dorsal/arxiv
View SchemaConsequences of coarse grained Vlasov equations
| Authors | Klaus Morawetz, Rainer Walke |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9807045 |
| URL | https://arxiv.org/abs/nucl-th/9807045 |
| Journal | Physica A 330/3-4, 469--495 (2004), errata in press |
Abstract
The Vlasov equation is analyzed for coarse grained distributions resembling a finite width of test-particles as used in numerical implementations. It is shown that this coarse grained distribution obeys a kinetic equation similar to the Vlasov equation, but with additional terms. These terms give rise to entropy production indicating dissipative features due to a nonlinear mode coupling The interchange of coarse graining and dynamical evolution is discussed with the help of an exactly solvable model for the selfconsistent Vlasov equation and practical consequences are worked out. By calculating analytically the stationary solution of a general Vlasov equation we can show that a sum of modified Boltzmann-like distributions is approached dependent on the initial distribution. This behavior is independent of degeneracy and only controlled by the width of test-particles. The condition for approaching a stationary solution is derived and it is found that the coarse graining energy given by the momentum width of test particles should be smaller than a quarter of the kinetic energy. Observable consequences of this coarse graining are: (i) spatial correlations in observables, (ii) too large radii of clusters or nuclei in self-consistent Thomas-Fermi treatments, (iii) a structure term in the response function resembling vertex correction correlations or internal structure effects and (iv) a modified centroid energy and higher damping width of collective modes.
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"abstract": "The Vlasov equation is analyzed for coarse grained distributions resembling a\nfinite width of test-particles as used in numerical implementations. It is\nshown that this coarse grained distribution obeys a kinetic equation similar to\nthe Vlasov equation, but with additional terms. These terms give rise to\nentropy production indicating dissipative features due to a nonlinear mode\ncoupling The interchange of coarse graining and dynamical evolution is\ndiscussed with the help of an exactly solvable model for the selfconsistent\nVlasov equation and practical consequences are worked out. By calculating\nanalytically the stationary solution of a general Vlasov equation we can show\nthat a sum of modified Boltzmann-like distributions is approached dependent on\nthe initial distribution. This behavior is independent of degeneracy and only\ncontrolled by the width of test-particles. The condition for approaching a\nstationary solution is derived and it is found that the coarse graining energy\ngiven by the momentum width of test particles should be smaller than a quarter\nof the kinetic energy. Observable consequences of this coarse graining are: (i)\nspatial correlations in observables, (ii) too large radii of clusters or nuclei\nin self-consistent Thomas-Fermi treatments, (iii) a structure term in the\nresponse function resembling vertex correction correlations or internal\nstructure effects and (iv) a modified centroid energy and higher damping width\nof collective modes.",
"arxiv_id": "nucl-th/9807045",
"authors": [
"Klaus Morawetz",
"Rainer Walke"
],
"categories": [
"nucl-th"
],
"journal_ref": "Physica A 330/3-4, 469--495 (2004), errata in press",
"title": "Consequences of coarse grained Vlasov equations",
"url": "https://arxiv.org/abs/nucl-th/9807045"
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