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This article is cited in 1 scientific paper (total in 1 paper)
Statistics of Energy Partitions for Many-Particle Systems in Arbitrary Dimension
Vincenzo Aquilantia, Andrea Lombardia, Mikhail B. Sevryukb a Dipartimento di Chimica, Università degli Studi di Perugia,
via Elce di Sotto 8, 06123 Perugia, Italy
b V. L. Talroze Institute of Energy Problems of Chemical Physics of the Russia Academy of Sciences,
Leninskii prospect 38, Building 2, 119334 Moscow, Russia
Abstract:
In some previous articles, we defined several partitions of the total
kinetic energy $T$ of a system of $N$ classical particles in ${\mathbb R}^d$ into
components corresponding to various modes of motion. In the present paper,
we propose formulas for the mean values of these components in the
normalization $T=1$ (for any $d$ and $N$) under the assumption that the
masses of all the particles are equal. These formulas are proven at the
“physical level” of rigor and numerically confirmed for planar systems
($d=2$) at $3\leqslant N\leqslant 100$. The case where the masses of the particles
are chosen at random is also considered. The paper complements our article
of 2008 [Russian J. Phys. Chem. B, 2(6):947–963] where similar numerical
experiments were carried out for spatial systems ($d=3$) at $3\leqslant N\leqslant
100$.
Keywords:
multidimensional systems of classical particles, instantaneous phase-space invariants, kinetic energy partitions, formulas for the mean values, hyperangular momenta.
Received: 27.03.2014 Accepted: 15.04.2014
Citation:
Vincenzo Aquilanti, Andrea Lombardi, Mikhail B. Sevryuk, “Statistics of Energy Partitions for Many-Particle Systems in Arbitrary Dimension”, Regul. Chaotic Dyn., 19:3 (2014), 318–347
Linking options:
https://www.mathnet.ru/eng/rcd157 https://www.mathnet.ru/eng/rcd/v19/i3/p318
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Abstract page: | 118 | References: | 30 |
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