Statistical mechanics of classical particles with gravitational interactions: Exactly solvable (for N {le} {infinity}) in d = 1 and d > 2
- Rutgers Univ., New Brunswick, NJ (United States). Dept. of Mathematics
This paper is concerned with a curious gap in a string of exactly solvable models, a gap that is suggestively related to a completely integrable nonlinear PDE in d = 2 known as Liouville`s equation. This PDE emerges in a limit N {r_arrow} {infinity} from the equilibrium statistical mechanics of classical point particles with gravitational interactions (SMGI) in dimension d = 2 which, according, is an exactly solvable continuum model in this limit. Interestingly, in d = 1 and all d >2, the SMGI can be, and partly has been, exactly evaluated for all N {le} {infinity}. This entitles one to suspect that the SMGI for d = 2 is likewise exactly solvable for N < {infinity}, but currently this is an unproven hypothesis. If this conjecture can be answered in the affirmative, spin-offs in various areas associated with Liouville` equation, such as vortex gases, superfluidity, random matrices, and string theory, can be expected.
- OSTI ID:
- 462624
- Report Number(s):
- CONF-9603223--
- Journal Information:
- International Journal of Modern Physics B, Journal Name: International Journal of Modern Physics B Journal Issue: 1-2 Vol. 11; ISSN IJPBEV; ISSN 0217-9792
- Country of Publication:
- United States
- Language:
- English
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