Nonlocal corrections to the Boltzmann equation for dense Fermi systems

Špička, Václav; Lipavský, Pavel; Morawetz, Klaus

doi:10.1016/s0375-9601(98)00061-9

Cited by 46 publications

(98 citation statements)

References 23 publications

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“…The collision will then cause both a dephasing and fluctuation by itself. This procedure without additional assumption about fluctuations has been given by the nonlocal kinetic theory [37][38][39] and applied to heavy ion collisions in [40][41][42]. We claim that the derived nonlocal off-set in the collision procedure induces fluctuation in the density and consequently in the meanfield which are similar to the one assumed ad-hoc in the approaches above.…”

Section: Introductionmentioning

confidence: 69%

“…Although their discussion is limited to the equilibrium, it marks a way how to introduce virial corrections also to dynamical processes. The kinetic equation for quasiparticles with non-instantaneous and non-local scattering integral has been derived in [37,54] as a systematic quasi-classical limit of non-equilibrium Green's functions in the Galitskii-Feynman approximation. It has been shown that the gradient corrections to the scattering integral can be rearranged into a form of a collision delay and space displacements reminiscent of classical hard spheres, i.e., into a form suitable for numerical simulations.…”

Section: Theoretical Preliminariesmentioning

confidence: 99%

“…In this contribution we will put these ideas of nonlocalities on the firm ground using the quantum kinetic equation with nonlocal scattering integrals which was derived from quantum statistics [37,54] to show how the effect of nonlocalities play a role in simulations of heavy ion reactions and compare them with experiment.…”

Section: Theoretical Preliminariesmentioning

confidence: 99%

“…The scattering integral of the non-local kinetic equation derived in [37] corresponds to a following picture of a collision as seen in Figure 1. Assume that two particles, a and b, of initial momenta k and p start to collide at time instant t being at coordinates r a and r b .…”

Section: A Nonlocal Kinetic Theorymentioning

confidence: 99%

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Midrapidity charge distribution in peripheral heavy ion collisions

et al. 2001

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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 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 mid-rapidity matter. The renormalisation of quasiparticle energies can be included in nonlocal scenarios and leads to a further enhancement of mid-rapidity matter distribution. This renormalisation 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 renormalisation by using the Pauli-rejected collisions which circumvent the problem of backflows in Landau theory. Using the maximum relative velocity of projectile and target like fragments we associate experimental events with impact parameters of the simulations. For peripheral collisions we find a 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.

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Section: Introductionmentioning

confidence: 69%

Section: Theoretical Preliminariesmentioning

confidence: 99%

Section: Theoretical Preliminariesmentioning

confidence: 99%

Section: A Nonlocal Kinetic Theorymentioning

confidence: 99%

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Midrapidity charge distribution in peripheral heavy ion collisions

et al. 2001

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“…For more nontrivial approximations as e.g. the ladder summation these correlated observables appear [20,21].…”

Section: Balance Equationmentioning

confidence: 99%

Transport with three-particle interaction

Morawetz

2000

Phys. Rev. C

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Starting from a point -like two -and three -particle interaction the kinetic equation is derived. While the drift term of the kinetic equation turns out to be determined by the known Skyrme mean field the collision integral appears in two -and three -particle parts. The cross section results from the same microscopic footing and is naturally density dependent due to the three -particle force. By this way no hybrid model for drift and cross section is needed for nuclear transport. Besides the mean field correlation energy the resulting equation of state has also a two -and three -particle correlation energy which are both calculated analytically for the ground state. These energies contribute to the equation of state and lead to an occurrence of a maximum at 3 times nuclear density in the total energy.

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Quasiparticle Boltzmann Equation for Nonlocal Binary Collisons

Morawetz

Špička

Lipavský

1999

Contrib. Plasma Phys.

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A b s t r a c tVirial corrections to the Boltzmann equation for quasiparticles are obtained from non-equilibrium Green's functions. These corrections are expressed in terms of shifts in space and time that characterize non-locality of scattering integrals. The space shifts parallel finite-diameter corrections to collisions of hard spheres. The time shift is identified as the collision delay. All shifts are given by derivatives of the phase shift in a binary collision. -1 IntroductionThe very basic idea of the Boltzmann equation (BE), to balance the drift of particles with dissipation, is used for the description of transport properties of gases, plasmas and condensed systems like metals or nuclei. In all these fields, the BE allows for a number of improvements which make it possible to describe phenomena beyond the range of validity of the original BE. In these improvements theory of gases differs from theory of condensed systems. Two principal streams of kinetic theory are thus established.In theory of gases, the focus was on so called virial corrections that take into account a finite volume of molecules. The BE includes a contradiction: the scattering cross sections reflect the finite volume of molecules, while the instant and local approximation of scattering events implies the equation of state of an ideal gas. To achieve consistency and extend validity of the BE to moderately dense gases, space non-locality of binary collisions have to be taken into account as it was firstly demonstrated in Enskog's equation [l].In the theory of condensed systems, modifications of the BE are determined by the quantum mechanical statistics. A headway in this field is covered by the Landau concept of quasiparticles [2]. There are three major modifications: the Pauli blocking of scattering channels; underlying quantum mechanical dynamics of collisions; and quasiparticle renormalization of a single-particlelike dispersion relation. With all these deep modifications, the scattering integrals of the BE remain local in space and time. In other words, the Landau theory does not include a quantum mechanical analogy of virial corrections.The aim of this article is to bridge these two streams of the kinetic theory. We follow the work [3] where the way how to derive the quasiparticle kinetic equation with nonlocal and noninstant kinetic equation is presented. Kinetic equationTo motivate our approach, let u s inspect how the Landau theory exploits information accessible from microscopic theory of binary collisions. Amplitudes of the wave function in individual scattering channels furnishes us with differential cross sections. Phase shifts in the non-dissipative (elastic zereangle) scattering channel provides the quasiparticle renor-

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Nonlocal corrections to the Boltzmann equation for dense Fermi systems

Cited by 46 publications

References 23 publications

Midrapidity charge distribution in peripheral heavy ion collisions

Midrapidity charge distribution in peripheral heavy ion collisions

Transport with three-particle interaction

Quasiparticle Boltzmann Equation for Nonlocal Binary Collisons

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