electric field is derived within the de Gennes approach. This condition provides a simple theory of the field effect on the critical temperature of superconducting layers.

Space-time versus particle-hole symmetry in quantum Enskog equations.

The nonlocal scattering-in and scattering-out integrals of the Enskog equation have reversed displacements of colliding particles reflecting that the scattering-in and -out processes are conjugated by the space and time inversions. Generalizations of the Enskog equation to Fermi liquid systems are hindered by the need for particle-hole symmetry which contradicts the reversed displacements. We resolve this problem with the help of the optical theorem. It is found that space-time and particle-hole symmetry can be fulfilled simultaneously only for the Bruckner type of internal Pauli blocking while the Feynman-Galitskii form allows only for particle-hole symmetry but not for space-time symmetry due to a stimulated emission of bosons.

Midrapidity charge distribution in peripheral heavy ion collisions

The charge density distribution with respect to the velocity of matter produced in peripheral heavy ion reactions around Fermi energy is investigated. The experimental finding of enhancement of midrapidity matter shows the necessity to include correlations beyond Boltzmann-Uehling-Uhlenbeck (BUU) which was performed in the framework of nonlocal kinetic theory. Different theoretical improvements are discussed. While the in-medium cross section changes the number of collisions, it leaves the transferred energy almost unchanged. In contrast the nonlocal scenario changes the energy transferred during collisions and leads to an enhancement of midrapidity matter. The renormalization of quasiparticle energies can be included in nonlocal scenarios and leads to a further enhancement of midrapidity matter distribution. This renormalization is accompanied by a dynamical softening of the equation of state seen in longer oscillation periods of the excited compressional collective mode. We propose to include quasiparticle renormalization by using the Pauli-rejected collisions which circumvent the problem of backflows in Landau theory. Using the maximum relative velocity of projectile and targetlike fragments we associate experimental events with impact parameters of the simulations. For peripheral collisions we find reasonable agreement between experiment and theory. For more central collisions, the velocity damping is higher in one-body simulations than observed experimentally, because of missing cluster formations in the kinetic theory used.

Time-dependent Ginzburg-Landau theory with floating nucleation kernel: Far-infrared conductivity in the Abrikosov vortex lattice state of a type-II superconductor

We formulate the time-dependent Ginzburg-Landau theory, with the assumption of local equilibrium made in the reference frame floating with normal electrons. This theory with floating nucleation kernel is applied to the far infrared conductivity in the Abrikosov vortex lattice. It yields better agreement with recent experimental data [Phys. Rev. B 79, 174525 (2009)] than the customary time-dependent Ginzburg-Landau theory.

Discontinuity of capacitance at the onset of surface superconductivity

The effect of magnetic field on a capacitor with a superconducting electrode is studied with the Ginzburg–Landau approach. It is shown that the capacitance has a discontinuity at the onset of the surface superconductivity, which is expressed as a discontinuity in the depth of penetration of the electric field into metals. This new effect establishes a macroscopic signal of the onset of superconducting correlations. This discontinuity is observable with recent bridges for both conventional and high-Tc superconductors.

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.