dorsal/arxiv
View SchemaA statistical theory of the mean field
| Authors | R. Caracciolo, A. De Pace, H. Feshbach, A. Molinari |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9705044 |
| URL | https://arxiv.org/abs/nucl-th/9705044 |
| DOI | 10.1006/aphy.1997.5731 |
| Journal | Annals Phys. 262 (1998) 105-131 |
Abstract
A statistical theory of the mean field is developed. It is based on the proposition that the mean field can be obtained as an energy average. Moreover, it is assumed that the matrix elements of the residual interaction, obtained after the average interaction is removed, are random with the average value of zero. With these two assumptions one obtains explicit expressions for the mean field and the fluctuation away from the average. The fluctuation is expanded in terms of more and more complex excitations. Using the randomness of the matrix elements one can then obtain formulas for the contribution to the error from each class of complex excitations and a general condition for the convergence of the expansion is derived. It is to be emphasized that no conditions on the nature of the system being studied are made. Making some simplifying assumptions a schematic model is developed. This model is applied to the problem of nuclear matter. The model yields a measure of the strength of the effective interaction. It turns out to be three orders of magnitude less than that calculated using a potential which gives a binding energy of about -7 MeV/nucleon demonstrating the strong damping of the interaction strength induced by the averaging process.
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"abstract": "A statistical theory of the mean field is developed. It is based on the\nproposition that the mean field can be obtained as an energy average. Moreover,\nit is assumed that the matrix elements of the residual interaction, obtained\nafter the average interaction is removed, are random with the average value of\nzero. With these two assumptions one obtains explicit expressions for the mean\nfield and the fluctuation away from the average. The fluctuation is expanded in\nterms of more and more complex excitations. Using the randomness of the matrix\nelements one can then obtain formulas for the contribution to the error from\neach class of complex excitations and a general condition for the convergence\nof the expansion is derived. It is to be emphasized that no conditions on the\nnature of the system being studied are made. Making some simplifying\nassumptions a schematic model is developed. This model is applied to the\nproblem of nuclear matter. The model yields a measure of the strength of the\neffective interaction. It turns out to be three orders of magnitude less than\nthat calculated using a potential which gives a binding energy of about -7\nMeV/nucleon demonstrating the strong damping of the interaction strength\ninduced by the averaging process.",
"arxiv_id": "nucl-th/9705044",
"authors": [
"R. Caracciolo",
"A. De Pace",
"H. Feshbach",
"A. Molinari"
],
"categories": [
"nucl-th",
"hep-th"
],
"doi": "10.1006/aphy.1997.5731",
"journal_ref": "Annals Phys. 262 (1998) 105-131",
"title": "A statistical theory of the mean field",
"url": "https://arxiv.org/abs/nucl-th/9705044"
},
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