Exact General Solutions to Extraordinary N-body Problems

Details Exact General Solutions to Extraordinary N-body Problems Exact General Solutions to Extraordinary N-body Problems

1998-08-17

arxiv.org/abs/cond-mat/9808173v1

Physics

Condensed Matter

Statistical Mechanics

15 pages, LaTeX. Accepted for publication in Proc. Roy. Soc. A

Scientific paper

We solve the N-body problems in which the total potential energy is any function of the mass-weighted root-mean-square radius of the system of N point masses. The fundamental breathing mode of such systems vibrates non-linearly for ever. If the potential is supplemented by any function that scales as the inverse square of the radius there is still no damping of the fundamental breathing mode. For such systems a remarkable new statistical equilibrium is found for the other coordinates and momenta, which persists even as the radius changes continually.

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