http://www.cnr.it/ontology/cnr/individuo/prodotto/ID57195

A dynamical classification of the range of pair interactions (Articolo in rivista)

Type

Articolo in rivista (Classe)
Prodotto della ricerca (Classe)

Label

A dynamical classification of the range of pair interactions (Articolo in rivista) (literal)

Anno

2010-01-01T00:00:00+01:00 (literal)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi

10.1007/s10955-010-0090-x (literal)

Alternative label

A. Gabrielli (1,2); M. Joyce (3,4); B. Marcos (5); F. Sicard (3) (2010)
A dynamical classification of the range of pair interactions
in Journal of statistical physics
(literal)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori

A. Gabrielli (1,2); M. Joyce (3,4); B. Marcos (5); F. Sicard (3) (literal)

Pagina inizio

970 (literal)

Pagina fine

989 (literal)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url

http://link.springer.com/article/10.1007%2Fs10955-010-0090-x (literal)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume

141 (literal)

Rivista

Journal of statistical physics (Rivista)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#note

fasc. (6). Springer. (literal)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo

6 (literal)

Note

ISI Web of Science (WOS) (literal)

Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni

(1) SMC, CNR-INFM, Physics Department, University \"Sapienza\" of Rome, Piazzale Aldo Moro 2, 00185-Rome, Italy (2) Istituto dei Sistemi Complessi - CNR, Via dei Taurini 19, 00185-Rome, Italy (3) Laboratoire de Physique Nucleaire et Hautes Energies, Universite Pierre et Marie Curie - Paris 6, CNRS IN2P3 UMR 7585, 4 Place Jussieu, 75752 Paris Cedex 05, France (4) Laboratoire de Physique Theorique de la Matiere Condensee, Université Pierre et Marie Curie - Paris 6, CNRS UMR 7600, 4 Place Jussieu, 75752 Paris Cedex 05, France and (5) Laboratoire J.-A. Dieudonne, UMR 6621, Universite de Nice -- Sophia Antipolis, Parc Valrose 06108 Nice Cedex 02, France (literal)

Titolo

A dynamical classification of the range of pair interactions (literal)

Abstract

We formalize a classification of pair interactions based on the convergence properties of the forces acting on particles as a function of system size. We do so by considering the behavior of the probability distribution function (PDF) P(F) of the force field F in a particle distribution in the limit that the size of the system is taken to infinity at constant particle density, i.e., in the \"usual\" thermodynamic limit. For a pair interaction potential V(r) with V(r??)?1/r ? defining a bounded pair force, we show that P(F) converges continuously to a well-defined and rapidly decreasing PDF if and only if the pair force is absolutely integrable, i.e., for ?d-1, where d is the spatial dimension. We refer to this case as dynamically short-range, because the dominant contribution to the force on a typical particle in this limit arises from particles in a finite neighborhood around it. For the dynamically long-range case, i.e., ??d-1, on the other hand, the dominant contribution to the force comes from the mean field due to the bulk, which becomes undefined in this limit. We discuss also how, for ??d-1 (and notably, for the case of gravity, ?=d-2) P(F) may, in some cases, be defined in a weaker sense. This involves a regularization of the force summation which is generalization of the procedure employed to define gravitational forces in an infinite static homogeneous universe. We explain that the relevant classification in this context is, however, that which divides pair forces with ?d-2 (or ?d-2), for which the PDF of the difference in forces is defined (or not defined) in the infinite system limit, without any regularization. In the former case dynamics can, as for the (marginal) case of gravity, be defined consistently in an infinite uniform system. (literal)

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