Suppression of the effect of collisions due to memory effects

Morawetz, Klaus; Walke, Rainer; Roepke, G.

doi:10.1016/0375-9601(94)90372-7

Cited by 22 publications

(6 citation statements)

References 23 publications

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“…The kinetic equation in Born approximation for spatial homogeneous media including complete time convolution (memory effect) but no damping is called Levinson equation and reads [12,13,14,15]…”

Section: Correlation Energy In Gradient Expansionmentioning

confidence: 99%

Formation of correlations and energy-conservation at short times

Morawetz

Köhler

1999

EPJ A

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Abstract. The formation of correlations due to collisions in an interacting nucleonic system is investigated. Results from one-time kinetic equations are compared with the Kadanoff and Baym two-time equation with collisions included in Born approximation. A reasonable agreement is found for a proposed approximation of the memory effects by a finite duration of collisions. This form of collision integral is in agreement with intuitive estimates from Fermi's golden rule. The formation of correlations and the build up time is calculated analytically for the high temperature and the low temperature limit. Different approximate expressions are compared with the numerical results. We present analytically the time dependent interaction energy and the formation time for Gauß-and Yukawa type of potentials.

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Section: Correlation Energy In Gradient Expansionmentioning

confidence: 99%

Formation of correlations and energy-conservation at short times

Morawetz

Köhler

1999

EPJ A

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“…This is the analytical quantum result of the time derivative of the formation of correlation for statically as well as dynamically screened potentials. For the classical limit h → 0 it is easy to integrate expression (12) with respect to times and arrive at…”

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confidence: 99%

“…Nevertheless, formula (13) can still almost reproduce the formation time but slightly shorter than compared with the simulation. This is due to non-ideality which was found to be an expression of memory effects [12] and leads to a later relaxation. For strongly coupled plasma the Born approximation fails, of course, to reproduce the correct equilibrium value, but reproduces the formation time fairly good.…”

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confidence: 99%

Formation of binary correlations in strongly coupled plasmas

1998

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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, 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 time dependency of the potential energy of binary interactions which measures the extent of correlations. We discuss the dynamical formation of screening and compare 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 dense metals.

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“…Recently, papers on non-Markovian nonlinear kinetic equations were published. They treat the first density correction to the Uehling-Uhlenbeck equation [15] and the case of the quantum Landau equation [16] which accounts for potential energy in lowest order only. Here, we present a kinetic equation that shows the global energy conservation in an approximation which, at equilibrium, is equivalent to the Debye-Hückel one.…”

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Pair Correlation Function and Nonlinear Kinetic Equation for a Spatially Uniform Polarizable Nonideal Plasma

Belyi

Kukharenko²,

Wallenborn

1996

Phys. Rev. Lett.

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Taking into account the first non-Markovian correction to the Balescu-Lenard equation, we have derived an expression for the pair correlation function and a nonlinear kinetic equation valid for a nonideal polarized classical plasma. This last equation allows for the description of the correlational energy evolution and shows the global conservation of energy with dynamical polarization. [S0031-9007 (96)00077-4] PACS numbers: 52.25.Dg, 05.20.Dd The importance of the polarization effects on plasmas in the kinetic regime has been recognized for a long time. A first attempt to include these effects in the linearized collisional integral was made by Gasirowicz, Neuman, and Riddell [1]. Later, the nonlinear equation for weakly coupled polarizable plasma was derived by Balescu [2] with the help of Prigogine's diagram techniques [3] and by Lenard [4] who solved the Bogoliubov equation [5] for the pair correlation function in the plasma approximation. These results were generalized to the quantum case by Konstantinov and Perel [6] and by Wyeld and Pines [7]. Kadanoff and Baym [8] and Klimontovich [9]have noticed that the Balescu-Lenard (BL) equation takes into account the polarization of the system only in the collision integral while the thermodynamics corresponds to the ideal gas; the dissipative and nondissipative phenomena are not treated on an equal footing. They have shown that this discrepancy can be avoided if non-Markovian effects are taken into account. This means that Bogoliubov's condition [5] of the total synchronization of all correlation functions with the one-particle distribution function (df ) must be omitted. Klimontovich [10] wrote the system of equations for the one-particle df and the pair correlations for the electric field and for the charge density, but he did not solve the equation for the pair correlation function and thus did not obtain a closed kinetic equation. On the other hand, Résibois [11] and Dorfman and Cohen [12] have formally derived the fully non-Markovian generalization of the BL equation, but their results are not easily tractable in a practical case. In particular, they did not give the explicit expression for the correlation energy.In this Letter we solve, in the plasma approximation, the equation for the pair correlation function considering the first non-Markovian correction. In this way, we obtain a nonlinear kinetic equation which generalizes the BL equation for weakly nonideal plasma. This equation, which includes the dynamical screening of the interaction potential, describes correctly the conservation of the total energy in a nontrivial way.The non-Markovian correction, which is responsible for the offset of the variation of kinetic energy by the variation of potential energy, is of order g 2 , where g is the plasma parameter, while the BL collision integral, which is the Markovian contribution in the plasma approximation, is of order g. The BL approximation is thus consistent with the conservation of kinetic energy without potential energy. However, Markovian contribution...

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Suppression of the effect of collisions due to memory effects

Cited by 22 publications

References 23 publications

Formation of correlations and energy-conservation at short times

Formation of correlations and energy-conservation at short times

Formation of binary correlations in strongly coupled plasmas

Pair Correlation Function and Nonlinear Kinetic Equation for a Spatially Uniform Polarizable Nonideal Plasma

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