NDLI: Statistical Mechanics of Many Interacting Point Masses in Spherical Geometry

Content Provider	Springer Nature Link
Author	Pomeau, Yves
Copyright Year	2003
Abstract	The long terms dynamics of point masses in a trapping potential interacting gravitationally cannot be derived from the usual ergodic assumption. The microcanonical partition function diverges for more than two particles because of the large volume allowed in momentum space when the potential energy of a close pair becomes very large negative. In the long term the trajectories explore by diffusion a phase space of infinite volume. This does not say what happens for a large number of self gravitating masses, like the globular clusters or even the galaxies perhaps. I reexamine below this question and try to point out the various difficulties faced by a rational approach. There is a small parameter, the inverse number of masses. At the lowest order in this parameter, the dynamics is given by solutions of the mean field Newton–Vlasov (N–V) kinetic equation. This yields well defined predictions for the steady state under given initial conditions, at least without initial angular momentum, because, besides the usual mechanical invariants, the N–V equation has as an invariant function, the histogram of the probability distribution in phase space. The next step is far more difficult: it requires to take into account the irreversible effects due to ‘collisions’. Actually, these irreversible effects are mostly coming from the resonant interactions between orbits of commensurate or close to commensurate period, not from close pair encounters as usually assumed. The evolution there is the one of slow changes of the steady states of N–V. I discuss briefly the possible solutions on the long time scale linked to the ‘collisions’.
Starting Page	753
Ending Page	758
Page Count	6
File Format	PDF
ISSN	14240637
Journal	Annales Henri Poincaré
Volume Number	4
Issue Number	2
e-ISSN	14240661
Language	English
Publisher	Birkhäuser-Verlag
Publisher Date	2003-01-01
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mathematical and Computational Physics Dynamical Systems and Ergodic Theory Quantum Physics Mathematical Methods in Physics Relativity and Cosmology Elementary Particles, Quantum Field Theory
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Nuclear and High Energy Physics Mathematical Physics

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